Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃

The resonance properties of a new Cu₂OSeO₃ ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequencyfield dependence of the ferrimagnetic spectrum described within the model of an anisotropic two-su...

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Дата:	2010
Автори:	Kobets, M.I., Dergachev, K.G., Khatsko, E.N., Rykova, A.I., Lemmens, P., Wulferding, D., Berger, H.
Формат:	Стаття
Мова:	English
Опубліковано:	2010
Назва видання:	Физика низких температур
Теми:	Низкотемпеpатуpный магнетизм
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/116899
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃ / M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, H. Berger // Физика низких температур. — 2010. — Т. 36, № 2. — С. 223-226. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	irk-123456789-1168992017-05-19T03:03:08Z Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃ Kobets, M.I. Dergachev, K.G. Khatsko, E.N. Rykova, A.I. Lemmens, P. Wulferding, D. Berger, H. Низкотемпеpатуpный магнетизм The resonance properties of a new Cu₂OSeO₃ ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequencyfield dependence of the ferrimagnetic spectrum described within the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corresponding to the gap in the spin wave spectrum has been estimated (3 GHz). It is found that the spectrum has a multicomponent structure which is due to the diversity of the types of magnetization precession. As the amplitude of the high-frequency magnetic field increased, an additional absorption was observed in the external magnetic field lower than the field of the main resonance. The detected additional absorption corresponds to the nonuniform nonlinear parametric resonance, connected with nonuniformity of magnetic structure in the ferrimagnetic crystal Cu₂OSeO₃. 2010 Article Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃ / M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, H. Berger // Физика низких температур. — 2010. — Т. 36, № 2. — С. 223-226. — Бібліогр.: 10 назв. — англ. 0132-6414 PACS: 76.50.+g, 75.50.Ee http://dspace.nbuv.gov.ua/handle/123456789/116899 en Физика низких температур
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 Kobets, M.I. Dergachev, K.G. Khatsko, E.N. Rykova, A.I. Lemmens, P. Wulferding, D. Berger, H. Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃ Физика низких температур
description	The resonance properties of a new Cu₂OSeO₃ ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequencyfield dependence of the ferrimagnetic spectrum described within the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corresponding to the gap in the spin wave spectrum has been estimated (3 GHz). It is found that the spectrum has a multicomponent structure which is due to the diversity of the types of magnetization precession. As the amplitude of the high-frequency magnetic field increased, an additional absorption was observed in the external magnetic field lower than the field of the main resonance. The detected additional absorption corresponds to the nonuniform nonlinear parametric resonance, connected with nonuniformity of magnetic structure in the ferrimagnetic crystal Cu₂OSeO₃.
format	Article
author	Kobets, M.I. Dergachev, K.G. Khatsko, E.N. Rykova, A.I. Lemmens, P. Wulferding, D. Berger, H.
author_facet	Kobets, M.I. Dergachev, K.G. Khatsko, E.N. Rykova, A.I. Lemmens, P. Wulferding, D. Berger, H.
author_sort	Kobets, M.I.
