Spin density wave and field induced phase transitions in magnetoelectric antiferromagnets

Physica B 211 (1995) 327-330

ELSEVIER

Spin density wave and field induced phase transitions in magnetoelectric antiferromagnets A.M. Kadomtseva a, Yu.F. Popov a, G.P. Vorob'ev a, A.K. Z v e z d i n b'* a Moscow State University, Dept. of Physics, 119899 Moscow, Russian Federation b Institute of General Physics, Russian Academy of Science, 38 Vavilov St., 117942 Moscow, Russian Federation

Abstract

An investigation was done of the field induced phase transition from the spatially modulated spin structures to the homogeneous antiferromagnetic state in magnetic ferroelectrics RxBil_xFeO3 (R = La, Nd) and magnCtoelectrics FexCr2-xO3 in pulsed magnetic field up to 30 T. It has been found that this transition is accompanied by a l~rge change in the magnitude of the magnetoelectric effect. In contrast to the RxBit _xFeO3, where the linear magnetoelectric effect appears in strong magnetic fields ( k / > He) in Fe~Cr2_xO3 such effect exists in the low-field phase (H < He). This is associated with the different character of the spatially modulated spin structure in these materials (cycloid structure in R~Bil -~FeO3 and cone spiral in Fej,Cr2_ xO3).

1. Introduction

A new type of phase transition is observed experimentally and explained theoretically. This is the transition induced by magnetic field from the space-modulated spin structure (SMSS) to the homogeneous antiferromagnetic state (HAFS). According to the theory this transition in the magnetic ferroelectrics RxBil-xFeO3 [1] and the magnetoelectrics Cr2-xFexO3 is accompanied by drastic change in the magnetoelectric effect (ME-effect). To detect the phase transition SMSS-HAFS we measured the ME-effect of these crystals in high magnetic fields up to 30 T, where this phase transition can occur.

2. BiFeO3

Crystals of BiFeO3 have the rhombohedrally distorted perovskite structure, the space group below Tc = 1083 K * Corresponding author.

is R3c = C36v. While the crystal symmetry of BiFeO3 allows a linear ME-effect, it cannot be observed because the antiferromagnetic order of BiFe03 below TN = 637K has the space-modulated spirt structure [2,3]. The quadratic ME-effect of BiFeO3 has been investigated in great details [4,5]. The aim of thisi work is to study the ME-effect in high magnetic field in which we expect the phase transition from the spaceimodulated structure to the homogeneous antiferromagn~tic state to be allowed [1]. We stress that a large jump of ME-effect is expected at the transition due to an increase of the linear ME-contribution. The electric polarization P induced by a pulsed magnetic field up to 30 T was studied over the temperature range 10-180K. The BiFeO3 crystals werei grown by spontaneous crystallization from molten solution [5]. Fig. 1 shows the field dependence of the 19ngitudinal polarization in the case when the field is along the [00 1] axis. At H < ½He the polarization is an esseniially quadratic function of the field. At Hc = 20 T, there is a sharp change in P(H), which apparently means a destruction of the cycloid spin structure [2,3]. This event! should be

0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 1 0 5 1 - X

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A.M. Kadomtseva et al. /Physica B 211 (1995) 327 330

we find the SMSS to be at

P, lO'ec/m 2

0 = q x X + qyY,

10

(3)

dp = arctan(qx/qy),

where the vector q = (qx, qy, 0) belongs to the star of wave vectors (rays) obtained from an arbitrary q by applying all elements of the R3c group. There is another solution which minimizes the free energy: 0 = const,

0

tp = const.

(4)

This solution describes HAFS. However we shall see that the structure (3) - SMSS corresponds to a minimum energy. The energy gain in the space-modulated state is AF(q0) = F(qo) - F(O) = - A q 2 + K , / 2 < 0,

(5)

where A is the exchange stiffness, K~ is single ion anisotropy constant, q = ct/4A and ~ is nonhomogeneous relativistic exchange constant, which is assumed to be proportional to Pz. Let us estimate AF(q), using the parameter values

-I0

[2,3]: -20 0

J 10

A ~ (2-4) 10 -7 erg/cm, 2O

H,T Fig. 1. Longitudinal electric polarization versus magnetic field along the [001] axis for BiFeO3 at T = 10K.

accompanied by the onset of the linear ME-effect. Magnitude of the polarization varies by less than 20% over the temperature range studied, while the critical field remains essentially constant. Measurements at T > 180K are complicated by the sharp increase in the conductivity of the sample. The origin of the SMSS in BiFeOz is connected with Lifshitz invariant of the type alJKLI~jL K of which only one is important for our purposes: ~tPz(LxOxL z + LydyL~),

(1)

where Li is projection of the antiferromagnetic vector, Pz is projection of the polarization into the Ca axis. These invariants can exist only in crystals without inversion center and they are caused by anisotropic relativistic interaction. The vector L can be written in the form Lx = L sin 0 cos q~, L r = L cos 0 sin q~,

Lz = L cos 0,

(2)

where 0 and ~b are the polar and azimuthal angles, defined in the usual way in the coordinate system in which the c axis is the polar axis. Minimizing the free energy of the crystal and taking the Lifshitz invariant into account,

q = 2n/2,

~. = 620A.

