Steplike magnetization of spin chains in a triangular lattice: Monte Carlo simulations

A two-dimensional Ising-like model for a triangular spin-chain lattice, where each spin-chain is treated as a rigid giant spin, is proposed to investigate the magnetization of a triangular spin-chain lattice by Monte Carlo simulation. The simulations show the steplike evolution of the magnetization at low temperature against an external magnetic field, namely two steps above $10\mathrm{K}$ and four steps below $10\mathrm{K}$, in quantitative agreement with experiments on a ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ compound. It is argued that the interchain interaction and magnetic inhomogeneity of the lattice are two important ingredients to induce the intriguing steplike feature of the magnetization below $10\mathrm{K}$.

Figure 1

(Color online) $M\left(h\right)$ curves in (a) the intermediate $T$ range, and (b) the low $T$ range.

Figure 2

$40\times 40$ spin snapshots of the triangular lattice for (a) $T=10\mathrm{K}$, $h=1.8\mathrm{T}$; (b) $T=2\mathrm{K}$, $h=0.6\mathrm{T}$; (c) $T=2\mathrm{K}$, $h=1.8\mathrm{T}$, and (d) $T=2\mathrm{K}$, $h=3.0\mathrm{T}$.

Figure 3

Simulated magnetic phase diagram. P, Fi, Fo, and DIS, are for paramagnetic, ferrimagnetic, ferromagnetic, and disordered magnetic states, respectively. A, B, and C represent the three states presented in the text.

Figure 4

(Color online) (a) $40\times 40$ spin snapshot of the triangular lattice with $span=0.05$ for $T=2\mathrm{K}$ and $h=0.6\mathrm{T}$. (b) $M\left(h\right)$ curves for different $span$ at $T=2\mathrm{K}$.