Ultrafast all-optical control of the magnetization in magnetic dielectrics

The purpose of this review is to summarize the recent progress on laser-induced magnetization dynamics in magnetic dielectrics. Due to the slow phonon–magnon interaction in these materials, direct thermal effects of the laser excitation can only be seen on the time scale of almost a nanosecond an...

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Дата:	2006
Автори:	Kirilyuk, A., Kimel, A., Pisarev, R.V., Hansteen, F., Rasing, T.
Формат:	Стаття
Мова:	English
Опубліковано:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2006
Назва видання:	Физика низких температур
Теми:	К 100-летию со дня рождения Б.Г. Лазарева
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Цитувати:	Ultrafast all-optical control of the magnetization in magnetic dielectrics / A. Kirilyuk, A. Kimel, F. Hansteen, R.V. Pisarev, T. Rasing // Физика низких температур. — 2006. — Т. 32, № 8-9. — С. 985–1009. — Бібліогр.: 106 назв. — англ.

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spelling	irk-123456789-1203302017-06-18T11:42:06Z Ultrafast all-optical control of the magnetization in magnetic dielectrics Kirilyuk, A. Kimel, A. Pisarev, R.V. Hansteen, F. Rasing, T. К 100-летию со дня рождения Б.Г. Лазарева The purpose of this review is to summarize the recent progress on laser-induced magnetization dynamics in magnetic dielectrics. Due to the slow phonon–magnon interaction in these materials, direct thermal effects of the laser excitation can only be seen on the time scale of almost a nanosecond and thus are clearly distinguished from the ultrafast nonthermal effects. However, via the crystal field, laser pulses are shown to indirectly modify the magnetic anisotropy in rare-earth orthoferrites and lead to the spin reorientation within a few picoseconds. More interesting, however, are the direct nonthermal effects of light on spin systems. We demonstrate coherent optical control of the magnetization in ferrimagnetic garnet films on a femtosecond time scale through a combination of two different ultrafast and nonthermal photomagnetic effects and by employing multiple pump pulses. Linearly polarized laser pulses are shown to create a long-lived modification of the magnetocrystalline anisotropy via optically induced electron transfer between nonequivalent ion sites. In addition, circularly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday effect. An all-optical scheme of excitation and detection of different antiferromagnetic resonance modes with frequencies of up to 500 GHz will be discussed as well. The reported effects open new and exciting possibilities for ultrafast manipulation of spins by light, and provide new insight into the physics of magnetism on ultrafast time scales. 2006 Article Ultrafast all-optical control of the magnetization in magnetic dielectrics / A. Kirilyuk, A. Kimel, F. Hansteen, R.V. Pisarev, T. Rasing // Физика низких температур. — 2006. — Т. 32, № 8-9. — С. 985–1009. — Бібліогр.: 106 назв. — англ. 0132-6414 PACS: 78.47.+p, 78.20.Ls, 75.30.Gw, 75.40.Gb http://dspace.nbuv.gov.ua/handle/123456789/120330 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	К 100-летию со дня рождения Б.Г. Лазарева К 100-летию со дня рождения Б.Г. Лазарева
spellingShingle	К 100-летию со дня рождения Б.Г. Лазарева К 100-летию со дня рождения Б.Г. Лазарева Kirilyuk, A. Kimel, A. Pisarev, R.V. Hansteen, F. Rasing, T. Ultrafast all-optical control of the magnetization in magnetic dielectrics Физика низких температур
description	The purpose of this review is to summarize the recent progress on laser-induced magnetization dynamics in magnetic dielectrics. Due to the slow phonon–magnon interaction in these materials, direct thermal effects of the laser excitation can only be seen on the time scale of almost a nanosecond and thus are clearly distinguished from the ultrafast nonthermal effects. However, via the crystal field, laser pulses are shown to indirectly modify the magnetic anisotropy in rare-earth orthoferrites and lead to the spin reorientation within a few picoseconds. More interesting, however, are the direct nonthermal effects of light on spin systems. We demonstrate coherent optical control of the magnetization in ferrimagnetic garnet films on a femtosecond time scale through a combination of two different ultrafast and nonthermal photomagnetic effects and by employing multiple pump pulses. Linearly polarized laser pulses are shown to create a long-lived modification of the magnetocrystalline anisotropy via optically induced electron transfer between nonequivalent ion sites. In addition, circularly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday effect. An all-optical scheme of excitation and detection of different antiferromagnetic resonance modes with frequencies of up to 500 GHz will be discussed as well. The reported effects open new and exciting possibilities for ultrafast manipulation of spins by light, and provide new insight into the physics of magnetism on ultrafast time scales.
format	Article
author	Kirilyuk, A. Kimel, A. Pisarev, R.V. Hansteen, F. Rasing, T.
author_facet	Kirilyuk, A. Kimel, A. Pisarev, R.V. Hansteen, F. Rasing, T.
author_sort	Kirilyuk, A.
title	Ultrafast all-optical control of the magnetization in magnetic dielectrics
title_short	Ultrafast all-optical control of the magnetization in magnetic dielectrics
title_full	Ultrafast all-optical control of the magnetization in magnetic dielectrics
title_fullStr	Ultrafast all-optical control of the magnetization in magnetic dielectrics
title_full_unstemmed	Ultrafast all-optical control of the magnetization in magnetic dielectrics
title_sort	ultrafast all-optical control of the magnetization in magnetic dielectrics
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2006
topic_facet	К 100-летию со дня рождения Б.Г. Лазарева
url	http://dspace.nbuv.gov.ua/handle/123456789/120330
citation_txt	Ultrafast all-optical control of the magnetization in magnetic dielectrics / A. Kirilyuk, A. Kimel, F. Hansteen, R.V. Pisarev, T. Rasing // Физика низких температур. — 2006. — Т. 32, № 8-9. — С. 985–1009. — Бібліогр.: 106 назв. — англ.
series	Физика низких температур
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first_indexed	2025-07-08T17:40:19Z
last_indexed	2025-07-08T17:40:19Z
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fulltext	Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9, p. 985–1009 Ultrafast all-optical control of the magnetization in magnetic dielectrics Andrei Kirilyuk1, Alexey Kimel1, Fredrik Hansteen1, Roman V. Pisarev2, and Theo Rasing1 1IMM, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands E-mail: A.Kirilyuk@science.ru.nl 2Ioffe Physico-Technical Institute, 194021 St.-Petersburg, Russia Received February 24, 2006 The purpose of this review is to summarize the recent progress on laser-induced magnetization dynamics in magnetic dielectrics. Due to the slow phonon–magnon interaction in these materials, direct thermal effects of the laser excitation can only be seen on the time scale of almost a nanosec- ond and thus are clearly distinguished from the ultrafast nonthermal effects. However, via the crystal field, laser pulses are shown to indirectly modify the magnetic anisotropy in rare-earth orthoferrites and lead to the spin reorientation within a few picoseconds. More interesting, how- ever, are the direct nonthermal effects of light on spin systems. We demonstrate coherent optical control of the magnetization in ferrimagnetic garnet films on a femtosecond time scale through a combination of two different ultrafast and nonthermal photomagnetic effects and by employing multiple pump pulses. Linearly polarized laser pulses are shown to create a long-lived modification of the magnetocrystalline anisotropy via optically induced electron transfer between nonequiva- lent ion sites. In addition, circularly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday effect. An all-optical scheme of ex- citation and detection of different antiferromagnetic resonance modes with frequencies of up to 500 GHz will be discussed as well. The reported effects open new and exciting possibilities for ultrafast manipulation of spins by light, and provide new insight into the physics of magnetism on ultrafast time scales. PACS: 78.47.+p, 78.20.Ls, 75.30.Gw, 75.40.Gb Keywords: magnetization dynamics, magnetic dielectrics, Faraday effects. 1. Introduction Ultrafast magnetization dynamics has attracted lively interest in recent years [1–10], stimulated on the one hand by the demand for increased speed of writing and retrieving magnetically stored informa- tion, and on the other hand by the development of ultrafast (femtosecond) laser sources [11]. Such lasers allow for excitation of magnetic systems at much shorter time scales than fundamental quantities such as spin precession or spin—lattice relaxation times. This type of photoexcitation brings a medium in a strongly nonequilibrium state, where a conventional description of magnetic phenomena in terms of ther- modynamics may no longer be valid. Therefore, in ad- dition to the potential applications, ultrafast magneti- zation dynamics is a subject of extreme fundamental interest in the physics of magnetism. The first ultrafast time resolved studies of the im- pact of laser pulses on the magnetization were done on Ni and Fe using picosecond laser pulses, but these were not successful in observing any magnetic effects up to the melting point of the samples [12,13]. Later, using time-resolved spin-polarized photoemission as a probe of the magnetization Vaterlaus et al. [14] succeeded in estimating the spin—lattice relaxation time in Gd films to be (100 80� ) ps. In 1996 Beaurepaire et al. [1] re- ported the first observation of subpicosecond demagne- tization in Ni induced by 60 fs laser pulses. This ultrafast magnetic response was explained by an effec- © Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing, 2006 tive electron-spin interaction mechanism among the strongly nonequilibrium photoexcited electrons, lead- ing to a rapid increase of the spin temperature and de- struction of the magnetization. The observation trig- gered the interest of several groups and similar experiments confirmed the ultrafast demagnetization in Ni, Co, and other metallic systems [15–18]. It was con- cluded that the magnetization follows the electron tem- perature with a possible delay between the electron ex- citation and the magnetic breakdown of no more than 50 fs. An experimental artifact was revealed by Regensburger et al. [19] and Koopmans et al. [20] who pointed out that the magneto-optical response does not always directly relate to the magnetization during the first few hundred femtoseconds as a result of hot elec- tron effects. The speed of the true demagnetization was consequently reduced to 0.5–1 ps and ascribed to an ef- fective spin–lattice interaction. The significant role of possible artifacts in time-resolved magneto-optical ex- periments was also demonstrated in ab initio calcula- tions [21]. Recently, however, it was shown that laser induced spin dynamics indeed does take place during the initial electron thermalization with a characteristic time of about 50 fs [22–24], thus again raising the question of the underlying mechanism. The complete interpretation of this rapid demagnetization is still not clear, partly because it is difficult to distinguish be- tween different processes in metallic systems due to their complex electronic structure and the continuum of transitions [21,25,26]. In addition to laser-induced demagnetization the triggering of spin waves by laser pulses have been studied [27–32]. The equilibrium orientation for the magnetization is believed to be changed through ther- mal modulation of the magnetic anisotropy (that in- cludes shape anisotropy), which causes the magnetiza- tion to precess. In fact, for all of the above-mentioned experiments on metallic systems, the observed mag- netic excitation was the result of optical absorption followed by a rapid temperature increase. Far more exciting is the possibility of ultrafast nonthermal con- trol of magnetization by light, where a change in the magnetization is not simply the result of a temperature increase. It provides much greater freedom for the ma- nipulation of the magnetization, and unwanted heat- ing and possible material damage in devices can be avoided. The nonthermal influence of light on magne- tization in metals has been predicted by theory [33], but many aspects of this are still subject to debate [21]. A few experimental attempts to observe a nonthermal influence of light on metallic magnetic systems have been reported [31,34]. However, no im- pact on the magnetization could be seen in the time af- ter the optical pulse. We believe that this is partly due to the dominating thermal effect in metals, and to the unfortunate coincidence of several processes in the same narrow time window which hampers the analysis [35,36]. Recently, a lot of attention has been attracted to novel ferromagnetic semiconducting compounds [37,38]. In this type of material the ferromagnetism is mediated by the free carriers, and highly effective nonthermal control of the magnetization by light was reported in static measurements [39]. However, these large values of the photoinduced magnetization