(6)

Substituting these values into Eq.(5), we find AF = 2 x 105 erg/cm 3. If the magnetic field then increases, the free energy of the HAFS falls more steeply than that of the SMSS. This leads to the phase transition SMSS-HAFS. There is a close analogy between this transition and the well known spin-flop transition in an antiferromagnet. The critical field for the SMSS-HAFS transition can be found from comparison of the free energies of SMSS and HAFS, and according to Ref. I-1-1: He =

/ 4Aq2. ~/ Za

(7)

The critical fields He for H = (Hx, Hy, 0) can be found from an expression like Eq. (7) if mz = ~ , where ms is the spontaneous magnetization of BiFeO3. Assuming Z± = 10- 5, and taking the value A q 2 from Eq. (6), we find H~ = (20-30) T in agreement with the value found from the experimental data.

3. RxBil-~FeO3 We studied also the field induced phase transition SMSS-HAFS in the crystals of magnetic ferroelectrics R~Bil-xFeO 3 (R = La, Nd). The investigation of these compounds gives the possibility to find how the substitution influences the condition for realization of SMSS. According to Eq. (5), SMSS may be destroyed at some particular values of the anisotropy constant. As it was stated in Ref. [51, five different modifications can exist in the solid solution LaxBia-~FeO3. Being such a strong

329

A.M. Kadomtseva et al./Physica B 211 (1995) 327 330

p , 1 0 "e C l m

H, T

2

20

20

1 10

16

X

)(

X

X

x

J

X

'

"I

10

2 -10

-20

o

Io

2°

n

o

too

T,K Fig. 2. Dependence of P(H) (PIIHtb[001]) for Ndo, lBio.gFeO3, (1) T = 111 K, (2) T = 10K and for Lao.lBio.gFeO3, (3) T = 120K.

factor, the substitution of La 3+ ions can be used to change substantially the anisotropy constant and hence to change the condition for the appearance of SMSS. A natural approach is to start the corresponding studies with small additions of La such that SMSS is kept and the structure is not destroyed very much. Fig. 2 (curve 3) shows the dependence of P(H) for compositions with x =0,1. As seen the P(H) dependence is qualitatively different in two regions: H < 15T and H > 15T. At H = 15T the dependence P(H) is drastically changed and becomes linear at higher fields. A linear dependence indicates apparently the destruction of SMSS at Hcrit = 15 T. The critical field here is less than in BiFeO3, because the anisotropy constant changes due to additional distortion of the perovskite cell. The critical field is practically independent of temperature in the range from 40-200 K (Fig. 3, curve 1) which is in accordance with fact that La ions are not magnetic. Below 40 K the critical field measurement was hampered by the drop of the longitudinal polarization value. The longitudinal polarization value is changed by an order of magnitude in this temperature range and becomes much lower below 40 K. The study of the magnetoelectric effect in the crystals with magnetic rare earth ions was

Fig. 3. The temperature dependence of the critical field: curve 1 for LaoABio.gFeO3;curve 2 for Ndo.lBio.gFeO31 carried out for the case of Nd ions. Fig. 2 (~urves 1, 2) displays the magnetic field dependence of th.~ longitudinal polarization along 1-00 1] for Ndo,lBio,9FeO3 composition. Here again the dependence of the I angitudinai polarization along [00 1] upon the magnel ic field becomes linear at Herit. As expected, the critical field for the composition with the magnetic ion diminist es with the temperature (Fig. 3, curve 2). We assume, b~ sed on this fact, that further increase of the Nd concenti ation could induce the spontaneous phase transition SI~ISS-HAFS with diminishing temperature. However, We failed to grow such crystals due to the deterioration of the crystal quality with increase of Nd concentration.

4. Cr2-xFexO3 The mixed magnetoelectric crystals ol the kind Cr2- xFexO3 are of principal interest for magnetism. The antiferromagnets ~t-Fe203 and Cr203 are wdll known in solid state physics. They both have the s~me crystal structure (space group R3c), however their magnetic structures are different. It causes a striking difference in their magnetic properties. Thus the hematite ot-Fe203

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A.M. Kadomtseva et al./Physica B 211 (1995) 3 2 ~ 3 3 0

the literature on the subject. We have studied this system using single crystals and high magnetic fields. We investigated antiferromagnetic single crystals Cr 2 _xFexO 3 with x = 0, 1, where the cone axis is parallel to the c-axis, and with x = 0, 3 where the axis is perpendicular to the c-axis with basal plane. The linear MEeffect has been discovered with the field along c-axis up to He, where the critical field He changes from H~ = 12 T at 280K to 2T at T = 10K (Fig. 4). In contrast to the bismuth ferrite, the linear ME-effect exists in the low-field phase of FeoACrl.903 that, which probably results from the different character of the SMSS in these materials. There is pronounced hysteresis in the dependence P(H) and the butterfly-like hysteresis of the ME-effect (Fig. 4, curve 1) appears for the same temperature. In the crystals Feo.3Crl.703 the linear magnetoelectric effect is found to be absent. This compound has a weak ferromagnetic moment of 0.2 G cm3/g.

p, 10 "e C l m 2 I0

°I0

Acknowledgements 0

0

110

16

H,T

The work was supported by the Russian Fundamental Research Foundation (Contract N 93-02-3214).

Fig. 4. The field dependence of the longitudinal polarization along the c-axis for Fe0.1Crt.903.

References

is a classical weak ferromagnet of the Dzaloshinskii-Morya-kind, but it does not show the linear magnetoelectric effect; and vice versa, the antiferromagnet CrzO 3 exhibits the linear magnetoelectric effect but it does not have the weak ferromagnetic moment. There is another interesting point connected with this interrelation, namely the existence of the modulated spin structure of the cone spiral in the mixed system [6]. Only a few studies, restricted to powder samples, were reported in

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