title	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃
title_short	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃
title_full	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃
title_fullStr	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃
title_full_unstemmed	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃
title_sort	microwave absorption in the frustrated ferrimagnet cu₂oseo₃
publishDate	2010
topic_facet	Низкотемпеpатуpный магнетизм
url	http://dspace.nbuv.gov.ua/handle/123456789/116899
citation_txt	Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃ / M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, H. Berger // Физика низких температур. — 2010. — Т. 36, № 2. — С. 223-226. — Бібліогр.: 10 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT kobetsmi microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT dergachevkg microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT khatskoen microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT rykovaai microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT lemmensp microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT wulferdingd microwaveabsorptioninthefrustratedferrimagnetcu2oseo3 AT bergerh microwaveabsorptioninthefrustratedferrimagnetcu2oseo3
first_indexed	2025-07-08T11:17:07Z
last_indexed	2025-07-08T11:17:07Z
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fulltext	© M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, and H. Berger, 2010 Fizika Nizkikh Temperatur, 2010, v. 36, No. 2, p. 223–226 Microwave absorption in the frustrated ferrimagnet Cu2OSeO3 M.I. Kobets, K.G. Dergachev, E.N. Khatsko, and A.I. Rykova B.Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: khatsko@ilt.kharkov.ua P. Lemmens and D. Wulferding Institute for Condensed Matter Physics, TU Braunschweig, D-38106 Braunschweig, Germany H. Berger Institute de Physique de la Matiere Complexe, EPFL, CH-1015 Lausanne, Switzerland Received August 27, 2009 The resonance properties of a new Cu2OSeO3 ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequency- field dependence of the ferrimagnetic spectrum described within the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corresponding to the gap in the spin wave spectrum has been estimated (3 GHz). It is found that the spectrum has a multicomponent structure which is due to the diversity of the types of magnetization precession. As the amplitude of the high-frequency magnetic field increased, an additional absorption was observed in the external magnetic field lower than the field of the main resonance. The detected additional absorption corresponds to the nonuniform nonlinear parametric resonance, connected with nonuniformity of magnetic structure in the ferrimagnetic crystal Cu2OSeO3. PACS: 76.50.+g Ferromagnetic, antiferromagnetic, and ferrimagnetic resonances; spin-wave resonance; 75.50.Ee Antiferromagnetics. Keywords: ferrimagnet materials, frequency-field dependence, magnetization precession. Introduction Ferrimagnetic materials have a great importance in present-day physics and engineering, which is due to their widespread use in ultrahigh radio frequency tech- nologies. Most of today’s known ferrimagnets are non- metallic compounds. The exchange interaction in ferri- magnets, like in antiferromagnets, imposes an antiparallel orientation on the moments belonging to different sub- lattices. A joint feature of these materials is the dis- similarity of their sublattices: their magnetization varies in magnitude generating spontaneous ferrimagnetic mo- ments. Such variations are possible either because the sublattices contain different numbers of ions or because these ions have different moments. Ferrimagnets are the most suitable objects to investigate magnetic oscillations in the magnetically ordered state. They form a unique class of magnetic substances offering major advantages in microwave technologies. The high-frequency (hf) properties of ferrimagnets are actually equivalent to the same properties of ferromagnets. In magnetically ordered crystals with any number of sublattices and a spontaneous exchange-type moment the spectrum of magnetic oscillations always contains one «ferromagnetic branch» which is independent of the exchange forces (mo- lecular field) [1]. The specific character of a non-com- pensated antiferromagnet manifests itself as a second «ex- change» resonance. Its eigenfrequencies now are