have not been reproduced or confirmed by dynamic mea- surements with subpicosecond time resolution [40,41], and similar experiments have only shown the thermal effects of light on the magnetic system [42,43]. A number of difficulties are associated with this relatively new class of materials, and the under- standing of their electronic, optical, and magnetic properties is currently very limited and controversial. When seeking to improve our understanding of ultrafast spin dynamics and searching for nonthermal photomagnetic effects, dielectrics possess some signifi- cant advantages over metals and semiconductors. The phonon—magnon interaction responsible for thermal effects is much slower in dielectrics than in metals and does therefore not obscure the interpretation of the processes on shorter time scales [44]. Moreover, the electron-spin scattering mechanism proposed in metals cannot exist in dielectrics due to the localized nature of their electronic states. And finally, magnetic dielec- trics, in contrast to the novel magnetic semiconduc- tors, are characterized by a well-defined electronic structure and their optical and magnetic properties are well understood. Magnetic garnets have been for a long time one of the most popular types of magnetic dielectric materi- als for both research and applications [45,46]. Their physical properties are well known and can be tailored over a wide range through chemical substitution and by varying their growth conditions. For decades they have been considered ideal model systems for the ex- perimental and theoretical investigation of magnetic phenomena. Their optical absorption in the infrared spectral region is very low and they exhibit large mag- neto-optical effects caused by strong spin–orbit cou- pling. The linewidth of ferrimagnetic resonance in garnets can be extremely narrow, implying a very low damping of magnetic excitations [45]. Additionally, static control of the magnetic anisotropy by light has been known for some time in this class of materials [47,48]. For these reasons they seem to be ideal mate- rials for the study of ultrafast spin dynamics in gen- eral and the search for nonthermal mechanisms for the optical control of magnetization in particular [49–51]. 986 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing Another interesting group of dielectrics, the rare-earth orthoferrites RFeO3, are also a well-studied family of magnetic materials with a rich array of magnetic proper- ties [52]. The orthoferrites are particularly interesting because of the presence of an antisymmetric exchange in- teraction which involves the vector cross-product of neighboring spins as opposed to the usual scalar product. In the absence of this interaction, the orthoferrites would be antiferromagnetic. Its presence leads to a small canting of the sublattices making the orthoferrites «weak» fer- romagnets with 4�Ms � 100 G. Another interesting fea- ture of these materials is the fact that some of them ex- hibit a transition as a function of temperature in which the direction of the antiferromagnetically ordered spins and consequently also of the net magnetization rotates by 90�. The combination of high magnetic resonance fre- quencies with very large magneto-optical effects makes the orthoferrites interesting objects for study of laser-in- duced dynamics [9,10]. The purpose of this paper is to summarize the re- sults from our recent extensive studies of ultrafast optical control of the magnetization in both ferri- magnetic garnet films and in weakly-ferromagnetic orthoferrites. Laser pulses of center wavelength � � = 805 nm and pulse width of about 100 fs were used to both excite and probe the magnetic response of the samples. We demonstrate the existence of different nonthermal photo- and optomagnetic effects, allowing for ultrafast control of both the magnetocrystalline anisotropy and the magnetization. Note that optomagnetic effects differ from the photomagnetic ones by the fact that the former are unrelated to the absorption of the light and can be seen most obviously in transparent crystals [49,53]. The light wave is then equivalent to an effective magnetic field. In the latter case the light, as it absorbed, excites electrons into the localized energy levels. Such redistribution of the electron density causes changes in the properties of the spin system, e.g., changes in the anisotropy constants. Thermal effects can be clearly distinguished from these nonthermal effects and are observed on the time scale of several hundreds of picoseconds in the vicinity of the Curie temperature, which is demonstrated in iron borate FeBO3. The paper is organized as follows: Experimental de- tails including sample characteristics, experimental setup, and principles of magnetic precession as the measured quantity are given in Chapter 2. Chapter 3.1 introduces the time scale of phonon–magnon relax- ation responsible for the thermal quenching of magne- tization. Then, Chapters 3.2, 3.3 deal with direct nonthermal excitation of the magnetization dynamics on a femtosecond time scale via the inverse Faraday ef- fect. In Chapter 4 we present and discuss the magneti- zation dynamics obtained via laser-induced modifica- tion of magnetic anisotropy, via thermal (Chapter 4.1) and nonthermal (Chapter 4.2) mechanisms. Finally, in Chapter 5 we demonstrate how a combina- tion of two pump pulses and/or different nonthermal effects can lead to a coherent control of magnetization dynamics, and illustrate this by the example of sin- gle-pulse ultrafast photomagnetic switching. 2. Experimental methods 2.1. Samples 2.1.1. Magnetic garnets The ferrimagnetic garnet samples studied in this work are 4–8 �m thick ferrimagnetic garnet films of the composition Lu3–x–yYxBiyFe5–zGazO12 grown on (001) oriented gallium gadolinium garnet (GGG) substrates by liquid phase epitaxy. All the results mentioned in this review are from samples with x � 0 65. , y � 0 66. , and z � 115. , but the effects that we observe are also present in a whole series of samples with similar composition. Small amounts of Pb impu- rities are known to exist in these types of films due to the flux from which they are grown. The films have in-plane magnetization, 4�Ms = 550 G and Curie temperature TC � 400 K. While bulk garnet crystals have cubic symmetry and possess a center of inversion, epitaxially grown thin garnet films seem to lack this center of symmetry, as has been demonstrated by the existence of a linear magnetoelectric effect [54] and by strong optical second-harmonic generation [55,56]. The linear optical absorption of these garnet films in the spectral region around � � 805 nm (1.54 eV) is small (� � 20 cm–1) and mainly due to spin- and parity-«for- bidden» d—d transitions in the Fe3+ ions and a tail from higher energy charge transfer transitions at 2.8 and 3.4 eV [45,46]. The magneto-optical properties of the material in the infrared part of the spectrum are dictated mainly by the tails of these high energy transitions. It is also well known that bismuth substitution strongly en- hances the magneto-optical response [45,46]. The Faraday rotation F measured with a saturat- ing external field normal to the film plane is shown as function of the sample temperature in Fig. 1,a for a 7.5 �m thick garnet film. M T( ) exhibits a second or- der phase transition with a critical exponent � 0 414. and a Curie temperature of TC � 400 K, both in agree- ment with previous studies of similar materials [45,46]. From the hysteresis loop in Fig. 1,b it can be seen that the sample exhibits no coercivity and has a large Faraday rotation of about 2.5� at room tempera- ture when saturated in the out-of-plane direction. The Faraday rotation measured at a small angle of inci- Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 987 dence with the applied magnetic field parallel to the sample plane is shown by the hysteresis loop in Fig. 1,c. It gives an estimate of the film in-plane ani- sotropy Ha of about 50 Oe. Vibrating sample magne- tometer (VSM) measurements reveal that this aniso- tropy has a fourfold symmetry in the plane. 2.1.2. Rare-earth orthoferrites Another class of dielectric magnetic materials are the antiferromagnetic rare-earth orthoferrites RFeO3, where R is a rare-earth ion, Dy or Tm in this paper. These materials crystallize in an orthorhombically distorted perovskite structure, with a space group symmetry D h2 16 (Pbnm) [52,57]. The iron moments order antiferro- magnetically, but with a small canting of the spins on different sublattices. The spins of the dysprosium and thulium ions are not ordered above 4 K, being in a para- magnetic state. The spins of the Fe3+ ions (3 5d , ground state 6A1g, S = 5/2) are coupled antiferromagnetically by isotropic exchange. The Dzyaloshinskii—Moriya in- teraction [58,59] leads to a slight canting of opposite spins with an angle of about 0.5�, giving rise to a sponta- neous magnetization Ms � 8 G. Despite the small mag- netization, this material exhibits a giant Faraday rota- tion of about 3000� cm–1 owing to its strong spin–orbit interaction [60]. The TmFeO3 and DyFeO3 single crystals used in our experiments were grown by the floating-zone method under optical heating [61]. The crystals were oriented by x-ray diffractometry. Since orthoferrites are optically biaxial crystals, the samples were pre- pared in the form of platelets polished down to a thickness of 60–100 �m, with the surface normal ori- ented perpendicular to the x, y, or z crystallographic axes to within a few degrees, as well as of platelets with the normal approximately aligned with the opti- cal axis lying in the yz plane. Rare-earth orthoferrites are optically biaxial crys- tals possessing inherent birefringence. Therefore, the polarization state of light propagating through these crystals changes. We measured the phase difference between the two orthogonal polarization components of light transmitted through a sample for each wave- length in the case where light is incident normal to the sample and is linearly polarized at 45� to the crystallo- graphic axes. Several orthoferrites are known for a strong tem- perature-dependent anisotropy [52,57]. Thus, as the temperature is lowered, spontaneous spin reorienta- tion occurs in TmFeO3 as a result of variation of the magnetic anisotropy. In this process, the ferromag- netic moment turns continuously from its position along the z axis at a temperature T2 to the position along the x axis at a temperature T1 (see Fig. 2,a). These points are the temperatures of second-order phase transitions (� � �4 24 2 ) [62] in which anomalies in the physical properties are observed. The temperature dependence of linear birefringence is plotted in Fig. 2,b and is indeed seen to exhibit two second order orientational phase transitions at temper- atures of 83 and 93 K. Below, in Chapter 3.1 we will show how such transitions can be triggered by a laser pulse on a time scale of a few picoseconds. Another considered orthoferrite, DyFeO3, has pro- perties similar to that of TmFeO3 except for a differ- ent type of phase transition happening at lower tem- perature. This transition, however, is of no concern for this review. 2.1.3. Iron borate FeBO3 Iron borate crystallizes in a calcite type structure with space group R c3 and has a N�el temperature TN � 348 K. Similar to the orthoferrites, the anti- ferromagnetic state of FeBO3 is characterized by a weak ferromagnetism due to a slight spin canting of about 1 degree in the (001) plane, which results in a magnetic moment oriented within this plane. Due to this magnetic moment one can turn the FeBO3 sample into a single domain state with the help of a small magnetic field and linear magneto-optical effects can be used to probe the antiferromagnetic ordering. Moreover, FeBO3 has the N�el point slightly above room temperature and is characterized by good trans- parency in the visible spectral range. Therefore this 988 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing 320 340 360 380 400 420 0 1 2 Temperature (K) –2 0 2 –2 0 2 External field ( kOe) –100 0 100 External field (Oe) a b c = 0.414 TC = 400 K (d e g .) F c0(T) = [1 – exp(T/T )] F F( d e g .) F(a .u .) Fig. 1. Garnet sample characteristics: (a) Measured Fara- day rotation �F at � = 805 nm as a function of tempera- ture with a saturating applied field Hext normal to the film plane. (b) Hysteresis loop at T = 300 K measured with Hext normal to the film. (c) Hysteresis loop mea- sured at a small angle of incidence with Hext in the sam- ple plane, indicating the presence of anisotropy fields of about 50 Oe [51]. compound is suitable for both study and potential ap- plications. The optical properties of FeBO3 are determined by the d—d transitions in the partially filled d-envelope of the Fe3+ ion. Figure 3 shows the relevant part of the electronic energy diagram as derived from the local symmetry of the Fe3+ ion. In the crystalline field, the 3d5 electrons of Fe3+ ions occupy the ground state 6 1� �(S � 5/2), which is an orbital singlet and the only spin sixtet state. The lowest excited state is trip- let 4 4� � (S � 3/2). The spin degeneracy is lifted due to the spin—orbit coupling and exchange interaction. The transition 6 1 4 4� �� is centered at 1.4 eV and is forbidden in the electric dipole approximation because of the selection rules