Orbitalordering probed by electron-spin resonance method in magnetic semiconductors Текст научной статьи по специальности «Физика»

XaK539.21:537.86

S. S. Aplesnin, A. M. Vorotynov, O. B. Romanova, M. A. Lopatina

ORBITAL ORDERING PROBED BY ELECTRON-SPIN RESONANCE METHOD IN MAGNETIC SEMICONDUCTORS*

The temperature dependence of the electron-spin resonance in the 80...300 K range temperature and magnetic field up to 5 kOe has been investigated in the substance of CoMnl_S solid solutions. From the temperature dependence of linewidth and g-value the orbital order is determined. The temperature hysteresis of ESR intensity in CoMnl_S is found at the cooling in the magnetic field and without it.

Keywords: magnetically ordered materials, spin-orbit efiects, electron-spin resonance, sulfides.

The electron-spin resonance (ESR) can be used to detect orbital-ordering (OO) and to monitor the evolution of the OO parameter. Probing the spin of the non-integer filled d shell of Mn(2 + s) ions by ESR, the anisotropy and temperature dependence of g-value and linewidth AH provide clear information on orbital order via spin-orbit coupling. Promising materials are Co^Mn S solid solutions, which assume orbital ordering [1-3]. The Co.MnS solid solutions can be attributed to the multiferroic class. In the temperature

ranges of T ~ (110______120) K and T ~ (230...260) K, the

correlation between the magnetic and electric subsystems has been found [3]. The presence of this correlation is confirmed by the magnetic field dependence of the temperature variation of the permittivity having maximum at these temperatures. The first maximum in the low-temperature range is caused by the change in the orbital ordering for cobalt ions surrounded with manganese ions; the second maximum is related to the orbital order in the manganese system.

The reduced ordered moment ^0 = 4.4^B in the AF structure of MnS may be the result of change of manganese ion valency Mn2±s or repartition of electron density between e - and L -orbitals. In any case the number of L the orbital g 2g J 2g

occupancy is not equal to n = 3. The uniform orbital occupancy at every site is formed at some high temperature. The MnS6 octahedra distortion is small and essentially undetectable in X-ray experiments on MnS. The crystal field acting on the Mn2 ±s ion is therefore nearly cubic, and heuristically one expects unquenched orbital moment. The spin dynamics of MnS are highly sensitive to the orbital occupancy and can provide important information in this regard.

The aim of the study is to bring to light on mechanism of origin of the correlation between the magnetic and elastic subsystems [3; 4], to establish the role of orbital fluctuations on the dynamical properties Co^Mn S sulfides in the wide frequency range.

The crystal structure of the Co^Mn S sulfides was studied with a DRON-3 facility in monochromatic CuKa-radiation at a temperature of 300 K. According to the X-ray difiraction data, the Co^Mn S samples with 0 < x <0.4 have the NaCl-type face-centered cubic (FCC) lattice. With an increase in concentration of cation substitution (x), the lattice

parameter linearly decreases from 5.222 E (x = 0) to 5.204 E (x = 0,4), which evidences the formation of the 6-MnS-based solid solutions in the system [2].

The degree of inhomogeneity of the magnetic system, the efiect of the orbital magnetic moment, and the relaxation mechanism can be established by an ESR method. Cobalt and its compounds are characterized by a high g-factor (g >3), which is not observed in the compound under study. This confirms magnetic homogeneity of the CoxMn1-xS solid solutions. The magnetic resonance measurements were performed with a Bruker Elexsys 580 spectrometer at X-band frequency, using a continuous gas-fiow cryostat for He. The sample was cooled from 300 K down to 80 K in zero magnetic field and in the field H =5 kOe. It enables to establish the dependence of the local magnetic characteristics of the sample on its magnetic prehistory and existence of degeneration on the orbital magnetic moment.

The efiective g-factor value geff = hH/(^BHres) is determined from the resonance field, which sharply increases in the temperature range 150 K< T< 180 K as shown in Fig. 1.

T, K

Fig. 1. Temperature dependences of the resonance field upon cooling in zero magnetic field (ZFC - 1) and in the field H =5 kOe (FC - 2) for Co0 05Mn095S.

The inset shows the temperature dependence of g-factor (1) and relative extension of sample dL/L (2)

* This study was supported by the Russian Foundation for Basic Research project № 09-02-00554_a; № 09-02-92001-NNS_a; ADTP “Development of scientific potential of the higher school” № 2.1.1/401.

Вестник Сибирского государственного аэрокосмического университета имени академика М. Ф. Решетнева

At T< 150 K, the g-factor is nearly temperature-independent and takes a value of about 1.3, whereas in the temperature range 190 K< T< 280 K its value varies within 1,7.. .1,75. Based on our data, we estimate Ag/g ~ 0.15, where g is the free-electron Lande factor and Ag is its shift in the crystalline environment.

In the absence of any appreciable static Jan-Teller distortion as observed experimentally by the X-ray difiraction data [2], one expects that the spin-orbit interaction splits the t2g multiplet of the cubic crystal field Hamiltonian into a quadruple degenerate ground state and a higher-lying Kramers doublet. Even if a static JT distortion at the limits of the experimental error bars is included, the orbital contribution to the moment remains significant to the spin moment [5].

