The Phase Transition of Square Lattice Antiferromagnets at Finite Temperature

TL;DR

This paper investigates the finite-temperature phase transitions in a two-dimensional antiferromagnetic $J_1$-$J_2$ model, revealing a first-order transition between Ne9el and collinear states influenced by single-ion anisotropy and doping.

Contribution

It introduces the finite-temperature phase transition behavior between Ne9el and collinear states in the $J_1$-$J_2$ model, highlighting the role of single-ion anisotropy and potential doping effects.

Findings

Existence of a first-order phase transition between Ne9el and collinear states.

Phase transition occurs below the Ne9el temperature when anisotropy is strong.

Doping can modify exchange ratios to induce the phase transition.

Abstract

The magnetic properties of the two-dimensional $J_{1}-J_{2}$ model with both exchanges $J_{1}$ and $J_{2}$ being antiferromagnetic and a single-ion anisotropy at nonzero temperature are investigated. As $J_{2}/J_{1}<1/2$ ($>1/2$), only the N\'{e}el (collinear) state exists. When $J_{2}/J_{1}=1/2$, both the N\'{e}el and collinear states can exist and have the same N\'{e}el temperature. The calculated free energies show that there can occur a phase transition between the two states below the N\'{e}el point when the single-ion anisotropy is strong enough. It is a first-order transition at nonzero temperature. It is possible that the doping in real materials can modify the ratio of $J_{2}/J_{1}$ to reach $1/2$ so as to implement the phase transition.