PHASE TRANSITIONS IN ANTIFERROMAGNETIC HEXAGONAL ISING CRYSTAL, CsCoCl3

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 direction, the sum over the nn pairs in the xy plane, and the sum over the next nn pairs in the xy plane. This compound shows two phase transitions and the critical temperatures are known to be T N ~ = 21 K and T N ~ = 9 K. The magnetic order parameter in the low tempe-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 region, 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 denotes the Boltzmann constant. A theoretical analysis based on the molecular field approximation predicted the values of J1 and J 2 as 0.21 K and 0.0005 K, respectively [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 J1 and J2, in this crystal, the conventional single-spin flip MC method fails to 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 developed 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 to 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 temperatures, the so-called ferrimagnetic structure 151, (-M, m, m) , is observed. The lower critical temperFig. 2. The Monte Carlo results of the sublattice magnetizations. See the text for the sublattice structure in the intermediate temperature region, TNP<T < TNl. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888667 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 magnetization as 1, 2, and 3, after each short-time (5 MC steps in our case) MC average. Repeating this procedure, we could compute the MC average of magnetizations 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 structure (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) susceptibility. The staggered susceptibility shows two anomalous behaviors at 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 proportional 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 J1 value. We have computed the sublattice magnetization within the sublattice-switching scheme for the intermediate temperature phase. The spin structure (M, 0, -M),, differs from the so-called partial disorder structure (M, 0, -M) [5]. We observe that the instantaneous 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 barrier between those spin states will lse very low in our spin system. Consequently our spin system will successively 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 Miyatake, 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) 1584.