Antiferromagnetic long-range order causes the splitting d - and d -orbitals as a result of spin-orbital interaction at

xz yz

T< TN, that leads to deformation octahedra. The temperature dependence of relative deformation AL/L for the CoxMn1-xS with x = 0.05 is similar to g(T) value as shown in insert to Fig. 1. These data prove a close relationship between spin and orbital magnetic moments, lattice deformation. The orbital ordered phase is characterized by an anisotropy of AH, which for polycrystalline samples reduces to a broad maximum in AH(T) [6]. For doped and pure LaMnO3 the expression for the linewidth ESR due to crystal-field efiects and accounting only for the rotations of octahedral were obtained [7]. This theoretical approach is summarized in the formula [8]:

* (T) =XT x

AH0

X(T)

T2P

Гсе/reg(9, Ф) + Гс

6(T - TN )

/divt9, Ф)

(1)

AH (T):

T

N

6(T - Tn )

(2)

density disappears at T > TN. The ESR linewidth in the field H = 3.35 kOe below the Neel temperature is also temperature-independent and may be related to localization of an spin-polaron with a small radius. The relaxation time is determined as 1/T1 = ®2,S ac/x [9], where o>LS is the energy of the spinorbital interaction of electron, x is the Fermi velocity of an electron (x ~ 106m/s), a is the size of an localized area close to the lattice constant, and c is the concentration of the spin polaron. For example, at c = 0.001 the spin-orbital interaction is roLS= 1012Hz.

with the free Curie susceptibility %0 ~ 1/T , the static susceptibility x(T), and т = 1 - T/Tjt The first and second term describes the regular and divergent crystal field contributions, respectively. Only the latter diverges for T ^ TN with an exponent a, whereas both terms decrease for T ^ TT with a critical exponent 2p. For polycrystalline compounds the averaging of angular factors /eg(9, Ф), /v(9, ф) gives constant. We neglected here angular dependence AH(9, ф) and the linewidth is well fitted by

T, K

Fig. 2. Temperature dependences of the linewidth for the resonance field Hr2 upon cooling in zero magnetic field (ZFC - 1) and in the field H =5 kOe (FC - 2), fitting curve (3) according to Eqn. 2 for Co005Mn0 95S.

The inset shows temperature dependence of the linewidth for the resonance field HrI upon cooling in zero magnetic field (ZFC - 1) and in the field H =5 kOe (FC - 2)

As shown in Fig. 2 (solid line) a qualitative description was obtained by fitting the AH(T) data with TCE =1.8 kOe, rCFD = 0.4 kOe and p = 0,14(2), a = 1,3(5) with fixed TN =165K, T„w = 460 K, T = 280 K. The critical indexes have been

CW 7 J1

satisfactory agreement with estimates p = 0.16(1), a = 1.8 for polycrystalline LaMnO3 [8].

Below the Neel temperature, one more weak resonance with g = 2.03 is observed in the field H whose intensity is lower than the main resonance intensity (I) by three orders of magnitude (insert in Fig. 2). This resonance may be associated with spin of conductivity electron of impurity ion Co+2 and magnons that formative spin polaron. Spin polaron

T, K

Fig. 3. Temperature dependences of the ESR spectra intensity for Co0 05Mn0 95S sample upon cooling in zero magnetic field (ZFC -1) and in the field H =5 kOe (FC - 2) in resonance field H .

r2

The inset shows temperature dependences of the ESR spectra intensity sample upon cooling in zero magnetic field (ZFC - 1) and in the field H = 5kOe (FC - 2) in resonance field Hr1

x

The intensity of the magnetic resonance line is determined as a product of signal amplitude and a square of linewidth Hp obtained from the distance between the absorption derivative peaks. In Fig. 3 the intensities ESR are shown to depend on the prehistory of sample. In the sample cooled in the external magnetic field H = 5 kOe, the signal intensity decreases approximately by 40.. .60 %. It may be explained by change of direction of magnetic moments in the unaxial antiferromagnet in the vicinity of spin-fiop field. At cooling in the field the vector AF is parallel to alternating magnetic field, that leads to absence of ESR in linear approximation.

Intensity I of the ESR in field Hr2 decreases with temperature across the phase transition paramagnetic-antiferromagnetic. In particular, in the magnetically ordered phase the ESR intensity is directly proportional to a number of magnons, I~ n ~ (5- <Sz >) or, in normalized units, I/I0 ~ (1 - m), where m is the sublattice magnetization normalized to spin.

The absence of the temperature dependence of the linewidth (Fig. 2) in the range 190K< T <270K allows one to consider the spin-orbital interaction to be the fundamental mechanism of spin relaxation and formation of short range orbital order.

Two frequencies of ESR are found in CoxMn1-xS solid solution below Neel temperature. These resonances are ascribed to spin polaron and spin of localized electrons. Temperature independent behavior of the ESR linewidth and temperature hysteresis of the intensity reveal at the cooling in the external magnetic field and without it in the paramagnetic state at T < 280 K, that is accounted for by formation of orbital disordered state.

References

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С. С. Аплеснин, А. М. Воротынов, О. Б. Романова, М. А. Лопатина

ОБНАРУЖЕНИЕ ОРБИТАЛЬНОГО УПОРЯДОЧЕНИЯ МЕТОДОМ ЭЛЕКТРОННОГО ПАРАМАГНИТНОГО РЕЗОНАНСА В МАГНИТНЫХ ПОЛУПРОВОДНИКАХ

На твердых растворах СоМп^Б проведены исследования электронного спинового резонанса в интервале температур 80...300 К и магнитных полей до 5 кЭ. Из температурных зависимостей ширины линии и величины g-фактора определено орбитальное упорядочение. В Со_Мп1_$ найден температурный гистерезис интенсивности электронного спинового резонанса, измеренной при охлаждении в магнитном поле и в нулевом магнитном поле.

Ключевые слова: магнитно упорядоченные материалы, спин-орбитальный эффект, электронный спиновый резонанс, сульфиды.

© Aplesnin S. S., Vorotynov A. M., Romanova O. B., Lopatina M. A., 2011