imposed on parity and spin. Nevertheless, from the absorption spectra mea- sured at 20 K four intensive spectral lines were distin- guished near the first d—d transition (see Fig. 3). At higher temperatures the splitting is not seen because of increased electron-phonon interaction and pho- non-assisted transitions. The studied sample was a plate of thickness 300 �m, oriented with its plane perpendicular to the hard mag- netic axis. 2.2. All-optical pump-probe measurements The samples were studied in transmission using an all-optical pump and probe technique. Regeneratively amplified 100 fs pulses of wavelength � � 805 nm emitted from a Ti:Sapphire laser system at a repetition rate of 1 kHz were split into two parts using a beam splitter. The most intense part (pump) was incident on the sample at near normal incidence. The magneti- zation dynamics induced by these pump pulses was followed in time by measuring the Faraday rotation F of the time delayed and much weaker probe pulses ( )I /Ipump probe � 100 as function of the variable pump-probe time delay �t. The Faraday angle F is proportional to the projection of the magnetization vector M along the wave vector k of the probe light: F � �M k. (1) In our geometry (see Fig. 4) the measured Faraday rotation is therefore essentially a probe of the out-of-plane Mz component of the magnetization. For sensitive detection of the magneto-optical Faraday ro- tation a balanced photodiode detector was used in combination with a box-car integrator [64]. A syn- chronized optical chopper operating at 500 Hz was placed in the pump beam path, thereby blocking every second pump pulse and creating alternating pump-on and pump-off conditions in the sample. For Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 989 F G x z F G z F G x z S1 2S 4S 3S S1 2S 4S 3S T 1 T 2 a b T2T1 � (G F )2 z x �24 � (G F ) 4 x z 6.1 6.2 6.3 40 E = 1.55 eV 3TmFeO n = n – ny zyz 3.95 3.90 2.4 2.3 n = n – ny xxy �n = n – nx zxz 2 z x� (G F ) 40 60 80 100 120 4 x z� (G F ) 60 80 100 120 Temperature ( K) B ir e fr in g e n ce (1 0 ) – 2 �24 Fig. 2. (a) Crystallographic and spin structure of TmFeO3 showing different phases as well as the reorientation of fer- romagnetic F S S S S� � � �1 2 3 4 and antiferromagnetic G S S S S� � � �1 2 3 4 vectors. (b) Temperature dependence of birefringence along the three principal crystallographic directions. The birefringence anomalies occur at the orientational-transition temperatures T1 and T2 [63]. 4�4 + 6�1 + Octahedral crystal field (3m) Spin-orbit coupling Photon energy (eV) O p tic al ab so rp tio n (c m ) – 1 (3d )5 Phonon- and magnon- assisted electronic band 1 234 1 2 3 4 1.2 1.4 1.6 100 200 0 pump p u m p ionFe3+ Fig. 3. The energy level scheme and the absorption spec- tra of FeBO3 at room temperature (solid line) and at 20 K (dashed line). The spectral lines from 1 to 4 correspond to the transitions from the ground state 6 1� � to the excited state 4 4� � split by the spin—orbit coupling [44]. every pump-probe delay �t the pump-induced Fara- day rotation was averaged over several excitation events by use of a lock-in amplifier. Pump-induced changes of the optical transmittivity of the sample were recorded simultaneously with the Faraday rota- tion, by measuring the intensity of the probe pulses in addition to their polarization rotation. In some cases, for example in orthoferrites in the absence of an external magnetic field, it was prefera- ble to use the linear magnetic birefringence as a probe for the magnetic order. Such probe is insensitive to the presence of 180� magnetic domains and gives a direct indication of the dynamics of antiferromagnetic order. Pump pulses of energy up to 20 �J were focused to a spot diameter of about 200 �m on the sample, corre- sponding to a photon density of approximately one photon per unit cell in the irradiated sample volume. The laser peak power density of about 1011 W/cm2 is still well below the threshold for continuum genera- tion in the garnet films. While the probe pulses al- ways were linearly polarized, the polarization of the pump pulses could be varied using a Babinet—Soleil compensator. A magnetic field was applied either in the xy-plane of the sample, see Fig. 4, or at an angle with respect to the sample normal, thereby pulling the magnetization M out of the film plane (� � 90�). The sample temperature could be controlled from room temperature up to well above the Curie point using a sample holder with a built-in heater and an electronic temperature regulator. Alternatively, the sample could be cooled down to about 5 K by using an optical flow cryostat, where the temperature was stabilized better than 0.5 K. 2.3. Magnetic precession as a key process In the following sections we present, interpret and discuss our experimental results from extensive stud- ies of optically induced magnetization dynamics in garnet films and orthoferrite single crystals. A re- markable amount of information about the underlying photomagnetic mechanisms can be obtained simply by analyzing time-traces of the precessional dynamics. Coherent precession is the fastest known way to al- ter the direction of the macroscopic magnetization in a material. Phenomenologically the process is described by the Landau—Lifshitz equation of motion [65,66], d dt M M H� � �� ( )eff . (2) It follows from this that the equilibrium orientation (d /dtM � 0) for the magnetization M is along the di- rection of the effective magnetic field Heff which is composed of the externally applied field Hext , the anisotropy field Han and the demagnetizing field Hdem � 4�Mz : Heff � H H Hext an dem+� . (3) The key to optical manipulation of the magnetiza- tion lies in the control of these fields by light. The description of spin dynamics in orthoferrites is only slightly more complicated because of the antiferromagnetic character of the exchange coupling. The equilibrium orientation of the spins in this mate- rial is given by the minimum of the thermodynamical potential � [52]: � � � � � � �J K S Sx x x( ) [ ] ( )S S D S S1 2 1 2 1 2 2 2 � � � � �K S S K S Sz z z x y( ) (1 2 2 2 4 1 4 1 4 � � � � � �S S S Sz x y z1 4 2 4 2 4 2 4 1 2) ( )H S S , (4) where S1 and S2 are the vectors that characterize the spins of the iron ions in the two magnetic sublattices, J is the nearest-neighbor isotropic exchange interac- tion constant; D is the Dzialoshinsky—Moriya antisymmetric exchange constant; Kx , Kz , K4 are constants of the magneto-crystalline anisotropy, and H is the external magnetic field. The constant J fa- vors an antiferromagnetic configuration of the Fe3+ spins, whereas the constant of the antisymmetric ex- change interaction D results in a slight canting of the spins from the antiparallel orientation over an angle � 0.5�, so that the system acquires a weak ferromag- netic moment. The resulting equations of motion for the antiferromagnetic spins S1 and S2 show that two dif- ferent resonance modes can exist with energies [52,57,67,68]: ��FM x zJS K K S� �24 ( ) , (5) 990 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing � z Fig. 4. Experimental geometry. Pump and probe pulses were incident on the garnet film at near normal incidence. The magnetization M of the sample forms an angle � with the sample normal [001] and an angle � with the crystal- lographic [100] x axis of the film. For linearly polarized pump pulses the angle of the electric field component of light E with respect to the sample x axis is denoted �. �� FM xJS DS K S� �24 6( tan ). (6) The first «quasi-ferromagnetic» mode softens in the spin reorientation region, where the modulus \| \|K Kx z� vanishes. The second «quasi-antiferromagnetic» mode is usually characterized by a weaker temperature de- pendence. The motion of spins corresponding to these modes is discussed below, in Chapter 3.3 and Fig. 13, where it has also been shown how these modes can be excited and observed in an all-optical scheme. Below we describe and discuss different photo- magnetic effects that have been found to trigger coher- ent precession of the magnetization. Thus, Chapter 3.1 describes thermally-induced quenching of magnetiza- tion in FeBO3 via the phonon—magnon relaxation mechanism. In Chapters 3.2, 3.3 an ultrafast non- thermal effect of circularly polarized laser pulses on the magnetization is discussed along with experimen- tal results on both garnet and orthoferrite samples. It is found that these pulses act as strong axial magnetic field pulses during their presence in the sample. The effect, also called inverse Faraday effect, is practically instantaneous and it causes the magnetization to start precessing immediately after the photoexcitation. Next, in Chapter 4.1 we demonstrate that spin reori- entation can be achieved on a picosecond time scale via ultrafast thermal modification of the anisotropy axis in TmFeO3. Further, in Chapter 4.2 we present results showing that linearly polarized laser pulses create a long-lived modification of the magneto- crystalline anisotropy in garnet films. This latter ef- fect is of nonthermal origin, even though it relies on the absorption, unlike the inverse Faraday effect. Using a two-pulse excitation scheme, we demonstrate how both of the effects could be used for truly ultrafast coherent control of the magnetization mo- tion. Moreover, these two nonthermal effects can also be combined as demonstrated in Chapter 5.3 to achieve a single-pulse switching of the magnetization on a femtosecond time scale. 3. Thermal and nonthermal effects of light on magnetization 3.1. Thermally induced quenching of magnetic order in FeBO3 Due to the absorption peak in the vicinity of the ex- citation wavelength, iron borate happened to be a convenient material to study the thermally-induced changes of magnetization. Measurements of the latter allowed us to determine the typical phonon–magnon relaxation time. Note that the optical pump pulse influences both the magnetic and the optical properties of the excited medium. Because the output of the used detection scheme depends on the intensity of the probe beam, knowledge of the transient transmission is necessary. This was measured by using a single-diode response with an amplitude modulation of the pump beam. We then calibrated the measured time depen- dencies of the Faraday rotation by dividing them by the associated transient transmissions (shown in Fig. 5,a). The resulting data show a peak during the overlap of the pulses that is followed by a slow break- down of the antiferromagnetic order . The amplitude of the initial peak was found to be a linear function of the pump fluence as shown in Fig. 5,b. The slow com- ponent of the Faraday rotation as a function of tem- perature and time is shown in Fig. 6. The dynamical changes of the Faraday effect are smaller at lower tem- peratures, while at T = 346.5 K the Faraday rotation rapidly decreases until a delay of about 500 ps, where the signal vanishes. The intrinsic Faraday effect is shown in Fig. 7 as a function of temperature. Since the Faraday rotation is proportional to the order parameter, its temperature dependence is generally given by [70] � � � F s N T T T ( ) � � � � �� 0 1 , (7) where TN is the N�el temperature, is the critical ex- ponent and Ts is the magnon temperature, which drives the order parameter. Fitting Eq. (7) to the cor- responding measurements that are represented by solid squares in Fig. 7 we obtained � 0.364 � 0.008 and TN � (347.0 � 0.1) K. These values are in good agreement with � 0.354 and TN � 348.35 K reported before [57]. Repeating those measurements at a negative delay of –20 ps we obtained identical results but shifted about 10 K towards lower temperature. This offset was due to heat accumulation caused by the repeated excitation of the sample. We minimized this effect by using the lowest possible repetition rate that yielded a reasonable signal-to-noise ratio. The measured magni- tude of the temperature offset was in good agreement with an estimate based on the optical and thermal Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 991 A sharp step-like reduction of the magneto-optical signal within 1 ps was occasionally observed similar to that reported in [69]. After additional experiments we concluded that in FeBO3 this step-like behavior is an artefact related to the pump-induced transmissivity changes (Fig. 5,a). Provided a proper calibration, the step-like contribution can be sup- pressed. properties of FeBO3 and was added to T when plot- ting the relevant data. Figure 7 also shows the difference between the in- trinsic magneto-optical signal and that at a time-delay of 500 ps. This difference increases drastically before dropping to zero at the N�el point. All these features strongly imply that the pump induced relaxation of the magneto-optical signal is related to an increase of the magnon temperature. At a temperature of T � 346.5 K and at a delay time of 500 ps the N�el point is reached and antiferromagnetism is destroyed. The temperature dependence of the Faraday rota- tion at zero time delay is shown in Fig. 7 by open cir- cles. The experimental data were fitted by Eq. (7) with and TN deduced from the previous fit and the result of the fit is shown by the dotted line. The similarity of the temperature behavior of the intrinsic Faraday rotation and that at zero time delay strongly suggests