Phonons and magnons in stripe-ordered nickelates. A Raman scattering study

Electronic correlation effects in La₂-xSrxNiO₄ (x = 1/3 and 0.225) lead to spontaneous phase separation into microscopic spin/charge stripes with commensurate and incommensurate order, respectively. Raman scattering experiments on such single crystalline materials show a rich phenomenology of...

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Datum:	2005
Hauptverfasser:	Gnezdilov, V., Kurnosov, V., Pashkevich, Yu., Lemmens, P., Tranquada, J., Choi, K.-Y., Güntherodt, G., Nakajima, K., Yeremenko, A.
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Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2005
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spelling	irk-123456789-1213932017-06-15T03:03:37Z Phonons and magnons in stripe-ordered nickelates. A Raman scattering study Gnezdilov, V. Kurnosov, V. Pashkevich, Yu. Lemmens, P. Tranquada, J. Choi, K.-Y. Güntherodt, G. Nakajima, K. Yeremenko, A. Низкотемпеpатуpный магнетизм Electronic correlation effects in La₂-xSrxNiO₄ (x = 1/3 and 0.225) lead to spontaneous phase separation into microscopic spin/charge stripes with commensurate and incommensurate order, respectively. Raman scattering experiments on such single crystalline materials show a rich phenomenology of phonon and magnon anomalies due to the new, self-organized periodicities. These effects are observable as function of temperature but can also be induced by cooling in a seemingly small magnetic field leading to a reorganization of stripe structure. 2005 Article Phonons and magnons in stripe-ordered nickelates. A Raman scattering study / V. Gnezdilov, V. Kurnosov, Yu. Pashkevich, P. Lemmens, J. Tranquada, K.-Y. Choi, G. Güntherodt, K. Nakajima, A. Yeremenko // Физика низких температур. — 2005. — Т. 31, № 2. — С. 205-212. — Бібліогр.: 39 назв. — англ. 0132-6414 PACS: 72.10.Di, 71.27.+a, 78.30.–j http://dspace.nbuv.gov.ua/handle/123456789/121393 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	Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм
spellingShingle	Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм Gnezdilov, V. Kurnosov, V. Pashkevich, Yu. Lemmens, P. Tranquada, J. Choi, K.-Y. Güntherodt, G. Nakajima, K. Yeremenko, A. Phonons and magnons in stripe-ordered nickelates. A Raman scattering study Физика низких температур
description	Electronic correlation effects in La₂-xSrxNiO₄ (x = 1/3 and 0.225) lead to spontaneous phase separation into microscopic spin/charge stripes with commensurate and incommensurate order, respectively. Raman scattering experiments on such single crystalline materials show a rich phenomenology of phonon and magnon anomalies due to the new, self-organized periodicities. These effects are observable as function of temperature but can also be induced by cooling in a seemingly small magnetic field leading to a reorganization of stripe structure.
format	Article
author	Gnezdilov, V. Kurnosov, V. Pashkevich, Yu. Lemmens, P. Tranquada, J. Choi, K.-Y. Güntherodt, G. Nakajima, K. Yeremenko, A.
author_facet	Gnezdilov, V. Kurnosov, V. Pashkevich, Yu. Lemmens, P. Tranquada, J. Choi, K.-Y. Güntherodt, G. Nakajima, K. Yeremenko, A.
author_sort	Gnezdilov, V.
title	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study
title_short	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study
title_full	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study
title_fullStr	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study
title_full_unstemmed	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study
title_sort	phonons and magnons in stripe-ordered nickelates. a raman scattering study
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2005
topic_facet	Низкотемпеpатуpный магнетизм
url	http://dspace.nbuv.gov.ua/handle/123456789/121393
citation_txt	Phonons and magnons in stripe-ordered nickelates. A Raman scattering study / V. Gnezdilov, V. Kurnosov, Yu. Pashkevich, P. Lemmens, J. Tranquada, K.-Y. Choi, G. Güntherodt, K. Nakajima, A. Yeremenko // Физика низких температур. — 2005. — Т. 31, № 2. — С. 205-212. — Бібліогр.: 39 назв. — англ.
