PHASE TRANSITIONS IN ANTIFERROMAGNETIC HEXAGONAL ISING CRYSTAL, CsCoCl3

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PHASE TRANSITIONS IN ANTIFERROMAGNETIC

HEXAGONAL ISING CRYSTAL, CsCoCl3

O. Nagai, J. Kim, K. Nishino, Y. Yamada

To cite this version:

fOURNAL DE PHYSIQUE

Colloque C8, Supplement au no 12, Tome 49, dkembre 1988

PHASE TRANSITIONS IN ANTIFERROMAGNETIC HEXAGONAL ISING

CRYSTAL, CsCoClg

0. Nagai,

J. J.

Kim, K. Nishino and Y. Yamada

Department of Physics, Kobe University, Rolkodai, Kobe 657, Japan

Abstract.

-

The magnetic properties of CsCoC13 are investigated by the multi-spin flip Monte Carlo simulations. The exchange parameters are determined by fitting the computed values to the experimental ones for the transition temperatures. The obtained values of the exchange parameters are considerably different from those proposed previously.

The crystal structure of CsCoCls is of ABX3-type and its magnetic lattice is composed of the stacked triangular lattices [I]. Cobalt ions are, in a good approximation, described by the Ising spins [I, 21. The interaction Hamiltonian is written as

where Jo, J1, and J 2 are all positive and Si =

f

1,

and where the summations denote res,pectively the sum over the nearest neighbor (nn) pairs along the z direc- tion, the sum over the nn pairs in the x y plane, and the sum over the next nn pairs in the x y plane. This compound shows two phase transitions and the critical temperatures are known t o be

T N ~

= 21 K and T N ~ = 9 K. The magnetic order parameter in the low tem- pe-ature,region, 0

<

T

<

T N ~ , is well-defined by the three-sublattice model as (-M, m, m)

,

where M and

m denote the staggered (in the z direction) sublattice magnetizations. In the intermediate temperature re- gion, TNB<T

<

T N ~ , the magnetic order parameter is not determined in experiment. It is believed that Jo is nearly equal to 37.5 K or 37.5

k~

[2], where kg de- notes the Boltzmann constant. A theoretical analysis based on the molecular field approximation predicted the values of J1and J 2 as 0.21 K and 0.0005 K, respec-

tively [3]. In this paper, we propose that J1= 0.72 K

and J 2 = 0.27 K.

We investigate the physical properties of CsCoC13 by use of the Monte Carlo (MC) simulations. Since the exchange coupling in the z direction, Jo, is extremely larger than J1and J2, in this crystal, the conventional

single-spin flip MC method fails t o predict the correct

Fig. 1. - The magnetic lattice of CsCoCl3.

behavior of its magnetic property. This difficulty can be removed if we use the multispin flip method devel- oped by ourselves [4]. Let us consider a spin cluster composed of n spins on a column parallel to the z axis. There are 2" possible spin states for the cluster. The spin state of the cluster can be determined by the MC method if the configuration of surrounding spins is known. That is, a renewed state is chosen among the 2" states of the cluster according t o the heat-bath importance s.ampling at each MC trial.

We performed the MC simulations for the crystal with 18 x 18 x 12 spins. Periodic boundary condition was assumed. In our multi-spin flip MC calculation, the MC average was taken over 5000 MC steps per cluster after discarding 5000 MC steps per cluster.

In figure 2, we show the sublattice magnetizations by assuming the three-sublattice model. At low tem- peratures, the so-called ferrimagnetic structure 151,

(-M, m , m)

,

is observed. The lower critical temper-

Fig. 2. - The Monte Carlo results of the sublattice mag- netizations. See the text for the sublattice structure in the intermediate temperature region, TNP<T

<

TNl.

C8 - 1454 JOURNAL DE PHYSIQUE

ature, TNz, is defined by the temperature at which the ferrimagnetic structure is destroyed. Above T N ~ , as the sublattice magnetizations show irregular behavior with respect to thk time evolution, we cannot determine T N ~ . In order to look into the phase transition at T N ~ , we tried to compute the sublattice magnetization in the L'sublattice-switching" MC scheme: We relabelled the three sublattices in order of magnitude of magne- tization as 1, 2, and 3, after each short-time (5 MC steps in our case) MC average. Repeating this proce- dure, we could compute the MC average of magneti- zations in the sublattice-switching (ss) scheme, (MI, M2, M3)ss. We observe the spin structure of (M, 0, -M)., in the intermediate temperature region, T N ~ < T

<

T N ~ , as seen in figure 2. Here we assume that T N ~ is defined by the temperature where the spin struc- ture (M, 0, -M)ss is destroyed. We find that T N ~ E 21 K and T N ~ E ~

K,

for the exchange parameters J o = 37.5 K, Ji = 0.72 K, and J 2 = 0.27 K.

Another evidence for the phase transitions can be found in the staggered (in the z direction) susceptibil- ity. The staggered susceptibility shows two anomalous behaviors a t the critical temperatures, as can be seen in figure 3.

In figure 4, we show the dependence of T N ~ and T N ~ on the values of J1 and J 2 . The value of J o (= 37.5 K)

Fig. 4.

-

The dependence of TN1 and : r ~ 2 on the values of exchange parameters.

was fixed. As seen from the figure, T N ~ is propor- tional to J 2 for J 2

<<

JO and T N ~ is proportional to

( 3 1

+

6J2)

.

Moreover, we find tha,t the T N ~ value is almost independent on the J1value.

We have computed the sublattice magnetization within the sublattice-switching scheme for the inter- mediate temperature phase. The spin structure (M, 0, -M),, differs from the so-called partial disorder struc- ture (M, 0, -M) [5]. We observe that the instanta- neous spin structure is given by (MI, -dl -M1 +d). There are many such spin states whose energies are very close to each other. Furthermore, the energy bar- rier between those spin states will lse very low in our spin system. Consequently our spin system will succes- sively take these spin states with time evolution. Thus, the magnetic order parameter will not be well-defined. This phenomenon was discussed by Coppersmith [6] for the case J 2 = 0.

Fig. 3. - The Monte Carlo results of the staggered (in the

z direction) susceptibility. The critical points are indicated by the arrows. The solid line denotes the MC result for the linear chain with the exchange coupling J o = 37.5 K.

[I] Mekata, M. and Adachi, K., J. Phys. Soc. Jpn 44 (1978) 806.

[2] Yoshizawa, H. and Hirakawa, K.,

J.

Phys. Soc. Jpn 46 (1979) 448.

[q Shiba, H., Prog. Theor. Phys.

64 (1980) 466. [4] Nagai, O., Yamada, Y., Nishino,

K.

and Miy-

atake, Y., Phys. Rev. B 35 (1987) 3425. [5] Mekata, M., J. Phys. Soc. Jpn 42 (1977) 76. [6] Coppersmith, S. N., Phys.

Rev.

B 32 (1985)