that no magnetic excitation occurs within 100 fs. This result proves that the time-resolved data (cf. Fig. 6) are not directly affected by the optical excitation itself since the life time of the electrons in the excited state is shorter than 100 fs as deduced from the huge linewidth of the 6 1 4 4� �� transition. This estimate 992 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing 0 0.8 1.6 2.4 10 20 30 Pump fluence (mJ/cm )2 0 200 400 600 800 –3.0 –2.0 0 Time delay (ps) � = 1.55 eV FeBO3 a � = 1.55 eV FeBO3 b –1.0 D iff e re n tia lt ra n sm is si o n (% ) Fa ra d ay ro ta tio n (m ra d ) Fig. 5. (a) The transmission as a function of time delay, (b) the intensity dependence of the ultrafast Faraday rotation (symbols); linear fit with a slope of (8 0.6) 10–5 rad cm2/mJ (line) [44]. Fa ra d ay ro t at io n (m ra d ) 6 5 4 3 2 1 0 0 200 400 600 800 Time delay (ps) 343.6 K 345.9 K 344.5 K 342.2 K 346.5 K 346.8 K FeBO3 T = 340.9 Kbias Fig. 6. The long term transient Faraday rotation measured as a function of temperature. The antiferromagnetic order is destroyed at a time delay of 500 ps for T = 346.5 K [44]. Bias temperature (K) 2.4 2.0 1.6 1.2 0.8 0.4 0 12 10 8 6 4 2 0 335 340 345 350330 1.50 0.75 0 0 1 2 Time (ns) � (–20 ps)F F� (0 ps) T (t ), K s (0 p s) , (– 2 0 p s) (m ra d ) F F (– 2 0 p s) – (5 0 0 p s) (m ra d ) F F Fig. 7. The Faraday rotation without pump (solid squares), at negative (solid circles) and at zero (open cir- cles) time delay as a function of the bias temperature with the fit to Eq. (7) (solid and dotted lines, respectively). The difference between the intrinsic magneto-optical sig- nal and that at 500 ps is shown by diamonds together with the calculation based on the fitted parameters (dashed line). The inset shows the transient component of the magnon temperature as a function of the time delay. The solid line is the fit according to Eq. (8) [44]. is justified by the dramatic changes of the absorption spectrum with temperature in Fig. 3, the fact that the transition takes place between states with different electronic configurations ( ) ( ) ( ) ( )t e t eg g g g2 3 2 2 4 1 and earlier reports [71], which all show that this transi- tion is accompanied by the excitation of optical phonons and that it is intrinsically broad. Possible minor contri- butions due to inhomogeneous broadening are negligible [71]. In order to derive information about the magnetiza- tion dynamics from the measured transient Faraday rotation � F t( ) plotted in Fig. 6, we converted the lat- ter into transient magnon temperatures T ts ( ) by means of Eq. (7) for all data below TN . Decomposing these temperatures into a static temperature T and an optically induced transient component �T ts ( ), we found all �T ts ( ) to be identical within the experimen- tal error. Their average is shown in the inset of Fig. 7 and is characterized by a monotonic increase that was fitted by the function �T t T t s s sl ( ) exp� � � � � �� 0 1 ! , (8) where Ts 0 is the amplitude of the dynamical tempera- ture and ! sl is the phonon—magnon interaction time. All the variables were set as fitting parameters and the result of the fit for Ts 0 = 1.4 K and ! sl = 700 ps is shown in the inset by a solid line. Using the deduced parameters Ts 0, ! sl and �0 we calculated the difference between the intrinsic Fara- day rotation and that at a time-delay of 500 ps as a function of temperature (dashed line in Fig. 7). Excel- lent agreement with the experimental data is found. Due to 6 1 4 4� �� excitation the electron poten- tial energy increases only by 1.4 eV, while the excess of the photon energy is either transferred to the lattice or the magnetic system. Generally magnon-assisted transitions are less intense than phonon-assisted ones [72]. Consequently, after the optical excitation the temperature of the phonons is higher than that of the magnons: T Tl s� . This difference gradually vanishes and the magnon temperature increases with a time constant determined by the phonon—magnon interac- tion that is predominantly related to the relativistic spin—orbit coupling in the magnetic ions and affected by magnetostriction only in the limited spectral range near the center of the Brillouin zone [73,74]. We found that the phonon—magnon interaction in FeBO3 has a characteristic time ! sl = 700 ps. The study of magnetization reversal by pulses of microwave radiation showed that the FeBO3 lattice is thermally insulated from the magnetic subsystem dur- ing about 16 ns after excitation [75]. This value is a factor of 20 larger than the phonon—magnon interac- tion time obtained in the present work. This large dif- ference originates from the fact that in our experiment the energy exchange between the magnons and phon- ons over the whole Brillouin zone is important, whereas in microwave experiments only magnons with small or zero wave vector are involved. As the colli- sion integral for these quasiparticles is relatively small, due to the conservation of energy and momen- tum, the equilibration of spin and lattice temperatures can be a 100 times faster than the decay of magnons with zero wave vector [74]. Thus the photoexcitation of iron borate results in heating of the lattice via phonon assisted transitions to the excited state and nonradiative relaxation. The antiferromagnetic order is subsequently destroyed via an energy transfer from the lattice to the magnetic subsystem that leads to an increase of the magnon temperature. This allows to determine the pho- non–magnon interaction time to be around 700 ps. This value is a factor of 20 smaller than found in ex- periments in the microwave region. The dynamics of the Faraday effect in the subpicosecond time domain is due to transitions of the Fe3+ ions to the excited low-spin state (S = 3/2), which does not lead to any magnetic excitations because of fast relaxation of the ions to the ground state (S = 5/2) within 100 fs. 3.2. Nonthermal optical control of magnetization in magnetic garnets 3.2.1. Experimental observations In contrast to iron borate, garnets show a minimum of absorption at the excitation wavelength. The key factor, however, in distinguishing the nonthermal effects described below was in their dependence on the pump pulse polarization. Thus, left- and right-handed circularly polarized laser pulses were used to excite the magnetic garnet film exposed to an in-plane ap- plied magnetic field Hext. Precession of M with an op- posite phase was triggered by pulses of helicity " � and " �, see Fig. 8. The initial phase of the signal reveals that M initially moves along the �z direction and therefore both M and Heff are parallel to the film plane immediately after the photoexcitation. Our experimental observations can be understood if during the presence of the laser pulse a strong magnetic field along the k vector of light is created. Such an ax- ial magnetic field HF can be generated by intense circu- larly polarized light through what is known as the in- verse Faraday effect [10,76–78] (see below). In our experiment these optically generated field pulses are much stronger than both anisotropy Han and the ap- plied field Hext and therefore completely dominate dur- ing the �t � 100 fs presence of the laser pulse. The mag- Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 993 netization will respond by precessing in the plane of the film (normal to HF) to a new in-plane orientation. Af- ter the pulse is gone, the magnetization will precess in the effective in-plane field # � � �H H H Heff ext an an$ , as illustrated in Fig. 8. The strength of the photoinduced field HF can be estimated from the precession amplitude %: H t F � � � � � % � pulse , (9) where � is the precession frequency, � is the gyromag- netic ratio and �tpulse is the duration of the optical pulse. We find that laser pulses of energy 20 �J create transient magnetic field pulses of about 0.6 T in the garnet films. The consistently large amplitude precession triggered by " � polarized pump pulses, irrespective of the applied field strength Hext, allows the external field dependence of the precession frequency�( )Hext to be accurately de- termined from the experimental data. As will be dis- cussed in Section 5.3 below, this is not the case for " � polarized excitation, which under certain conditions does not trigger any precession (see Fig. 27). The preces- sion frequency is given by the Kittel formula [79] and can, for our geometry, be expressed as � � � �� # � # �BH M H H H Hs( )( )4 an ext an ext , (10) where the small photoinduced modification $Han of the anisotropy field has been included in Han � � � �H Han an$ . Figure 9 shows the measured � as a function of the applied magnetic field for the " � po- larized pump excitation. The solid line represents a best fit using Eq. (10) and gives an Han of about 50 Oe, in accordance with the results of Fig. 1. 3.2.2. Phenomenological model of the inverse Faraday effect The normal Faraday effect can be viewed as due to a difference in the refractive indices for the two circu- larly polarized eigenmodes of light propagating in a magnetized medium. The inverse process, where circu- larly polarized light creates a magnetization or an ef- fective magnetic field is also possible [10,77,78] and known as the inverse Faraday effect. Strictly speaking this effect is classified as an optomagnetic effect as it, in contrast to photomagnetic effects, does not depend on absorption [49]. Phenomenologically the creation of an axial magnetic field by circularly polarized light can be described as $ & � � � �H E E E Ei F ijk j k k j( ) [ ( ) ( ) ( ) ( )]* 0 � � , (11) where & ijk is a third rank axial tensor with nonzero components for crystals of any symmetry [80]. The magnetic field is created by elliptically or circularly polarized light along its k vector. The field changes sign when the circular polarization is changed from left-handed to right-handed. The effect does not rely on absorption but becomes possible due to strong spin—orbit coupling in a material. The optically in- duced magnetic field pulse appears to act only during the presence of the laser pulse in the material [10]. Its strength depends on the value of the relevant & ijk components and is directly related to the Verdet constant. For our garnet films we can estimate the op- tically induced effective field strength from the re- sulting precession dynamics. At the wavelength of 994 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing " " + –2 0 2 0 1 2 3 Time delay (ns) –1 � M / M (% ) z �Han �Han – Fig. 8. Precession following excitation with circularly po- larized light. The two helicities �� and �� give rise to pre- cession with an opposite phase and a different amplitude. During the 100 fs presence of the laser pulse the magneti- zation precesses in the dominating axial magnetic field HF created by the circularly pump pulse. Subsequent pre- cession takes place in the effective magnetic field � �H H Heff eff an� [50,51]. 2 40 5 10 External field (kOe) Fr e q u e n cy (G H z) Fig. 9. Precession frequency as function of the externally applied magnetic field, measured with �� polarized excita- tion. Circles represent measurements and the solid line is a best fit using 4 550�Ms � G and Han = 50 Oe [51]. 805 nm used in our experiments we find HF � 0 6. T for a pump irradiance of about 1011 W/cm2. 3.2.3. Microscopic model of the inverse Faraday effect In this section we discuss a possible microscopic mechanism for the creation of an axial magnetic field by light and argue that it can be both efficient and ultrafast. In the electric dipole approximation an optical transition cannot change the spin state of an electron. After electric dipole transitions the next most likely type of transition is a magnetic dipole transition, which is due to the interaction between the electron spin and the oscillating magnetic field of the incident electromagnetic radiation. Magnetic dipole transitions allow spin flip but typically are about 105 times less probable than similar electric dipole transitions. The strong effect that we see indicates a mechanism that allows change of the electron spin with higher effi- ciency than expected from a magnetic dipole transi- tion. Moreover, the mechanism should not rely on ma- terial properties specific to garnets, as the reported effect has also been shown to exist in other magnetic materials such as rare earth orthoferrites [10] and me- tallic alloys [36]. A stimulated Raman-like coherent optical scat- tering process has been suggested to account for both the speed and the efficiency of the excitation [10,77,81,82]. Two frequency components of electro- magnetic radiation, both present in the 100 fs wide la- ser pulse take part in the process (see Fig. 10). The frequency �1 stimulates an optical transition from the ground state \|1' to a virtual state with a strong spin—orbit interaction. Due to this strong spin—orbit coupling there is a large probability of flipping the electron spin. Radiation at the frequency �2 also pres- ent in the optical pulse, stimulates the relaxation back into the spin split ground state with the electron spin reversed. The relaxation is accompanied by the coher- ent emission of a photon of energy � ( )�1 � (m and the creation of a magnon of energy (m . This process can be much more efficient than a simple magnetic di- pole