series	Физика низких температур
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fulltext	Fizika Nizkikh Temperatur, 2005, v. 31, No. 2, p. 205–212 Phonons and magnons in stripe-ordered nickelates. A Raman scattering study V. Gnezdilov1, V. Kurnosov1, Yu. Pashkevich2, P. Lemmens3, J. Tranquada4, K.-Y. Choi5, G. Güntherodt5, K. Nakajima6, and A. Yeremenko1 1 B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: kurnosov@ilt.kharkov.ua 2 A. Galkin Donetsk Physico-Technical Institute of the National Academy of Sciences of Ukraine 72 R. Luxemburg Str., Donetsk 83114 , Ukraine 3 MPI for Solid State Research, MPI-FKF, Stuttgart D-70569, Germany 4 Brookhaven National Laboratory, Upton, New York 11973, USA 5 Physikalisches Institut, RWTH Aachen, Aachen 52056, Germany 6 Neutron Scattering Laboratory ISSP, University of Tokyo, Tokai, Ibaraki, Japan Received June 8, 2004, revised September 2, 2004 Electronic correlation effects in La2–xSrxNiO4 (x = 1/3 and 0.225) lead to spontaneous phase separation into microscopic spin/charge stripes with commensurate and incommensurate order, re- spectively. Raman scattering experiments on such single crystalline materials show a rich phenom- enology of phonon and magnon anomalies due to the new, self-organized periodicities. These ef- fects are observable as function of temperature but can also be induced by cooling in a seemingly small magnetic field leading to a reorganization of stripe structure. PACS: 72.10.Di, 71.27.+a, 78.30.–j Introduction Stripe ordering of charge and spin in transi- tion-metal oxides has been of intense interest in con- densed-matter physics from the theoretical and experi- mental point of view as an example of a nontrivial ordering phenomenon that originates from the inter- play between charge hybridization and interaction. Historically, the first evidence for unusual magnetic correlations was obtained in doped nickel oxide, namely on a single crystal of La1.8Sr0.2NiO3.96 in a neutron diffraction study [1]; similar magnetic order- ing was also observed in La2NiO4.125 [2]. A second set of superlattice peaks, indicative of charge order, was detected in a series of La2–xSrxNiO4+� samples by electron diffraction [3]. Neutron diffraction studies [4,5] on a crystal of La2NiO4+� with � = 0.125 were the first to detect the magnetic and charge-order su- perstructure peaks simultaneously. The observed su- perstructure provided clear evidence for a highly cor- related state in which the dopant-induced holes segre- gate into periodically spaced stripes that separate antiferromagnetic domains. Later a static form of this modulation has been clearly identified in the system La1.6–xNd0.4SrxCuO4 [6], where an anomalous sup- pression of superconductivity was found for x � � 1/8. A model of a dynamical form of this modula- tion was exploited for interpreting the spin correla- tions in La2–xSrxCuO4 [7] with x � 1/8 and YBa2Cu3O6+� [8]. Here we will focus mainly on the La2–xSrxNiO4+� system, which exhibits stripe ordering over wide range of hole concentration [3,4]. Before continuing, it may be useful to review briefly some of the basic know- ledge, notations, and relevant work. The structure of the parent compound La2NiO4 consists of NiO2 planes separated by La2O2 layers. Within a NiO2 plane, Ni ions form a square lattice with oxygen atoms bridging © V. Gnezdilov, V. Kurnosov, Yu. Pashkevich, P. Lemmens, J. Tranquada, K.-Y. Choi, G. Güntherodt, K. Nakajima, and A. Yeremenko, 2005 the nearest-neighbor sites. The unit-cell vectors a1 and a2 are parallel to nearest-neighbor Ni–O bonds within the planes, and a3 is perpendicular to the planes. There are two NiO2 planes per unit cell, and they are related by the basic vector 1 2a1 + 1 2 a2 + 1 2 a3. For each Ni ion there is one out-of-plane oxygen atom directly above and one atom below (along a3 axis) effectively completing a tetragonally-distorted octahedron of ox- ygen ions. La ions sit above and below the centers of the squares formed by the Ni ions. The simple struc- ture described above is known as the High