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 x_c of the Néel state is 0.303 and the percolation threshold x_p is 0.500. The ground state in x_cp is the disordered state with the spin gap. For S ≥q 1 the long range Néel order vanishes at x_p=0.500. These results explain qualitatively the experimental results of La₂Cu_1-xMg_xO₄ (S=1/2) and K₂Mn_1-xMg_xF₄ (S=5/2). The difference of x_c 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-xMg_xO₄ in x_cp at low temperatures.