Compensation in trilayered anisotropic 6-state clock model

Abstract

The equilibrium behaviours of a trilayered 6-state clock model have been investigated by Monte Carlo simulation. The intralayer interaction is considered ferromagnetic, whereas the interlayer interaction is antiferromagnetic. Periodic boundary conditions(PBC) are applied in XY plane and open boundary condition (OBC) is applied along Z-direction. The thermodynamic behaviours of sublattice magnetisation, total magnetisation, magnetic susceptibility and the specific heat are studied as functions of the temperature. The interesting compensation phenomenon, when the total magnetisation vanishes keeping the nonzero sublattice magnetisations, has been observed. The compensation temperature and the critical temperature are found to depend on the strength of single-site anisotropy. The comprehensive phase diagram is shown in the temperature-anisotropy plane. The larger systems show the growth of the height of the peak of the susceptibility near the critical temperature.

Figures (10)

• Figure 1: Thermal variation of (a) total magnetisation $(M)$ , (b) susceptibility $(\chi)$ and (c) specific heat $(C)$ for isotropic regime $(D=0)$. The transition temperature is found to be $T_c \approx 1.0$ and the compensation temperature $T_{comp} \approx 0.40$, both determined from the positions of the peaks of the susceptibility. The corresponding specific heat $C(T)$ also exhibits peaks at the respective temperatures.
• Figure 2: Thermal variation of sublattice magnetisation component (a) $m_x$ and (b) $m_y$ for three layers in the isotropic regime $D=0$. Layers 1 and 3 exhibit positive $m_x$ and $m_y$ values, while layer 2 shows negative contributions. At compensation temperature $T_{comp}=0.40$, each sublattice retains a finite magnetisation, but their vector sum cancels out resulting in vanishing total magnetisation.
• Figure 3: Spin morphology for layers at four characteristic temperatures ($T_{high}$, Near $T_c$, $T_{comp}$ and $T_{low}$) in the isotropic regime ($D=0$) for system size $L=32$. Each colour represents one of the six clock states corresponding to the spin angle. The snapshot illustrates the evolution from high-temperature paramagnetic phase through thermodynamic phase transition near $T_c$, the compensation point $T_{comp}$ to the low temperature ordered state.
• Figure 4: Normalised spin population as a function of six clock state (discrete spin angles) for three layers at four characteristic temperatures $T_{high}$, $T_c$, $T_{comp}$ and $T_{low}$. The vertical axis represents the fraction of spins in each angle state (normalized to the total spin count of 1024 in each layer). At high temperature, the distribution is equal, whereas upon cooling, distinct states(angles) eventually catch on: spins at layer 1 and 3 align at $\theta=2\pi/3$($n_i=2$), while layer 2 aligns at $\theta=5\pi/3(n_i=5)$, consistent with spin morphology.
• Figure 5: Thermal variation of (a) total magnetisation $(M)$, the dotted horizontal line is a reference for $M=0$, (b) susceptibility $(\chi)$ and (c) specific heat $(C)$ for different anisotropy values $D=1.0,2.5,4.0$. The critical temperature $T_c$ and compensation temperature $T_{comp}$ determined from the positions of susceptibility peaks, both shift towards higher values with increasing D, indicating enhanced thermal stability.