Tempera- ture Tetragonal (HTT) phase of the K2NiF4 structure. Upon cooling, La2NiO4 undergoes two structural phase transitions at 650 and 75 K. Thus, with decreas- ing temperature, the phase transitions (and space groups) are HTT (I4/mmm) � LTO (Abma) � LTT (P42/ncm). The NiO2 planes can be doped with holes both by Sr substitution and by addition of excess oxygen. However, contrary to conventional expectations, the material remains nonmetallic up to quite large hole concentrations [9–11]. The insulating behavior occurs because the dopant-induced holes tend to order them- selves in periodically spaced stripes. Nevertheless, these is considerable evidence for one-dimensional charge transport along the charge rows in the static stripe ordered phase both for La2–xSrxNiO4+� and La2–x–yNdySrxCuO4 systems [12,13]. These charge stripes run diagonally relative to the square lattice de- fined by the Ni–O–Ni bonds. In the essentially undoped regions between the stripes the Ni spins can order antiferromagnetically, with the charge stripes acting an antiphase domain walls [1,2,4,5]. The anal- ysis of results on stripe order for a number of doped La2NiO4 shows that the charge orders at a higher tem- perature (Tco) than the spins (Tm) and that both the Tco and Tm increase systematically with holes concen- tration increasing [14]. This fact indicates the primary role of charge in driving the ordering. The average structure of the compositions under study remains in the high-temperature tetragonal (HTT) phase (space group I4/mmm) down to at least 10 K [15]. The charge and spin order are more easily described in a unit cell size 2 2a a c� � . Then, the charge density modulation is characterized by the wave vector g2� = (2�,0,0,) and the characteristic wave vector for the spin-density modulation is g� = = (1+ �,0,0,) (in real space modulation periods are a/2� and a/�, respectively). In the first studies of La2–xSrxNiO4 it has been suggested that ordering of the dopant-induced holes occurs only commensurately at special values of x, such as 1/2 and 1/3 [3,16]. Later it was found that a single crystal with x = 0.2, although not at a special value of x, shows commensu- rate order [17], albeit with a short in-plane correlation length of � 40 Å. In contrast, the stripe or- der in La2NiO4+� [4,5] and La1.775Sr0.225NiO4 [15] was found to be incommensurate, with the wave vec- tor varying significantly with temperature. Since the stripes are charged, they will repel each other. As a re- sult, the stripes will arrange themselves so as to main- tain the maximum possible spacing, with the constrain that each stripe is centered on a Ni (site-centered stripes) or O (bond-centered stripes) site. For the case of x = 1/3, it was shown [18] that in the temperature range Tco > T > Tm the domain walls are bond cen- tered. For T < Tm the density of stripes decreases, and the stripes become increasingly site centered. Stripe models for x = 1/3 are illustrated in Fig. 1. In the real case, the spins are collinear and are shifted by angle � relatively the stripe direction [19,20]. It was found � = 53° at T = 14 K in La5/3Sr1/3NiO4 [21]. For the incommensurate stripe order, direct evidence for alter- nating site- and body-centered stripes within the NiO2 plane was presented in the transmission-electron-mi- croscopy study of La1.725Sr0.275NiO4 crystal [22]. Despite very intense studies in the stripe physics field, it is somewhat surprising that there are only a few Raman scattering (RS) studies of this exotic form of order [12,23–26] and some deficiencies in our knowledge of light scattering in striped phases are now evident. For example, under the discussion is the question of RS from spin waves. Another problem, which has not been studied yet, is phonon dynamics in the direction perpendicular to the NiO2-planes. Experiment In our RS experiments two La2–xSrxNiO4 (x = 1/3 and 0.225) samples were studied. Single-crystals were grown by rf induction melting [27]. Measurements 206 Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 V. Gnezdilov