Magnetic Impurity Density Dependence of the Neel Temperature and Spontaneous Magnetization in a Two-Dimensional Antiferromagnet

Abstract

In this paper, the model is proposed to theoretically explain the phenomenon of the rapid decrease of antiferromagnetic order of the Mott insulator with the increase of the density of the magnetic impurities injected by the external magnetic impurities in the antiferromagnetic Mott insulator. In addition, the RKKY-method was applied to this model to develop the Hamiltonian that can explain the microscopic nature of macroscopic phenomena occurring in real materials. In other words, for Cu local spins of the Cu-O₂ 2-dimensional plane, which form an antiferromagnetic order before injecting an external magnetic impurity into the system, we applied the anisotropic Heisenberg model, taking into account the magnetic anisotropic effect in the molecular field approximation. Next, the interaction between the injected magnetic impurities and the copper local spins with the jump term describing the motion of the magnetic impurities injected into the system (Cu-O₂ 2D plane) was applied to the Kondo interaction model to construct the total Hamiltonian of the system with the magnetic impurities injected. In addition, the RKKY method was applied to this model to derive an effective Hamiltonian that is mathematically convenient and intuitively reflected the phenomenon of the antiferromagnetic order reduction with increasing magnetic impurity density. And based on this effective Hamiltonian, we have considered the dependence of the impurity density of the spontaneous magnetization and the Neel temperature of a two-dimensional antiferromagnet.