Coherence and stiffness of spin waves in diluted ferromagnets

TL;DR

This paper numerically investigates magnon spectra in diluted ferromagnets, revealing how boundary conditions and supercell size influence low-energy excitations and enabling efficient determination of spin-wave stiffness, with applications to Mn-doped semiconductors.

Contribution

The study introduces a formalism for analyzing magnon spectra in disordered ferromagnets and relates spin stiffness to Curie temperature in Mn-doped semiconductors.

Findings

Low-energy spectral regions show coherence and boundary condition sensitivity.

Supercell size dependence aids in determining spin-wave stiffness D.

The ratio of Curie temperature to D varies similarly with Mn concentration in GaAs and GaN.

Abstract

We present results of a numerical analysis of magnon spectra in supercells simulating two-dimensional and bulk random diluted ferromagnets with long-ranged pair exchange interactions. We show that low-energy spectral regions for these strongly disordered systems contain a coherent component leading to interference phenomena manifested by a pronounced sensitivity of the lowest excitation energies to the adopted boundary conditions. The dependence of configuration averages of these excitation energies on the supercell size can be used for an efficient determination of the spin-wave stiffness D. The developed formalism is applied to the ferromagnetic Mn-doped GaAs semiconductor with optional incorporation of phosphorus; the obtained concentration trends of D are found in reasonable agreement with recent experiments. Moreover, a relation of the spin stiffness to the Curie temperature Tc has been studied for Mn-doped GaAs and GaN semiconductors. It is found that the ratio Tc/D exhibits qualitatively the same dependence on Mn concentration in both systems.