et al. a b Fig. 1. Ni-centered domain walls (a); O-centered domain walls (b). Stripe models for 1/3 doping [18]. Arrows in- dicate correlated Ni magnetic moments; circles indicate ox- ygen sites; filled circles indicate locations of doped holes on oxygen sites. Bold dashed lines indicate positions of domain walls, while bold solid lines outline a magnetic unit cell. The two-magnon Raman process is shown also: bold arrows demonstrate spins on adjacent sites and curved lines indicate broken magnetic bonds. were performed in a backscattering configuration using Raman spectrometer DILOR XY with 5145 Å laser light of 20 mW. The incident laser beam was fo- cused onto 0.1 mm diameter spot on the mirror-like polished and chemically cleaned crystal surface. The spectra were recorded on a liquid nitrogen-cooled CCD. The laboratory coordinate system was locked to the axes of the crystal (x \|\| a, y \|\| b, z \|\| c). The x’ and y’ axes are rotated by 45° from x and y. The a, b, and c crystallographic axes in the I4/mmm setting were de- termined by x ray Laue diffraction. The measurements were performed in an optical cryostat in helium gas at- mosphere. For the measurements in a magnetic field, the crystal was mounted in a cryostat with a horizon- tal-field superconducting magnet. The [110] axis of the crystal was aligned parallel to the magnetic field. Results and discussion For the tetragonal K2NiF4 structure, of the total twelve zone center phonon modes, four (2A1g + 2Eg) ones are Raman active. Figures 2 and 3 show room temperature RS spectra in x’x’ scattering geometry for both samples under study. In this geometry A1g lines are allowed. First of them at around 230 cm–1 was as- signed to the La stretching mode [28–31]. The second one at around 450 cm–1 was identified as the oxygen stretching mode [28–31]. Above the charge ordering temperature all the observed modes are weak; the 230 and especially 450 cm–1 modes are broad, indicating strong polaronic effects and inhomogeneous charge distribution [23,32]. Notable changes in the RS spec- tra are observed below Tco. The charge ordering gives rise to formation of a superlattice, multiplies the unit cell size, and lowers the crystal symmetry. It leads to the appearance of new �-point Raman-active phonon modes in the spectra. The origin of the extra lines in the stripe-ordered state and their assignment were made in Ref. 26. Now we turn to the measurements in zz polarization configuration. For the crystal with x = 1/3 two lines of A1g symmetry at 232 and 448 cm–1 are observed at room temperature as shown in Fig. 4. The disadvan- tage of the Sr-doped La2NiO4 system is that the dop- ant positions are fixed at relatively high temperature and may be random. At room temperature we do not see any dopant-induced extra features in the low fre- quency part of the spectra. It is possible also to assume a regular order of the Sr ions within the crystal struc- ture in the special cases of doping (x = 1/2, 1/3, or 1/4) like the interstitial order in the oxygen-doped La2NiO4. The line shape of the Ni–O2 bond stretching mode at 448 cm–1 is asymmetric. This asymmetry can be explained by a random distribution of holes on oxy- gen above Tco. Phonons and magnons in stripe-ordered nickelates. A Raman scattering study Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 207 0 400 800 1200 200 400 600 800 295 K Raman shift, cm –1 5 K In te n si ty , a rb . u n its Fig. 2. The x’x’ Raman spectra of the single crystal La5/3Sr1/3NiO4 at 5 and 295 K. 0 400 800 1200 200 400 600 800 295 K 5 K Raman shift, cm –1 In te n si ty , a rb . u n its Fig. 3. The x’x’ Raman spectra of the single crystal La1.775Sr0.225NiO4 at 5 and 295 K. The changes in phonon spectra are observed below Tco — new phonon peaks at approximately 130, 145, 160, 285, 330, 386, 488, and 520 cm–1 appear. To ex- plain this, we ought to analyze the stripes alignment in the neighboring NiO2 layers. As it was supposed in earlier publications [5], the charge stripes align them- selves from one layer to the next so as to