dependent on the molecular field. They belong to the far IR region and are too difficult to observe. Many ferrimagnets exhibit a narrow resonance line and are suitable to investigate instability related resonance and nonlinear phenomena. The aim of this study is investigation of resonant properties of a new ferrimagnetically ordered Cu2OSeO3 compound at liquid helium temperature. The crystal Cu2OSeO3 is a magneto-capacitive system described by the cubic spatial symmetry group P213 with M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, and H. Berger 224 Fizika Nizkikh Temperatur, 2010, v. 36, No. 2 the lattice parameter a = 8.923 Å [2] at room temperature. Magnetic Cu2+ ions, arranged tetrahedrally along the space diagonal [111], are the main element of the crystal structure, which complies with the general concept of ferrimagnetic compounds [3]. It is found [3] that cubic single crystals with negative anisotropy constant K1 have directions of hard magnetization along the cubic cell edges and easy magnetization along the space diagonals of the cube. Fragments of the crystalline and magnetic structures of Cu2OSeO3 (taken from [2]) are shown in Figs. 1 and 2. It is seen that the oxygen atoms form square-pyramids as well as bi-pyramids around the tetrahedral arranged Cu2+. In Cu2OSeO3 the ground state is a non-compensated antiferromagnet (three spins are in the same direction and one spin is opposite). Geometrically, the compound has a spin frustrated structure. As Cu2OSeO3 is multiferroic, the magnetoelectric coupling effects may play significant role in its behavior. Resonance absorption was observed using a tuned- frequency radio spectrometer with different types of re- sonators (cylindrical and rectangular), each operating in its particular frequency range. The resonators were designed to include a device rotating the sample about the axis perpendicular to the applied permanent magnetic field H. The microwave field h was polarized perpendicular to the applied magnetic field. Experimental results and discussion The resonance properties of Cu2OSeO3 were measured thoroughly in the frequency interval of 17–142 GHz in magnetic fields up to 75 kOe at liquid helium temperature. The size of the samples was smaller than the resonance wavelength. The samples were situated in a homogeneous ac magnetic field. The experimental width of the principal resonance line of the ferrimagnetic resonance in Cu2OSeO3 is 0 18 HΔ ≤ Oe (the real one is much smaller because we see already broadened lines) in the orientation H \|\| l. The experimental frequency-field dependencies (mea- sured at the low pumping power P ~ 100 µW) of the fer- rimagnetic spectrum along the easy axis ([111]) are shown in Fig. 3. It is seen that the experimental dependencies of the resonance spectrum do not coincide with the theoretical interpretation of low-frequency oscillations for a two- sublattice ferrimagnet and cannot be described by the simple equation obtained for isotropic ferrimagnets in relatively low magnetic fields (smaller than an exchange field): eff 0.Hω = γ (1) The frequency-field dependences (Fig. 3) taken in a zero magnetic field have a gap of 3 GHz (1 kOe) in the spin-wave spectrum. Рис. 1. A fragment of the crystal structure of single-crystal Cu2OSeO3. Cu1 Cu2 O O1 O1 O1 O4 O4 O4 O4 O4 O3 O3 O3 O3 O3 O3 O3 O3 O3 O3 O3 O2 O2 O1 O1 a c b B AO C Рис. 2. The magnetic structure of single-crystal Cu2OSeO3. 10 20 30 40 50 60 70 800 20 40 60 80 100 120 140 160 0 2 4 6 8 10 6 12 18 24 30 H, kOe H, kOe � /g , G H z ef f Рис. 3. The frequency-field dependence of ferrimagnetic resonance in Cu2OSeO3, T = 4.2 K: points — experiment, dashed line — simple theory for an isotropic ferrimagnet, and solid line cor- responds to Eq. (2 ). Inset: a magnified part of the frequency — field dependence of the ferrimagnetic resonance. Microwave absorption in the frustrated ferrimagnet Cu2OSeO3 Fizika Nizkikh Temperatur, 2010, v. 36, No. 2 225 When the pumping power is going up, the resonance spectrum is transformed and some new features appear (see Fig. 4). 1. The spectrum consists of many components, very narrow absorption peaks appear in the resonance curve and the curve itself broadens. The number of peaks is dependent on the dimensions of the sample and on the structure of the hf variable magnetic field at the resonator location. As an example, Fig. 4 shows the resonance absorption curve measured at eff/f = ω γ = 21.32 GHz, which has four distinct maxima at the pumping power P ~ 150 µW. The curve obtained at eff/ω γ = 32.27 GHz with the same microwave pumping has only two resonance absorption maxima. 