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

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.