minimize the long range part of the Coulomb interaction. However the pinning of the charge stripes to the lattice means that the shift of the stripe pattern from one layer to the next can only occur in increments of the lattice spacing. For this sample, with the stripe spacing of 3/2a it is possible to have a perfectly body-centered stacking. Such a symmetric stacking of the layers of stripes can lead to forbidden superlattice peaks corre- sponding to the charge order. Inset on Fig. 4 shows the possible arrangement of the charge stripes in the neighboring layers for the x = 1/3 crystal. In this case an additional periodicity along the c axis can also lead to forbidden superlattice peaks that are most likely observed in our experiments. Let us analyze now the situation with the x = 0.225 composition (see Fig. 5). Whereas x’x’ and x’y’ spec- tra are very similar in both compounds, pronounced differences are observed in zz scattering geometry. In contrast to the x = 1/3 sample, the spectra of the x = 0.225 sample even at room temperature have very complicated shape. Under lowering temperature, the shape does not change, with the exception of a contin- uum, which low-frequency portion reduces in inten- sity with temperature reduction. To explain this, we oblige to suppose that for the not special case (as x = = 1/2, 1/3, or 1/4) the random dopant ions (and holes) distribution lead to a break of long ranger order in c direction. In this case k conservation is not re- quired and the first order Raman spectrum is a mea- sure of the density of vibrational states. If this as- sumption is correct, stripe ordering below Tco should not result in the occurrence of new features in the spectra. Moreover, for our sample with an average stripe spacing of about 1.82a, it is not possible to have a perfectly body-centered stacking. A similar conclu- sion was firstly reached in neutron diffraction study [33] of the sample with average stripe spacing of about 1.75a (x = 0.275) and confirmed in the high-res- olution transmission-electron-microscopy study [22]. For both La5/3Sr1/3NiO4 and La1.775Sr0.225NiO4 two relatively strong bands at � 720 cm–1 (740 cm–1) and � 1110 cm–1 (1130 cm–1) were observed at low temperature in x’y’ polarization [23,24,26]. These bands were interpreted as two-magnon scattering [23,24,26]. What was the reason for this attribution? Two-magnon scattering involves a simultaneous exci- tation of a pair of magnons with equal and opposite momenta k on each of the sublattices. In total, excita- tions from the entire Brillouin zone lead to a band of Raman frequencies that reflects the magnon density of states. Since the density is sharply peaked at the zone-boundary, Raman scattering probes preferential- ly localize antiferromagnetic order. If two spin devia- tions are created on sites far apart, the excitation fre- quency is 2(JSz + g�BBA), where z is the number of nearest neighbors, BA is the effective anisotropy field, and J is the exchange interacting constant. In the case of two spin deviations are created on adjacent sites, the excitation frequency is only J(2Sz – 1) + 2g�BBA because the presence of the first spin deviation leads to a reduction in the energy required for the second spin deviation. The undoped La2NiO4 antiferromagnetic 208 Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 V. Gnezdilov et al. 0 200 400 600 800 1000 1200 300 600 900 1200 1500 1800 2100 5 K 100 K 150 K 200 K 250 K 295 K Raman shift, cm –1 In te n si ty , a rb . u n its ñ Fig. 4. Temperature dependent Raman spectra for zz po- larization of single crystal La5/3Sr1/3NiO4. Inset shows an idealized structure of the stripe-ordered phase in the plane perpendicular to the charge domain walls for 1/3 doping. The open circles indicate correlated in the NiO2 layers spins at Ni2+ sites. The filled circles show locations of doped holes on Ni sites. 