transition as it is coherently stimulated by radia- tion at a frequency of �2 present in the laser pulse. Moreover, as the energy of the virtual state is of the order of the photon energy E � �� 1.54 eV the tran- sition can be fast, of the order of ! � �h/E 3 fs. 3.3. Optical excitation of antiferromagnetic reso- nance in DyFeO3 Thanks to this optomagnetic inverse Faraday ef- fect, circularly polarized pulses can be used to excite magnetization dynamics in a situation when any other method is difficult or impossible to apply. Thus in this Chapter we describe optical excitation of different modes of antiferromagnetic resonance in DyFeO3. For the detection of the optically induced magneti- zation we used the direct magneto-optical Faraday ef- fect, which was possible due to the presence of a weak ferromagnetic moment. Figure 11 shows the temporal evolution of the Faraday rotation in a z-cut DyFeO3 sample for two circularly polarized pump pulses of op- posite helicities. On the scale of 60 ps one can clearly distinguish two different processes that start after ex- citation with a pump pulse. At zero time delay instan- taneous changes of the Faraday rotation are observed, that result from the excitation of virtual and real tran- sitions in the Fe3+ ions from the high-spin ground state S = 5/2. The instantaneous changes of the Fara- day rotation are followed by oscillations with a fre- quency of about 200 GHz, that can clearly be assigned to oscillations of the magnetization. It is seen from Fig. 11 that the helicity of the pump light controls the sign of the photo-induced magnetization. This obser- vation unambiguously indicates that the coupling be- tween spins and photons in DyFeO3 is direct because the phase of the spin oscillations is given by the sign of angular momentum of the exciting photon. Figure 12 shows the difference between the Fara- day rotations induced by right- and left-handed circu- larly polarized pump light in the z-cut sample for the temperature range between 20 and 175 K. It is seen that an increase of the temperature results in an increase of the frequency of the oscillations up to 450 GHz at 175 K, while the amplitude of the oscilla- tion decreases. This behavior is in excellent agreement with previous Raman experiments in DyFeO3 Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 995 � �( ) � �1 �2 � m � �–1 m �1 �2 �m Fig. 10. Illustration of the stimulated Raman-like coher- ent scattering mechanism believed to be responsible for the ultrafast optically generated magnetic field. Two fre- quency components of electromagnetic radiation from the spectrally broad laser pulse take part in the process. The frequency �1 causes a transition into a virtual state with strong spin—orbit coupling. Radiation at the frequency �2 stimulates the relaxation back to the ground state with the creation of a magnon. [67,83,84]. The damping of the oscillations in the range of 200 ps is due to magnon scattering on phon- ons and spins of dysprosium ions. The highest value of the amplitude of the photo-induced oscillations is ob- served between 20 and 50 K. The amplitude of the os- cillations corresponds to a photo-induced change of the magnetization �M Ms� 0 06. , where Ms is the sat- uration magnetization. This ratio is obtained from hys- teresis measurements in a static magnetic field, that show that the saturated Faraday rotation in a single domain z-cut sample is about � )�. From Figs. 11 and 12 one can distinguish not only oscillations but also an exponential decay of the equi- librium level on a time scale of about 100 ps. This can be explained by a photo-induced change of the equi- librium orientation of the magnetization and subse- quent decay of the equilibrium orientation to the ini- tial state. Although in principle the effect of optically induced magnetization does not require the absorption of photons, the laser control of the spontaneous mag- netization and the excitation of coherent spin oscilla- tions is equivalent to photoexcitation of magnons and thus requires some energy. The inset in Fig. 12 shows the amplitude of the photoexcited spin oscillations as a function of the pump intensity. The linearity of this dependence indicates that the photoexcitation of magnons is a one-photon process. Note that extrapo- lation of the intensity dependence shows that the photoinduced effect on the magnetization would reach the saturation value of Ms at a pump fluence of about 500 mJ/cm2. The effect of such 100 fs laser pulse on the magnetic system would be equivalent to the appli- cation of a magnetic field pulse of about 5 T. Accord- ing to our measurements, the absorption in DyFeO3 in the near infrared spectral range is on the order of 100–200 cm–1. Given this low value of the absorption, a photoexcitation of 500 mJ/cm2 is still below the damage threshold of DyFeO3 and thus quite feasible, provided a sample of high optical quality is available. Due to the strong anisotropy of the magnetic sus- ceptibility in DyFeO3, magnetic field pulses in differ- ent directions should trigger different types of spin os- cillations (Fig. 13). A magnetic field pulse directed along the z axis excites oscillations that correspond to the quasi-antiferromagnetic resonance mode, while a field pulse along the x axis will excite the quasi-ferro- magnetic resonance mode [67]. These predictions are in excellent agreement with the experimentally ob- served temperature dependences of the frequency of the oscillations for z-cut and x-cut samples. These closely resemble the temperature dependence for the quasi-antiferromagnetic and the upper quasi-ferro- magnetic resonance mode in DyFeO3, respectively (see Fig. 13). 996 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing T = 95 K– + Fa ra d ay ro t a tio n (d e g ) – + H+ 0 15 30 45 60 0 0.1 0.2 Time delay (ps) H– Fig. 11. Magnetic excitations in DyFeO3 probed by the magneto-optical Faraday effect. Two processes can be dis- tinguished: 1) instantaneous changes of the Faraday effect due to the photoexcitation of Fe ions and relaxation back to the high-spin ground state S = 5/2; 2) oscillations of the Fe spins around their equilibrium direction with an approximately 5 ps period. The circularly polarized pumps of opposite helicities excite oscillations of opposite phase. Inset shows the geometry of the experiment. Vectors �H� and �H� represent the effective magnetic fields induced by right-handed �� and left-handed �� circularly polarized pumps, respectively [10]. 115 K, 327 GHz (x3) 155 K, 406 GHz (x6) 75 K, 211 GHz 60 K, 175 GHz 50 K, 159 GHz 40 K, 153 GHz 30 K, 151 GHz 18 K, 151 GHz 0 50 100 150 200 250 300 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time delay (ps) 25 50 75 Fa ra d ay ro ta tio n (d e g ) A m p lit u d e (a rb . u n its ) 135 K, 372 GHz (x3) 95 K, 271 GHz (x3) 175 K, 433 GHz (x6) 1.0 0.5 0 Pulse fluence (mJ/cm )2 Fig. 12. Excitation of the spin oscillations in DyFeO3 mea- sured at different temperatures in the range between 18 and 175 K. In order to exclude effects not relevant to magnetic excitations, the difference between the signals for right- and left-handed circularly polarized pump pulses is plotted. Every new curve is shifted from the previous one along the vertical axis by 0.06�. Inset shows the amplitude of the spin oscillations as a function of pump fluence [10]. Note that the application of a static external mag- netic field up to 0.5 T in a direction parallel to the wave vector of light only resulted in a slight change of the frequency (about 1%), again confirming that the effective photo-induced field is dominating the dy- namics. It is thus clear that with circularly polarized femto- second laser pulses one can purely optically and thus nonthermally excite and coherently control also the antiferromagnetic precession. Using circularly polar- ized photons one can affect an ensemble of strongly correlated spins, excite coherent spin oscillations and control the phase of these oscillations with the helicity of light. The decisive prove of this direct coupling is that the phase of the spin oscillations is controlled by the sign of the angular momentum of the exciting pho- tons and changes sign by going from right to left helicity of the exciting laser pulse. This mechanism was discussed above in Chapter 3.2. Such optical pulses are shown to be equivalent to magnetic field pulses of large amplitude. In view of the great variety of magnetic materials, the direct effect of light on the spontaneous magnetization in other materials and at higher temperatures is foreseen. Our findings open new insights into the understanding of ultrafast mag- netic excitation and, taking into account recent prog- ress in the development of the compact ultrafast lasers [11], may provide new prospects for applications of ultrafast photomagnetic phenomena. 4. Laser-induced changes of magnetic anisotropy In contrast to the previous chapter, where the laser pulse was affecting the magnetization itself, whether thermally or nonthermally, here we deal with the la- ser-induced changes of the magnetic anisotropy. That is, the laser pulse changes the equilibrium direction of the magnetization, thus forcing the latter to precess around this new equilibrium. 4.1. Thermally-induced spin reorientation in TmFeO3 The temperature-dependent anisotropy energy in TmFeO3 has the form [85,86] F T F K T K( ) ( )sin sin ,� � �0 2 2 4 4 (12) where is the angle in the xz plane between the x axis and the AFM moment G, see Fig. 2, and K2 and K4 are the anisotropy constants of second and fourth or- der, respectively. Applying equilibrium conditions to Eq. (12) yields three temperature regions correspond- ing to different spin orientations: �4 20( ): , ,G F T Tx z � �2 1 1 2 ( ): ,G F T Tz x �� + , �24 2 2 4 1 22 : sin ( ) , � � + + K T K T T T , (13) where T1 and T2 are determined by the conditions K T K2 1 42( ) � � and K T2 2 0( ) � and the �‘s indicate the representations of the respective symmetry groups [87]. Therefore, depending on the anisotropy con- stants, a spin reorientation may be expected that shows two second-order phase transitions at T1 and T2. The temperature dependence of in the phase �24 is determined by K T2( ), which varies roughly lin- early with temperature [62]. As also shown in Fig. 2, the transition between the two spin configurations in the antiferromagnet can be monitored with the help of linear birefringence, when the refractive index n of a medium depends on the orientation of the light polarization. For light propa- gating along the z axis through a birefringent medium, the refractive indices for light polarized along the x axis and the y axis are different, where �nxy charac- terizes the birefringence and is determined by a differ- ence in the diagonal components of the dielectric permittivity tensor: Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 997 150 300 450 25 50 75 100 125 150 175 Temperature (K) H S2 Y Z k + S1 X Z YX k + H quasi-FM mode quasi-AFM mode Fr e q u e n cy (G H z) Temperature (K) A m p lit u d e (a rb .U n .) 1.0 0.1 0.01 20 50 80 110 140170 Fig. 13. Temperature dependence of the frequencies of the observed spin oscillations. Filled and open circles show the frequencies of the excited oscillations for laser pulses propa- gating along the z and x axis, respectively. Lines show the frequency of the quasi-antiferromagnetic (quasi-AFM) and the quasi-ferromagnetic (quasi-FM) resonance modes from Refs. 67, 83, 84. Top right inset shows the temperature de- pendence of the oscillation amplitudes. Top left and bottom right insets are, respectively, schematic representations of the quasi-FM and quasi-AFM modes of the spin resonance. Vectors �H show the directions of the instantaneous mag- netic field that is equivalent to the photoexcitation [10]. �n nxy xx yy � �, , 2 . (14) Regarding the change of the diagonal components induced by the presence of the AFM vector G, that is , , ii ii iijk j kG G� �( )0 , one can find for TmFeO3 that � � � �n n( ) ( )2 4- . Thus, the birefringence serves as a direct measure of the orientation of the AFM vector G. Measurements of the absorption showed that at a photon energy of 1.55 eV, the laser pulse is absorbed in the sample via the excitation of the localized electronic states of the Fe3+ and Tm3+ ions. The resulting changes of the birefringence are summarized in Fig. 14 [9]. In the time domain, the relaxation process can be divided in three distinct regions. First, the excitation decays via phonon cascades and the phonon system thermalizes in a very short time (process 1 in Fig. 14, with a time constant of around 0.3 ps). This time is in approximate agreement with earlier results [44]. The phonon- phonon interaction sets a new lattice temperature so that the equilibrium anisotropy axis is changed. Under such conditions in a FM material, the magnetization vector would precess around its new equilibrium direc- tion, approaching it due to the damping (see Fig. 15) [88]. In an antiferromagnet, the exchange coupled spins start to precess in opposite directions, thus creat- ing a strong exchange torque Tex that opposes this pre- cession (see Fig. 15). The resulting motion of the spins to the new equilibrium should then occur in the plane spanned by HA and S. This process is marked 2 in the time dependencies of Fig. 14 and has a characteristic time of