2. As the high-frequency field power is raised to P ~ 400 µW and higher, an additional broad absorption line is observed in a magnetic field lower than the main resonance field (see Fig. 4, eff/ω γ = 25.8 GHz and eff/ω γ = 27.11 GHz). When the temperature increases the threshold of the (hf) field rises. At T = 20 K it reaches 700 µW. The effects of resonance absorption observed in the experiments on Cu2OSeO3 can be interpreted as follows. Real ferrimagnets possess magnetic anisotropy. In par- ticular it is the magnetic crystalline anisotropy which includes the energy of magnetostrictive stresses. Because of this the effective magnetic crystalline anisotropy is significant when magnetization inhomogeneities are avai- lable over the crystal [4], and the resonance equation for the [111] direction becomes 1 eff 0 4 3 S K H M ω = γ ± , (2) where 1K is the magnetic anisotropy and SM is the saturation magnetization. Equation (2) can describe the frequency-field dependencies of Cu2OSeO3 quite adequa- tely if the total magnetic anisotropy is 3 GHz. Thus existence of anisotropy leads to the gap in the ferro- magnetic resonance spectrum of Cu2OSeO3. Theoretically [5,6], the multicomponent structure (independent of pumping power) of resonance spectra ta- ken on large and small samples can be explained assuming that small magnetic inhomogeneities (that are always available in ferrimagnets and couple uniform precession and spin waves to the wave vector 0k ≠ [7] produce a diversity of types of magnetization precession, which show up as absorption maxima. One of these types is a uniform precession, the rest are non-uniform, i.e. the amplitudes and phases of ac magnetization in the sample are de- pendent on its coordinates. The character of this depen- dence determines the type of precession. The resonance absorption maxima corresponding to uniform and non- uniform types of magnetization precession are shown in Fig. 4. For example, for two frequency 32.27 GHz high field line corresponds to uniform precession, and low field line corresponds to nonuniform presession. The intensity of excitation of different precession types depends on the structural similarity of the external variable field and the particular non-uniform type of magnetization — the closer the similarity the higher the intensity. This correlation determines the variation of absorption peaks and their intensities with the position of the sample in the resonator. Comparatively narrow resonance curves suggest that different types of precession are excited successively with varying ω or H0, which was observed experimentally. Individual absorption peaks are best observed when the crystal is oriented along the easy magnetization axis. The presence of magnetic inhomogeneities leads [8] to excitation of degenerate uniform-precession spin waves with 0k ≠ which takes the energy from the uniform pre- cession and transfers it over to the crystal lattice. This increases the magnetic losses (proportional to 0M ) and hence broadens the resonance curve. Thus, the maxima, their amplitudes and their broadening are determined by the dimensions of the sample, its magnetic inhomoge- neities and the structure of the ac magnetic field at the sample location. The frequency-field dependencies of resonance ab- sorption were taken at the lowest power of (hf) field pumping (~ 100 µW). The additional absorption and the saturation of the resonance line are nonlinear effects occurring when high frequency field h exceeds its threshold value for a fer- rimagnet with small magnetic inhomogeneities. The non- linear phenomena in ferrimagnets are caused by some instability making the oscillation amplitudes increase with time. This was detected for the first time in experiments on Рис. 4. The spectra of resonance absorption of the Cu2OSeO3 crystal in an external magnetic field along the [111] direction at different frequencies and microwave powers: The arrows show the parametric excitation. T = 4.2 K. 121197 H, kOe 14131086 A b so rp ti o n ,r el . u n it s 21.72 GHz 32.27 GHz 27.1 GHz 25.81 GHz P ~ 150 mW M.I. Kobets, K.G. Dergachev, E.N. Khatsko, A.I. Rykova, P. Lemmens, D. Wulferding, and H. Berger 226 Fizika Nizkikh Temperatur, 2010, v. 36, No. 2 