Modeling the Berezinskii-Kosterlitz-Thouless transition in NiGa2S4

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 NiGa(2)S(4) compound is of BKT type. The spin-freezing state observed in the NiGa(2)S(4) possesses the power-law decayed spin correlation.