about 4 ps. This relaxation time corresponds to an AFM resonance frequency of 80 GHz. The ampli- tude of this spin reorientation reaches 30 degrees in our experiment (see Fig. 16), this value being obtained with the help of the static birefringence data from Fig. 2. After the initial relaxation, the antiferromagnetic vector oscillates around its new equilibrium (process 3), with a temperature dependent frequency and am- plitude. Particularly strong oscillations are observable in the range of 80–90 K, i.e., in the region of the reorientational transition (Fig. 16). In fact, the tem- perature dependence of the derived frequencies should closely resemble that of the spin waves with k = 0, shown by a thin line in Fig. 16 [86]. Such spin waves are equivalent to a homogeneous precession of magne- tization observed at such conditions in ferromagnets [29]. In our case, however, the amplitudes of the oscil- lations are so large, up to ten degrees, that the ob- served modes are quite different from the small-ampli- tude spin waves. As a matter of fact, the damping of such large-amplitude AFM oscillations is expected to differ from that of the AFM resonance and should be studied separately. Note that Fig. 11 also shows that the frequencies of the oscillations may increase with delay time, in par- ticular visible for the data at T � 78 K. This can easily be understood, because the optically induced tempera- ture increase pushes the AFM vector into the region of 998 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing 1 2 3 10 K 15 K 25 K 35 K 45 K 55 K 65 K 70 K 74 K 76 K 84 K 86 K 88 K 90 K 105 K 125 K 78 K 80 K 82 K 160 K 0 2 4 6 8 10 30 50 70 Time delay (ps) P h o to -i n d u ce d b ir e fr in g e n ce spin-reorientation spin-oscillations Fig. 14. Excitation and relaxation of the AFM moment mea- sured via changes in the magnetic birefringence. On the fig- ure one can distinguish three processes: 1) electron-phonon thermalization with 0.3 ps relaxation time; 2) rotation of the AFM vector with 5 ps response time; 3) oscillations of the AFM vector around its equilibrium direction with an ap- proximate 10 ps period [9]. HA M ferromagnet S1 Tex S2 antiferromagnet HA Fig. 15. Schematically spin relaxation in an antifer- romagnet as compared to that in a ferromagnet: in con- trast to the spiral FM precession, the AFM vector moves in a plane [9]. the reorientation. Therefore, the starting frequency is low. During the process of relaxation, however, the temperature decreases and restores the effective aniso- tropy field value, resulting in the observed frequency increase. The experiment shows that the AFM spins in TmFeO3 are reoriented by several tens of degrees dur- ing only a few picoseconds. For comparison, in a ferromagnet with an anisotropy energy similar to that in TmFeO3 (104 J/m3 [57]) the magnetization pre- cesses with a period of several hundred picoseconds [6,89]. We should also remind here that a relaxation time of about 700 ps was measured for the laser-induced de- struction of the AFM order in FeBO3 (see above Chapter 3.1). In contrast, the spin reorientation hap- pens to be a much faster process. The measured maximum of the reorientation ampli- tude of 30 degrees, in fact, is only related to the problem of the instantaneous and homogeneous heating of a bulk sample and can easily be overcome in smaller structures, where such reorientation is of practical importance. For example, in an exchange-coupled FM/AFM bilayer, the laser-induced reorientation of the AFM vector by 90 degrees will trigger, via the exchange coupling, a preces- sion of the FM moment into the opposite state [9]. Thus, in addition to increasing the stability of magnetic nanoelements [90], the AFM layer can also play an ac- tive role in the switching process. Thus we an ultrafast spin reorientation in anti- ferromagnetic TmFeO3 can be induced by a laser pulse. Optical excitation leads, via electron—phonon relaxation and phonon—phonon interaction, to a sub- picosecond change of the anisotropy axis. Such change is equivalent to an ultrafast magnetic impact. It has also been shown that the linear magnetic birefringence appears to be a sensitive experimental technique to study the motion of the AFM vector. Thus the dynam- ics of the AFM moment can be influenced and de- tected with an all-optical pump-probe method. Last but not least, in contrast to the spins in a ferromagnet, the AFM spins can be fully reoriented within a few pi- coseconds, without the application of an external magnetic field. 4.2. Ultrafast modification of anisotropy via direct photomagnetic interaction The just described dynamics in TmFeO3 was caused by a laser pulse that could be of any polarization, via heat-induced phase transition. It is a dependence on the pump pulse polarization, however, which is the finger- print of a nonthermal effect. Such nonthermal modifi- cation is clearly demonstrated in thin garnet films, with laser wavelength in the transparency region. 4.2.1. Experimental observations Applying an external magnetic field Hext in the plane of a magnetic garnet sample (so that M is in-plane, � � 90�) and pumping with linearly polarized laser pulses, optically triggered precession of the mag- netization M was observed, see Fig. 17,a. In the opti- cal transmittivity of the sample, see Fig. 17,c, a sudden drop is seen which does not relax significantly within 3 ns. Intriguingly, the amplitude and phase of the pre- cession in Fig. 17,a was found to depend on the plane of polarization of the pump pulses as shown in Fig. 17,b. Negative values of the amplitude indicate precession of M with the opposite phase. Maxima of the precessional amplitude (of the opposite phase) were ob- served for every 90� rotation of the polarization, and at some polarizations no precessional dynamics was trig- gered. From this dependence on pump polarization it is evident that the underlying effect must be nonthermal. An ultrafast heating effect would only reduce the mag- nitude of the magnetization and the anisotropy field in- dependently of the pump polarization. Heating effects thus cannot be responsible for triggering magnetization dynamics that exhibit polarization dependence of the type that we observe in Fig. 17. It is also interesting to note that M always starts its precessional motion by moving normal to the film Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 999 Fr e q u e n cy (G H z) A m p lit u d e (d e g ) 0 40 80 120 160 0 10 20 30 40 50 60 70 80 90 100 110 Temperature (T) oscillation amplitude reorientation amplitude HA S1S2 Fig. 16. Temperature dependencies of the amplitudes and frequencies of the observed oscillations, as well as the am- plitude of the spin reorientation. Thin line shows the fre- quency change at the reorientational transition from Ref. 86. Inset shows the oscillations of spins in the xz plane. Nonzero reorientation amplitude at T = 55 K corresponds to an instantaneous local laser-induced heating of more than 25 K [9]. plane along the � �z direction. This follows from the ini- tial phase of the measured signal in Fig. 17,a which al- ways starts from the inflection point where Mz is changing most rapidly. From the Landau—Lifshitz equation [Eq. (2)] it can be inferred that immediately after the photo excitation both M and Heff are in the film plane but not parallel to each other. Conse- quently, the observed magnetization dynamics must be due to an ultrafast change of the magnetization $M, the anisotropy field $Han, or a combination of the two, that effectively creates an in-plane angular dis- placement % � .( , )M Heff between M and Heff. It is possible to distinguish between these possibilities by analyzing the precession amplitude % as function of the applied field. The result is shown in Fig. 18. If triggered by an ultrafast rotation of the magnetization M M M � $ , the amplitude % of the subsequent pre- cession should be independent of the strength of the applied magnetic field as .( , )M Heff does not depend on Hext. However, if the precession is caused by a change in the effective field through a photoinduced anisotropy field $Han, the precession amplitude % is expected to decrease with increasing applied magnetic field as % � . � � � ( , ) \| \| H H H H H eff eff an ext an $ 1 , (15) which is valid for small amplitude precessions. As shown by the fitted curve in Fig. 18 (solid line) the measurements exhibit the exact behavior that one expects for a photoinduced anisotropy field $Han [Eq. (15)]. Based on the precession amplitude, the magnitude of the photoinduced field can be estimated to $Han = 0.5 Oe for the present geometry (� � 90�). A graphical illustration of the excitation process and the subsequent precession is shown in Fig 19. For the present geometry, with the applied field in the plane of the film, changing the polarity of the mag- netic field Hext does not affect the measured signal for any given polarization of the pump. The fact that the precession phase and amplitude are both unaffected by reversing the polarity of the external field (see Fig. 17,b) shows that $Han must be odd with respect to M: when changing the polarity of the external field both M and the anisotropy field Han in Eq. (3) change sign. It then follows from Eq. (2) that the photoinduced $Han also must change sign, i.e., $ $H Han an � in or- der to give rise to the same signal. By applying the external field at an angle with respect to the film plane, the magnetization can be tilted out of the film plane (� � 90�). The actual angle � that the magnetization makes with the film normal is determined by the balance between the applied field, the anisotropy field, and the demagnetizing field. When pumping with linearly polarized laser pulses in this configuration, a larger amplitude precession was observed, see Fig. 20,a. This precession is superim- posed on a slowly decaying exponential background caused by the relaxation of the photoinduced aniso- 1000 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing = 100� 80� 60� 40� 20� 0 1 2 3 0 2 4 Time delay (ns) 0 1 2 3 –4 –2 0 Time delay (ns) a (deg) 0 180 360 –1 0 1 b c � M / M (% ) z � M / M (% ) z T (% ) Fig. 17. Coherent precession of the magnetization triggered by linearly polarized laser pulses. (a) Time dependence of the precession for different planes of pump polarization �, with an applied field of \|Hext\| = 350 Oe in the plane of the sample. Circles represent measurements and solid lines sim- ulations based on the Landau–Lifshitz equation. (b) Preces- sional amplitude as a function of the plane of pump polar- ization. Round and square symbols represent amplitudes extracted from measurements at Hext. The solid line is a best fit. (c) Pump-induced change of the sample trans- mittivity �T [51]. 2 4 0 1 External field (kOe) � M / M (% ) z Fig. 18. Dependence of the precessional amplitude on the ap- plied in-plane magnetic field Hext. Round and square symbols represent amplitudes extracted from measurements at Hext. t < 0 t = 0 t > 0 �Han �Han Fig. 19. Graphical illustration of the process of pho- toinduced magnetic anisotropy caused by linearly polarized laser excitation and the subsequent precessional dynamics. tropy. In contrast to the in-plane applied field geome- try (where � � 90�), the initial phase of the precession in Fig. 20,a reveals that for M tilted out of the film plane (� � 90�) the initial motion of M is nearly paral- lel to the film plane. This implies that the laser-in- duced $Han is directed essentially along the z direc- tion. The dependence of the precession amplitude and phase on the polarization of the pump pulses becomes gradually smaller as M is tilted further out of the film plane. At about � � 60�, all polarization dependence is practically gone and changing the polarity of the ex- ternal field gives a near 180� phase shift in the mea- sured signal. The diminishing influence of the pump polarization is caused by the dominating z component of $Han, and will be discussed further in Section 4.2.2. From the precession amplitude in Fig. 20,a the strength of the photoinduced anisotropy field is esti- mated to be $Han = 1.5 Oe. Laser heating effects in the sample, if present, are likely to be more pronounced in this geometry than in the in-plane field geometry as a thermal reduction of M also changes the equilibrium Heff and leads to a re- orientation of M along the z direction. However, in our experiments the optical excitation of coherent spin waves is ultrafast (see Fig. 20,b, where very fast ini- tial relaxation of less than a few picoseconds is indi- cated), much faster than the phonon–magnon interac- tion time which is about 1 ns in this material [45], and therefore cannot be of thermal origin. As was dis- cussed above in Chapter 3.1 (see also Ref. 51), ther- mal effects can be seen on the time scale of a nanosec- ond when the sample is heated to temperatures near the Curie point. Based on the results in Fig. 20,a one can argue that the lifetime ! of $Han is longer than the time texp ns� 3 accessible in this experiment. As the pre- cession of M is always around the effective magnetic field H H Heff eff an� � � $ , any relaxation of $Han should be visible in the time trace of the precession. Note in Fig. 20,a how M precesses around an equilib- rium Heff � that is different from the initial t � 0 state. Some relaxation of Heff � can be seen (the slow overall change of the fast oscillating signal) but is not suffi- cient to restore the original equilibrium on the time scale of the experiment. This indicates that after texp ns� 3 $Han has still not decayed completely. An- other observation that supports this conclusion is the photoinduced change in the sample transmittivity �T shown in Fig. 17,c, which also does not relax signifi- cantly during 3 ns. There appears to be a linear relation between the precession amplitude and the pump power (Fig. 21) up to pulse energies of almost 10 �J. At higher pulse energies the effect saturates completely. Based on the absorption coefficient the estimated density of ab- sorbed photons is about one per hundred unit cells in the illuminated crystal volume. Saturation effects are therefore not expected unless they are caused by the presence of low concentration impurities. This will be discussed in more detail in the Section 4.2.3 on the microscopic basis of the photomagnetic effect. 