Spin Dependence of the Critical Concentration for the Neel State of 2D Impure Heisenberg Antiferromagnets

TL;DR

This paper investigates how nonmagnetic impurities affect the Neel order in 2D Heisenberg antiferromagnets, revealing critical impurity concentrations and the emergence of a spin gap, aligning with experimental observations.

Contribution

It introduces a theoretical analysis of impurity effects on Neel order using spin-wave theory and coherent potential approximation, providing quantitative critical impurity concentrations for different spins.

Findings

Critical impurity concentration for S=1/2 is 0.303.

Long range Neel order vanishes at impurity concentration 0.5 for S>=1.

Spin gap appears in the disordered phase between critical and percolation thresholds.

Abstract

The spin-wave theory and the coherent potential approximation are applied to a spin S Heisenberg antiferromagnet with nonmagnetic impurities on square lattice. The impurity effects are taken into account by substituting S(1-x) for S and using the coherent potential approximation to the exchange interaction, where x is the impurity concentration. At T=0 for S=1/2 the critical impurity concentration xc of the Neel state is 0.303 and the percolation threshold xp is 0.500. The ground state in xc<x<xp is the disordered state with the spin gap. For S>=1 the long range Neel order vanishes at xp=0.500. These results explain qualitatively the experimental results of La2Cu(1-x)Mg(x)O4 (S=1/2) and K2Mn(1-x)Mg(x)F4 (S=5/2). The difference of xc between these materials is caused by the decrease in the magnitude of the effective spin with impurity doping. The spin gap is expected to be observed for La2Cu(1-x)Mg(x)O4 in xc<x<xp at low temperatures.