0 200 400 600 800 1000 1200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 5 K 50 K 100 K 150 K 200 K 250 K 295 K Raman shift, cm –1 In te n si ty , a rb . u n its Fig. 5. Temperature dependent Raman spectra for zz po- larization in single crystal of La1.775Sr0.225NiO4. insulator was studied by Sugai et al. [34]. The B1g spectra exhibits a band peaked at � 1640 cm–1 that has been assigned to a scattering by two-magnons. The es- timated J was 240 cm–1 on the assumption that the peak energy is 6.7J for the S = 1 nickel oxide. For doped La2–xSrxNiO4 the band near 1640 cm–1 was not observed in Raman experiments at any tem- peratures. Instead, two broad peaks in x’y’ polariza- tion appear in the high frequency region under tem- perature lowering. Temperature dependent Raman spectra for x’y’ polarization of single crystals La2–xSrxNiO4 (x = 1/3 and 0.225) are shown in Fig. 6. In Fig. 7 the temperature dependence of the in- tegrated intensity for both bands in the x = 0.225 crys- tal is given. The first band was assigned to the two-magnon excitation within the antiferromagnetic domain and the second one to the excitation across the domain wall [23,26] or to the excitation on the Ni2+–Ni3+ bond [24]. Accurate account of the spin-1 system gives peak positions of �1 � 3J and �2 � 4J for the x = 1/3 Ni-centered stripes. Thus, the peak posi- tions for the two-magnon excitations within the antiferromagnetic domain and across the domain wall are �1 = 720 cm–1 and �2 = 960 cm–1 for the value of J = 240 cm–1, respectively. On the first sight it seems consistent with experiment. Not recently this assignment was criticized in Ref. 35. It was disclosed that the band at � 730 cm–1 is due to a one-phonon excitation and only the � 1120 cm–1 ex- citation is due to the magnetic excitation related to the stripe structure. The 685 cm–1 band, which ap- pears in La2NiO4.15 at temperature lowering, was at- tributed to phonon excitation [25] because its energy coincides with one-phonon peak in La2NiO4.0. There are some doubts in last motivation by the following reasons. 1. The bands at � 730 cm–1 in La2–xSrxNiO4 and at 685 cm–1 in La2NiO4.15 are much broader than one-phonon lines observed in lightly doped cuprates [36] and nickelates [25,34]. 2. The temperature dependencies of the frequency position and integrated intensity for the � 730 cm–1 peak differ from those of the one-phonon peak at 684 cm–1 in undoped La2NiO4.0 and of one-phonon peaks at lower frequencies in doped nickelates and are similar to the corresponding dependences for the sec- ond wide band at � 1120 cm–1. 3. In our RS spectra two sharp lines at 580 and 630 cm–1 are superposed on the broad band (see Fig. 6). Moreover, the Fano lineshape seen for the 580 cm–1 line is clearly seen in Fig. 8. The Fano effect in Raman scattering is observed as a characteristic change in the usually Lorentzian-lineshape of phonon peaks in the spectra – the phonon lineshape becomes asymmetric. It means that a coherent interaction exists between the two scattering sources. We believe that the observed effect is connected with an interaction between the phonon, which shows a Fano effect and the charge carriers excitations [12] (dashed line in Fig. 8) causing the background. However, we do not exclude the possibility of an interaction with the exci- tation causing the wide band at � 730 cm–1. The pro- bability of the latter assumption is now analyzed theo- retically. In Ref. 35 only one band was attributed to two-magnon scattering in the case where the spin ex- change occurs near the diagonal charge domain wall. However, it was examined the case of one domain wall without taking into account the width of Phonons and magnons in stripe-ordered nickelates. A Raman scattering study Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 209 0 800 1600 200 400 600 800 1000 0 800 1600 Raman shift, cm –1 5 K 50 K 100 K 150 K 200 K 250 K 295 K 125 K 150 K 200 K 295 K 100 K 50 K 5 K In te n si ty , a rb . u n its Fig. 6. Temperature dependent Raman spectra for x’y’ po- larization of La5/3Sr1/3NiO4 (a) and La1.775Sr0.225NiO4 (b) single crystals. 