4.2.2. Phenomenological model of photoinduced magnetic anisotropy In this section we give a macroscopic phenome- nological description of the observed photoinduced mag- netic anisotropy. The model is not concerned with the microscopic mechanism of the effect, but gives some in- sight into its symmetry properties. The creation of a static magnetic field $Han( )0 in the sample can be described as a combination of the Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 1001 1.22 kOe 0.75 0.24 –0.26 –0.77 –1.23 0 1 2 3 0 5 10 15 Time delay (ns) / 0 50 100 Time delay (ps) a b � M M (% ) z / � M M (% ) z Fig. 20. (a) Precession of the magnetization following ex- citation with linearly polarized light for different values of the magnetic field applied at an angle of about 45� with the sample normal. (b) The excitation shown on a finer time scale [51]. 10 200 2 Pulse energy ( J) M / M (% ) � z Fig. 21. Dependence of precession amplitude on the exci- tation pulse energy [51]. nonlinear process of optical rectification [91] and a linear magnetoelectric effect [92]: $ & � �H E E Mi ijkl j k l an( ) ( ) ( ) ( )0 0� . (16) Here E is the electric field component of light and M is the magnetization of the garnet film. The fourth rank polar tensor & ijkl has nonzero components for crystals of any symmetry [80]. When taking the experimental geometry (Fig. 4) and the symmetry of & ijkl for the 4mm point group of our samples into account, only four independent non- zero components of the tensor & ijkl remain, A xxxx yyyy� �& & , B xyxy xxyy yxyx yyxx� � � �& & & & , C xyyx yxxy� �& & , D zxxz zyyz� �& & , (17) and the vector components of the photoinduced aniso- tropy field are then given by $ � /H E M A Cx s an � � �0 2 sin [( ) cos � � �( ) cos sin sin ]A C Bcos2 2 2 / / , (18) $ � /H E M A Cy s an � � �0 2 sin [( )sin � � �( ) sin cos ]A C Bcos sin2 2 2 / / , (19) $ �H E M Dz s an � 0 2 cos . (20) Here $Hi an is the photoinduced field along the i direc- tion, i = {x y z, , } refers to the crystal axes of the sam- ple, / denotes the azimuthal angle between the sample x axis and the projection of the magnetization vector on the film plane and � is the angle between the film normal and the magnetization, as shown in Fig. 4. From these equations one can see that if the magne- tization M is in the film plane, the out-of-plane compo- nent $Hz of the photoinduced anisotropy field does not contribute as cos� � 0. This is in accordance with our experimental results from Fig. 17 which show an in-plane $Han . However, in order for the above equa- tions to describe a field $Han consistent with the polar- ization dependence of the precession amplitude, shown in Fig. 17,b, the number of independent tensor compo- nents must be further reduced. The fact that there is no amplitude offset in the curve shown in Fig. 17,b re- quires that A C� � so that the first term in Eqs. (18) and (19) vanishes. Furthermore, the sinusoidal shape of the curve implies that A B� and leaves us with only two independent components of the tensor & ijkl , A xxxx yyyy xyyx yxxy� � � � � � �& & & & � � � �& & & &xyxy xxyy yxyx yyxx , D zxxz zyyz� �& & . (21) These additional equalities indicate that the & ijkl ten- sor has a higher symmetry than the garnet crystal. However, this does not violate Neumann’s principle which states that the symmetry elements of any phys- ical property of a crystal must include all the symme- try elements of the point group of the crystal. This does not prevent that property from having a higher symmetry than the crystal. The optically induced ani- sotropy field can now be written as $ � / /H AE Mx s an � �0 2 2 2sin (sin sin cos cos ),(22) $ � / /H AE My s an � �0 2 2 2sin (sin cos cos sin ), (23) $ �H DE Mz s an � 0 2 cos . (24) For the in-plane field geometry (cos� � 0) this de- scribes a vector of constant length and with a direc- tion depending on the angle / of the magnetization with respect to the x axis and the plane of polariza- tion of the pump pulses. The $Hz an component ac- counts for the observed behavior in Fig. 20 with the applied field at an angle so that � � 90�. Computer simulations based on this simple model and the numerical integration of Eq. (2) exhibit good agreement with our experimental results, both for the in-plane Hext geometry shown in Fig. 17,a, where the results of the simulation are shown by solid lines, and for the out-of-plane Hext geometry in Fig. 20 (simula- tions are not shown). The latter indicate that the ten- sor component D is larger than A by a factor of 3. This is not surprising in view of the symmetry distortion along the z axis known to exist in films of this type [54,55,93]. One could have noted above, in Fig. 8, that circu- larly polarized pulses of opposite helicity excite pre- cession of somewhat different amplitude. In order to understand this, we analyze our model of the pho- toinduced anisotropy [Eq. (16)] for circularly polar- ized light E � �E / x iy0 2( � �) : $ � /H AE Mx s an � 0 2 sin cos , (25) $ � /H AE My s an � � 0 2 sin sin , (26) $ �H DE Mz s an � 0 2 cos . (27) We find that a photoinduced $Han can still exist which only depends on the direction / of M with respect to the crystal axes. This is reasonable as has no meaning for circularly polarized light. For an 1002 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing in-plane magnetization the photoinduced $Han is par- allel to the film plane. However, it does not depend on the helicity of light and can therefore not account for the opposite phase of precession induced by the light of opposite helicities. The asymmetry seen in the signal amplitude be- tween the " � and " � helicities in Fig. 8 stems from the simultaneously created photoinduced anisotropy $Han which is independent of the pump helicity [see Fig. 8 and Eqs. (25)–(27)]. For the " � helicity M precesses in the direction of the optically modified effective field Heff � during the presence of HF. This gives rise to a precession with a small amplitude around Heff � after the pulse is gone. For the " � helicity M precesses in the opposite direction during the presence of HF , moving further away from Heff � . After the pulse is gone a large amplitude precession sets in. 4.2.3. Microscopic justification Photomagnetic effects are known to exist in garnets containing certain dopants [94,95], in particular Si and Co [47,48]. Optically induced electron transfer between ions on nonequivalent sites in the crystal is believed to cause a change in the magnetocrystalline anisotropy due to a redistribution of ions [96]. This ef- fect is strong in crystals doped with elements that can assume different valence states, and where their con- tribution to the anisotropy is different. However, it has also been observed in undoped garnet samples con- taining Pb impurities [97], which we believe is the case in our experiments. The linear dependence of $Han on the pump power shown in Fig. 21 suggests that linear optical absorp- tion is the dominating absorption process. The satu- ration of $Han at high pump intensities may be att- ributed to the Pb impurities. Divalent Pb2+ ions substitute trivalent Lu3+ ions on dodecahedral sites in the crystal and act as electron acceptors. This is a p-type doping which creates holes that are usually as- sumed to be located on iron ions in tetrahedral sites [46,98]. To maintain overall charge neutrality in the crystal, some tetrahedrally coordinated trivalent iron ions change their valency to 4+ . Photoexcitation can induce a charge transfer between these Fe4+ ions and Fe3+ magnetic ions on octahedral sites, thus effec- tively «moving» the Fe4+ ions to sites with different symmetry (see Fig. 22), and thereby causing a change in the magnetic anisotropy. The low concentration of Pb impurities creates a limited number of photoactive ions and the photo- magnetic effect can therefore be expected to saturate under intense illumination. An estimate for our sample shows that the illuminated volume of garnet film con- tains about 1012 Pb ions. An optical pulse of 20 �J de- livers 1014 photons from which about 1% is expected to be absorbed. This allows in principle, for all of the photoactive ions to be excited and it is thus not sur- prising that saturation can occur at these pump inten- sities. The pump-induced change in transmittivity is also believed to be related to the photoexcitation of impurities [99]. Finally, we would like to notice that an ultrafast effect of light on magnetic anisotropy has been also observed in antiferromagnetic dielectric NiO [100]. 5. Coherent control of magnetic precession The primary advantage of the nonthermal control of spins is the possibility of very high repetition rates, without the need to wait for the usually involved heat dissipation. In this Chapter we demonstrate the prac- tical realization of this concept based on an experi- mental scheme with two pump pulses. 5.1. Double-pump coherent magnetization control via inverse Faraday effect For this optomagnetic mechanism, ultrafast coher- ent control of the magnetization can be very easily demonstrated by using multiple laser pulses in rapid succession. In a double pump experiment employing two circularly polarized pump pulses with opposite helicity and almost equal power, we achieved stop- ping of the precessional dynamics as well as doubling of the amplitude. Here as well as below, in the case of linearly polarized pulses, we operate at a fixed time delay between the two pump pulses, and adjust the frequency of precession by an external magnetic field in order to vary the arrival time of the second pump pulse with respect to the phase of the already present precession. Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 1003 {c} (d) [a] Fig. 22. Illustration of the photoexcitation of electrons between iron ions in different crystallographic sites. A la- ser pulse induces electron transfer from a Fe3+ ion in the octahedral site (denoted by [a]) to a Fe4+ ion in the tetra- hedral site (denoted by (d)). The dodecahedral site with the divalent lead impurity is denoted by {c}. In Fig. 23 it is shown how a pump pulse of helicity " � arriving at t � 0 triggers precession of the magneti- zation, as explained in the previous section. A second pump pulse of helicity " � arriving after an odd number of half precessional periods rotates the magnetization further away from Heff causing the subsequent preces- sion to have almost twice the amplitude. If, however, this second pump pulse arrives after an integer number of full periods, the magnetization is rotated back into its original equilibrium orientation along Heff and no further precession takes place. Figure 24 gives a picto- rial illustration of these two situations. This experiment clearly demonstrates that femto- second optical pulses can be used to directly and co- herently control spin dynamics. Depending on the phase of the precession when the second pulse arrives, energy is either transferred from the laser pulse to the magnetic system (amplification of the precession) or from the magnetic excitation to the optical pulse (stopping of the precession). A stimulated Raman pro- cess of scattering on magnons is believed to be respon- sible for the inverse Faraday effect [81] (see above), and we expect that further support for this mechanism can be found in the frequency spectrum of the second pump pulse. Stokes or anti-Stokes peaks should be ob- servable in the spectrum, depending on whether the precession is amplified or stopped, respectively. In view of the low intrinsic damping in these garnet films, and therefore the long lifetime of magnetic exci- tations, it is remarkable how ultrashort laser pulses can completely stop the long period coherent preces- sion of spins instantaneously by transfer of the energy into the optical pulse. This process can also be viewed as coherent laser cooling of magnons. In order to demonstrate the really ultrafast magneti- zation control with inverse Faraday effect, one should turn the attention to experiments in antiferromagnetic orthoferrites, with characteristic precession periods of a few picoseconds. In Fig. 25 is shown how two pump pulses, separated in time by about 16–18 ps, can be used to trigger and control the precession of M. By carefully timing the arrival of the second pump pulse amplification as well as complete stopping of the pre- cession can be achieved. This is the so-far best demon- stration of the unsurpassed speed with which magneti- zation control can be achieved using laser techniques. Strikingly, a change in the arrival time of the second pump pulse by only about a picosecond decides whether the system will be left in a stable state (lower curve) or with a large precession amplitude (upper curves). No existing electronics can even remotely ap- proach these timescales. It should be pointed out that the present double pump experiments, that demonstrate control of the magnetization in ferrimagnetic garnets and antifer- romagnetic orthoferrites, are considerably different from those previously reported in diamagnetic and paramagnetic materials. During the past two decades a great number of publications have been devoted to the photoexcitation of a nonequilibrium spin polariza- tion in direct band gap semiconductors through the phenomena of optical orientation [101–103]. In these 1004 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing –4 0 � T (% ) 0 0.5 1.0 1.5 0 1 2 Time delay (ns) "+ "– M / M (% ) � z Fig. 23. Double pump experiment with circularly polarized laser pulses of opposite helicity and 15 �J pulse power. The upper panel shows the pump-induced change of the sample transmittivity due to the photoexcitation of impurities. The lower panel shows how amplification and complete stop- ping of the magnetization precession can be achieved de- pending on the phase of the precession when the second la- ser pulse arrives. The time delay between the two pump pulses is fixed at approximately 0.6 ns, and the precession frequency is controlled by varying the external field [51]. 