Effects of dilution and disorder on magnetism in diluted spin systems

TL;DR

This paper investigates how dilution and configurational disorder affect the magnetic properties and Curie temperature of diluted Heisenberg spin systems, using Green's functions, supercell models, and formalism for disorder averaging.

Contribution

It introduces a method combining supercell approach and augmented space formalism to distinguish effects of dilution and disorder on magnetism in diluted spin systems.

Findings

Dilution increases average distance between magnetic ions, reducing Curie temperature.

Spatial disorder causes slight variations in ferromagnetic transition temperature.

Distance-dependent exponential damping significantly lowers Curie temperature, impacting phenomenological models.

Abstract

The influence of configurational disorder on the magnetic properties of diluted Heisenberg spin systems is studied with regard to the ferromagnetic stability of diluted magnetic semiconductors. The equation of motion of the magnon Green's function is decoupled by Tyablikov approximation. With supercell approach, the concentrations of magnetic ions are determined by the size of the supercell in which there is only one magnetic ion per supercell in our method. In order to distinguish the influence of dilution and disorder, there are two kinds of supercells being used: the \textit{diluted and ordered} case and the \textit{diluted and disordered} case. The configurational averaging of magnon Green function due to disorder is treated in the augmented space formalism. The random exchange integrals between two supercells are treated as a matrix. The obtained magnon spectral densities are used to calculate the temperature dependence of magnetization and Curie temperature. The results are shown as following: (i) dilution leads to increasing the averaged distance of two magnetic ions, further decreases the effective exchange integrals and is main reason to reduce Curie temperature; (ii) spatial position disorder of magnetic ions results in the dispersions of the exchange integrals between two supercells and slightly changes ferromagnetic transition temperature; (iii) the exponential damping of distance dependence obviously reduces Curie temperature and should be set carefully in any phenomenological model.