0 50 100 150 200 250 300 0 0,2 0,4 0,6 0,8 1,0 T, K Tco Tm In te n si ty , a rb . u n its Fig. 7. The temperature dependence of the scattering in- tensity integrated above the charge carriers background for 740 (�) and 1130 (�) cm–1 bands in La1.775Sr0.225NiO4. a b antiferromagnetic domain that lead to incorrect calcu- lation of nearest neighbors number. Not any feature was observed in the single-magnon dispersion which would correlate with the lower-en- ergy two-magnon peak in the inelastic neutron scatter- ing measurements of the stripe-ordered nickelate La1.69Sr0.31NiO4 also [37]. Next we have tried to analyze the two-magnon scat- tering theoretically. A simple square plane array of paramagnetic ions was implemented for the calcula- tions. The site-centered model of charge ordering was used, and thus paramagnetic ions inside the domain walls were considered to be frustrated. So, the pattern of spins for approximation of the La5/3Sr1/3NiO4 magnetic structure was similar to those showed in Fig. 1,a or in Ref. 21. Four exchange integrals be- tween nearest and next-nearest neighbors were taken into account. Two of them are found to be identical to J and J’ labeled exchange integrals introduced in Ref. 21. The exact solution for two-magnon light scat- tering line shape was obtained with the following re- strictions: (i) zero temperature or temperature much smaller than TN; (ii) Heisenberg character of spin ex- change; (iii) small single-ion anisotropy, in compari- son with exchange energy. Two-magnon band shape was calculated in the exchange approximation of the Moriya theory using real polarizability tensors con- nected with the respective exchange integrals. Before the appearance of Ref. 21 the values of ex- change integrals were unknown. We did only esti- mates using the value for undoped La2NiO4 for an ex- change integral which bonds spins inside a single antiferromagnetic domain. By the way, our previous attempts to approximate both bands failed. The calcu- lated shapes cannot be fitted to the experimental spec- tra at any value of exchange integrals and respective values of polarizability constants we used. Recent experimental data of neutron inelastic scat- tering [21] have just supplied the needed exchange in- tegral values. Using those we have obtained a reason- ably good description of the band at � 1110 cm–1 with the following values of the exchange integrals and respective polarizability constants relation: J = = 242 cm–1 (30 meV), J2 = 109 cm–1 (13.5 meV), P2/P = – 0.75. Our values of exchange integrals are twice higher then the respective values of J and J’ 210 Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 V. Gnezdilov et al. 520 540 560 580 600 620 640 660 Raman shift, cm –1 In te n si ty , a rb . u n its In te n si ty , a rb . u n its 600 800 1000 1200 Raman shift, cm–1 Fig. 8. Fano lineshape of the phonon at 580 cm–1 for x’y’ polarization of La5/3Sr1/3NiO4 single crystal at T = 5 K. The solid line is a theoretical fit to the experimental curve using Lorentzian-lineshape of phonon peak. Inset show experimental spectrum in the frequency region of 500–1200 cm–1. Dot lines represent a fit with Lorentzian lineshapes, dashed line is a charge carriers scattering [12]. 0 500 1000 1500 Raman shift, cm –1 In te n si ty , a rb . u n its Fig. 9. Theoretical approximation of Raman spectra for x’y’ polarization of La5/3Sr1/3NiO4 single crystal at T = 5 K. Solid line is the experimental spectrum, dashed line is the calculated two-magnon band, triangles present a sum of some reasonable spectral shapes to fit band at � 720 cm–1 and wide background, open circles represent total fitting spectrum. from Ref. 21 due to a different kind of summation over the spin pairs in the Hamiltonians. The result of the best fit is shown in Fig. 9. It is clear that narrow de- crease of intensity at � 1200 cm–1 in the theoretical two-magnon band (dashed curve in Fig. 9) has inter- ference nature and probably is a result of above-men- tioned restrictions connected with the real type of polarizability constants. Because of the absorption at the exciting laser wavelength in the RS experiments in La5/3Sr1/3NiO4, it is reasonable to