100 fs < t < t 2 2t < t < t 2 + 100 fs t > t 2+100 fs a 100 fs < t < t 2 t > t 2 +100 fs b +100 fst < t < t2 2 Fig. 24. Illustration of the double pump experiment for circularly polarized pump pulses of opposite helicity arriv- ing at an (a) odd number of half precessional periods and (b) an integer number of full precessional periods. The magnetization is either rotated further away from the ef- fective field direction causing subsequent precession to take place with almost twice the original amplitude, or the magnetization is rotated back into the effective field direction and no further precession takes place. materials, absorption of circularly polarized photons may lead to a nonequilibrium population of spin po- larized electrons and holes in the conduction band and valence band, respectively. In paramagnetic semicon- ductors these spin polarized carriers can cause partial alignment of the moments of magnetic ions due to a sp-d exchange interaction, and thereby also affect their precession in a magnetic field [104]. Using this phenomena of optical orientation Akimoto et al. [106] have demonstrated control of the precession of Mn2+ moments in CdTe/Cd1–xMnxTe quantum wells. Note that this approach, in contrast to our experiment, is based on the absorption of photons. A nonabsorptive mechanism for manipulation of spins in Zn1–xCdxSe quantum well structures was reported by Gupta et al. [106], who used below band gap optical pulses to con- trol the spin precession of photoexcited electrons in the conduction band via the optical Stark effect. How- ever, these experiments were performed on paramag- netic materials, while in the present case we have suc- ceeded to control the collective motion of the strongly coupled spins in a magnetically ordered compound. Additionally, the experimental conditions differ strongly in the two cases; control of the spin preces- sion in paramagnetic semiconductors requires very low temperatures, typically below 10 K, and strong mag- netic fields of several Teslas. In contrast, the optical control of magnetization that we report here was done at room temperature and in magnetic fields well below 1 kOe. 5.2. Double-pump control of anisotropy In order to investigate the possibility of coherently modifying and controlling also the effective anisotropy fields on a time scale shorter than their relaxation time, a double-pump experiment was conducted on the mag- netic garnet samples. Using a Michelson interferome- ter-like configuration, the pump pulses were split into two with a beam splitter cube, and one part was de- layed with respect to the other. As before, a fixed time delay was used and the timing of the arrival of the sec- ond pump pulse with respect to the precessional dy- namics was controlled by varying the precession fre- quency (applied field). By use of a quarter wave plate the linear polarization of the second pump pulse was set to be orthogonal with respect to the first one. A mag- netic field was applied in the plane of the sample, and the dynamics triggered by the individual pump pulses was first recorded by blocking one of the pump pulses at a time. The results are shown in Fig. 26. The two or- thogonally polarized pump pulses (denoted by pump #1 and pump #2) trigger precession with the same am- plitude and opposite phase, a result which was also known from Fig. 17,b. When allowing both pump pulses to reach the sample, the resulting dynamics (de- noted combined) in the time after the second pump pulse (t > 0.6 ns) is almost identical to the sum of the response of the two individual pump pulses. If the sec- ond pump pulse arrives after approximately one full precessional period, as shown in the top panel, it causes quenching of the subsequent dynamics. However, the Ultrafast all-optical control of the magnetization in magnetic dielectrics Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 1005 0 20 40 60 Time delay (ps) Fa ra d ay ro ta tio n pump #2 pump #1 Fig. 25. Direct optical control of the magnetization dy- namics in the dysprosium orthoferrite sample by two circu- larly polarized pump pulses of the same helicity. De- pending on the time of arrival of the second pump pulse the precession can be amplified or stopped completely. 0 1 2 3 –2 0 Time delay (ns) T (% ) � 0 2 0 2 Pump #1 Pump #2 Combined Pump #1 Pump #2 Combined � M / M (% ) z � M / M (% ) z Fig. 26. A double-pump experiment with two 6 �J or- thogonal linearly polarized pump pulses separated in time by approximately 600 ps. Timing with respect to the spin precession is done by varying the in-plane applied mag- netic field and thereby the precession frequency. The bot- tom panel shows the photoinduced change of sample transmittivity. Partial quenching (top panel) and amplifi- cation (middle panel) of the precession was achieved [51]. timing was not accurate enough to completely quench the precession in the present case. If the second pump pulse arrives after one and a half periods it causes sub- sequent precession with twice the amplitude, as shown in the middle panel. The two pump pulses appear to act completely independently, indicating that we are oper- ating in the regime of linear response (see Fig. 21). However, the experiment does not provide an answer to whether the long lived anisotropy $Han created by the first pump pulse is destroyed by the second pulse, or if the second pulse just creates additional anisotropy in the opposite direction. 5.3. Single-pump ultrafast photomagnetic switching A proper combination of the inverse Faraday effect and the photoinduced anisotropy allows for an inter- esting demonstration of photomagnetic switching on a femtosecond time scale [50]. When the laser pulse is circularly polarized, the direction of $Han depends only on the initial angle / of the magnetization with respect to the crystal axes. Therefore, it can be tuned by rotating the sample with respect to the applied field. We have verified experimentally that this is the case. Alternatively, since the initial equilibrium of Heff, which is determined by the balance between the magnetocrystalline anisotropy field Han and the exter- nally applied field Hext, it can also be tuned simply by varying the strength of the applied field. In Fig. 27 the coherent precession of the magnetiza- tion following excitation with pulses of helicity " � and " � is shown for different values of Hext. The am- plitude of precession is consistently larger in the case of " � , as during 0 < t < 100 fs, M precesses away from the new equilibrium created by $Han, as explained above in Section 4.2.2. For pulses of helicity " �, this precession is towards the new equilibrium, leading to smaller precessional amplitude in the time after the pulse. With an applied field of \| \|Hext � 150 Oe, no pre- cession is triggered due to a perfect balance of two ef- fects: The in-plane precession of the magnetization during the 100 fs magnetic field pulse $HF brings the magnetization exactly to its new equilibrium orienta- tion created by the optically modified anisotropy field. It remains stable in this orientation until the anisotropy field relaxes back to its original state, i.e., for several nanoseconds. An illustration of this switch- ing process is shown in Fig. 28. Note also that for the " � helicity at weak applied fields the precession has an opposite phase compared to the precession in stronger applied fields, and that this phase is the same as for the precession triggered by the " � pulses. At weak fields the direction of the photoinduced $Han is such that the precession of M in HF during the optical pulse is not sufficient to bring it into the direction of #Heff . At stronger fields, however, $Han is in a different direction producing a #Heff that is less inclined with respect to the original effective field. During the presence of HF the magnetization now precesses past the direction of #Heff , and therefore with the opposite phase in the time directly after the laser pulse. 1006 Fizika Nizkikh Temperatur, 2006, v. 32, Nos. 8/9 Andrei Kirilyuk, Alexey Kimel, Fredrik Hansteen, Roman V. Pisarev, and Theo Rasing 0 1 2 0 2 4 6 8 10 12 14 Time delay (ns) –352 Oe –221 Oe –151 Oe –77 Oe 65 Oe 135 Oe 206 Oe 348 Oe 0 1 2 Time delay (ns) "– "+ � M / M (% ) z Fig. 27. Precession of the magnetization triggered by left- and right-handed circularly polarized laser pulses at differ- ent values of the in-plane applied magnetic field. For the �� helicity, at an applied field of � 150 Oe, no preces- sion is observed due to a perfect balance of the two photomagnetic effects �Han and HF. Initial state t < 0 0 < t < 100 fs t > 100 fs Final state Han Fig. 28. Illustration of the switching process. Initially at t � 0 the magnetization is along Heff. During the presence of the laser pulse 0 < t < 100 fs photoinduced modifica- tion of the anisotropy fields leads to a new long-lived equilibrium along Heff. Simultaneously, the strong optomagnetically generated field HF causes the magnetiza- tion to precess into the new state. After t > 100 fs the op- tical pulse is gone and the approximately 0.6� switching of M is complete [51]. 6. Conclusion In this paper we have summarized our recent work on laser-induced magnetization dynamics in magnetic dielectrics. We have shown that in contrast to what was accepted earlier, such dynamics can occur at very short time scales. This happens due to the presence of strong photo- and optomagnetic effects in these mate- rials. The latter are particularly interesting because the optical absorption is not involved in the process. Instead, the effective mechanism is due to a Raman-like scattering process and, similar to the mag- neto-optical Faraday or Kerr effect, is described via the optical dispersion. From this, it may look like this «opto-magnetism» is just an inverse form of the usual magneto-optics. Partially this is also true as the two phenomena are described by the same material param- eters [77,78]. The most important difference, how- ever, is that while the usual magneto-optical effects always serve as measurement tools, the inverse effects provide means for full control on the spin system. We have started by elucidating thermal effects and have shown on the example of iron borate that heating of the spin system happens via phonon—magnon cou- pling. Although the latter was shown to be stronger than expected [44], the characteristic relaxation time was still about 700 ps. Thus thermal interactions could be easily excluded in the treatment of the ultrafast nonthermal photo- and optomagnetic effects. Using such effects, we have shown that the magne- tization in garnet films and orthoferrite single crystals can be directly and coherently controlled on the femtosecond time scale with ultrashort laser pulses. Two distinct nonthermal effects that facilitate such control have been identified. A long-lived photomagnetically induced magnetic anisotropy field can be created by both linearly and circularly polar- ized laser pulses. In addition, strong transient mag- netic field pulses can be generated by circularly polar- ized light via optomagnetic inverse Faraday effect. Applying a small external field allows for the careful timing and balancing of these two effects, thus mak- ing complete nonthermal and coherent control of the magnetization possible. Moreover, by using multiple excitation pulses, any of these two effects can be used for a full coherent control of magnetic precession, with repetition frequencies of up to Terahertz. 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Ultrafast all-optical control of the magnetization in magnetic dielectrics

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