ferrimagnetic resonance in nickel ferrite in large amplitude (about 1 kW) pumping fields [9]. The instability related phenomena (auto-oscillations, parametric excitation, auto- parametric processes, etc.) are quite multiform in nonlinear systems. The occurrence of forced oscillations at fre- quencies different from the pumping ones is one of the fundamental properties of such systems. The theory of nonlinear absorption was developed by Suhl [10]. According to [10], the increase in the micro- wave field amplitude up to the threshold magnitude entails a parametric increase in the amplitudes of the spin waves with frequency ω (ac field frequency) and wavelengths of ~ 10–5 cm. The amplitude of the spin waves with the frequency spω = ω / 2 as well as the wavelength tending to infinity are also increasing. The first phenomenon leads to a broadening of the line of ferrimagnetic resonance with uniform precession. The other causes additional absorption in magnetic fields slightly lower than uniform resonant, (0.5–0.9)Hres. The spin waves are excited at the expense of the energy of uniform-precession oscillations. This causes additional at- tenuation of the uniform precession seen as resonance line broadening. It must be noted that in our case the threshold of nonlinear effects is very low (lower then 1 mW) in contrast to well known case of ferrites [9] The threshold field is [10]. 0 thres 04 kH H h M Δ Δ = π , (3) where kHΔ is the half-width of the spin-wave resonance curve, 0HΔ is the half-width of the main resonance curve, and 04 Mπ is the demagnetization factor. The threshold field decreases with the width of the ferromagnetic reso- nance line, i.e. with decreasing magnetic losses at a low power level. The value of thresh — decreases considerably [10] when the field required to excite spin waves with spω = ω / 2  coincides with the main resonance (Fig. 4, eff/ω γ = 25.81 GHz, P ~ 400 µW). The threshold power increases appreciably with temperature of the sample, particularly near ,cT because the magnetization of the ferrimagnet decreases. It can be concluded that the observed additional ab- sorption is caused by the parametric excitation of both short- and long- wavelength spin waves corresponding to the sizes of the available inhomogeneities. Conclusions The experimental results and their analysis can be summarized as follows. The resonance properties of a new Cu2OSeO3 ferrimagnet have been investigated in a wide range of frequencies (17–142 GHz) at liquid helium temperature. The resonance data were used to plot the frequency-field dependence of the ferrimagnetic spectrum which is descri- bed within the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corres- ponding to the gap in the spin wave spectrum has been estimated (3 GHz ~ 1 kOe). It is found that with increasing of pumping level the spectrum obtains a multicomponent structure, which is due to a diversity of types of mag- netization precessions. As the amplitude of the ac magnetic field increases, an additional absorption is observed in the external magnetic field lower than the field of the main resonance. The detected additional absorption corresponds to the nonu- niform nonlinear parametric resonance, connected with nonuniformity of magnetic structure in the ferrimagnetic Cu2OSeO3. The threshold of nonlinear excitations in this fer- rimagnet appears to be very low (P < 400 µW) The authors would like to thank Dr. V. Gnezdilov for fruitful discussions. Work at the EPFL was supported by the Swiss NSF and by the NCCR MaNEP. 1. E.A. Turov, Physical Properties of Magnetically Ordered Crystals (in Russian), AN SSSR Publ., Moscow (1963). 2. Jan-Willem G. Bos, Claire V. Colin, and Thomas T.M. Palstra, Phys. Rev. B78, 094416 (2008). 3. N.S. Akulov, Ferromagnetism, (in Russian), ONTI, Mos- cow-Leningrad (1939). 4. A.G. Gurevich, Ferrites at Ultrahigh Frequencies (in Rus- sian), Phys.-mat. Literature Publish., Moscow (1960). 5. R.L. White and I.H. Solt, Phys. Rev. 104, 56 (1956). 6. J.E. Mercereau and R.P. Feynman, Phys. Rev, 104, 63 (1956). 7. E. Schlömann, J. Phys. Chem. Solids, 6, 242 (1958). 8. A.M. Clogston, H. Suhl, L.R. Walker, and P.W. Anderson, J. Phys. Chem. Solids, 1, 129 (1956). 9. N. Bloembergen, R.W. Damon, Phys. Rev. 85, 699 (1952). 10. H. Suhl, J. Phys. Chem. Solids 1, 209 (1957).

Microwave absorption in the frustrated ferrimagnet Cu₂OSeO₃

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