use complex type of these constants. Such calculations are now in prog- ress. These results show evidence for not simple two-magnon nature of the band at � 730 cm–1. Per- haps possible effects connected with the interaction between spin excitations and collective motion of charge domain-walls [21,38] are necessary to be taken into account. As it was shown in the neutron diffraction experi- ments [18], the application of a magnetic field in the regime T > Tm induces a staggered magnetic order of period 3a due to the net magnetic moment of the high-temperature bond-centered stripes, together with the odd number of Ni spins across an antiferro- magnetic domain. To test the effect of a magnetic field on stripe ordering, we performed a RS experiments on a piece of the same La1.775Sr0.225NiO4 crystal that we have been characterized in detail elsewhere [12,15,26]. In this sample the hole density per Ni site along a stripe is significantly less than 1 (electron fil- ling fraction � > 0) in contrast to the x = 1/3 sample, where the density is exactly 1. The sample was cooled from 295 K to 5 K in the magnetic field of 0.5 T and after that the field was switched off RS experiments in quasi-backscattering geometry were performed. Representative scans are shown in Fig. 10. As it is seen from Fig. 10,a, freezing in a magnetic field does not affect the spectra measured in x’x’ scattering geo- metry. A surprising result was obtained in x’y’ scat- tering geometry (Fig. 10,b). The second band at � 1130 cm–1 disappears nearly completely (some ex- cess Raman signal above the background is still visi- ble) after freezing the sample in the magnetic field. It is clear, that applied magnetic field leads to a stripe structure reorganization. However, to understand ful- ly the observed effects, further experimental and theo- retical efforts are needed. It is supposed, for example, to examine the situations of: i) Low-temperature bond-centered stripes with a period of 2/3a. In this state the domains are 3 spins wide and an uncompensated moment appear. The ad- jacent across the domain wall spins are ferromagne- tically aligned. ii) In-phase domain walls. As it was experimentally established, neighboring antiferromagnetic domains, separated by a charge stripe, have an antiphase rela- tionship. But in contrast with common folklore, it was recently shown theoretically [39] that the hole rich stripes are not necessary antiphase domain walls of antiferromagnetic spin domains and a phase transition from antiphase to in-phase domain-wall configuration has to occur as a function of increased electron filling fraction of the domain wall. Moreover, «empty» do- main walls are always antiphase. Concluding remarks Although the basic nature of the charge and associ- ated spin order in cuprates and nickelates has now been fairly well been established, many questions con- cerning this order remain to be answered. One of our goals here was to elucidate some problems that are un- der discussion at present. Unquestionable, Raman scattering will continue to be an essential tool as we try to improve our understanding of stripe ordering and other complex correlation effects. This work was supported by NATO Collaborative Linkage Grant PST.CLG.977766, INTAS Grant 96-0410, and Ukrainian Grant ¹ 3-026. Phonons and magnons in stripe-ordered nickelates. A Raman scattering study Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 211 0 400 800 1200 1600 50 100 150 0 100 200 300 400 500 b 0 T (cooled at 0.5 T) 0 T (cooled at 0 T) Raman shift, cm –1 0 T (cooled at 0.5 T) 0 T (cooled at 0 T) a In te n si ty , a rb . u n its 5 K 5 K Fig. 10. Raman spectra in x’x’ (a) and x’y’ (b) polariza- tion configuration of the La1.775Sr0.225NiO4 crystal cooled in zero and 0.5 T magnetic field. 1. S.M. Hayden, G.H. Lander, J. Zaretsky, P.B. Brown, C. Stassis, P. Metcalf, and J.M. Honig, Phys. Rev. Lett. 67, 1061 (1992). 2. K. Yamada, T. Omata, K. Nakajima, Y. Endoh, and S. Hosoya, Physica C221, 355 (1994). 3. C.H. 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