Modeling the Berezinskii-Kosterlitz-Thouless transition in ${\text{NiGa}}_2{\text{S}}_4$

In the two-dimensional superfluidity, the proliferation of the vortices and the antivortices results in a class of phase transition, the Berezinskii-Kosterlitz-Thouless (BKT) transition. This class of phase transition is also anticipated in the two-dimensional magnetic systems. However, its existence in the real magnetic systems still remains mysterious. Here we propose a phenomenological model to illustrate that the spin-freezing transition recently uncovered in the nuclear magnetic-resonance experiment on the ${\text{NiGa}}_2{\text{S}}_4$ compound is of BKT type. The spin-freezing state observed in the ${\text{NiGa}}_2{\text{S}}_4$ possesses the power-law decayed spin correlation.

Figure 1

(Color online) (a) The spin structure observed by the neutron scattering in Ref. 4. There are two arrows on every site. The colored one is the spin orientation, and the thin black one is the local easy axis. (b) The ground state of the antiferromagnetic quantum Ising model on the triangular lattice. “$-$” indicates the local “$-1$” state and “$+$” is the local “$+1$” state. “Zero” is the linear superposition of the “$+1$” and “$-1$” states.

Figure 2

(Color online) The system size is $10\times 10$ with 100 spins in the calculation. The theoretical result has the same structure as the experiments. At the dip of ${\chi }^{-1}$, marked as $T_f$, the spin-freezing transition occurs as found in the Ga-NMR experiments.

Figure 3

(Color online) The result of $\xi \left(T\right)$. The temperature is in the unit of $J$, and the correlation length is in the unit of lattice constant $a$. At the high-temperature side of $T_c$ $\left(\sim 0.3J\right)$, the spin correlation is exponentially decayed, and the correlation length diverges at $T_c$. Below $T_c$, the phase has the power-law spin correlation. The green line is the theoretical fit of the 2D XY universality class.

Figure 4

(Color online) $\xi \left(T,M\right)$ at $T=0.2J$ and $0.4J$. The vertical axis is $\xi \left(T,M\right)$, and $M$ is in the unit of the lattice constant $a$. At $T=0.4J$, the correlation length saturates exponentially. At $T=0.2J$, the linear scaling implies the critical phase as explained in the text. The two lines are the functional fit to the data.

Figure 5

(Color online) The temperature is in the unit of $J$. The vertical axis is the initial slope of $\xi \left(T,M\right)$ defined in the text. If there is no phase transition, the initial slope should be exponentially and monotonically increasing. However, there is a discontinuity at $T=0.3J$, which indicates a phase transition.

Figure 6

(Color online) The temperature dependence of the specific-heat capacity. The temperature is in Kelvin.