Magnetic spin excitations in diluted ferromagnetic systems: the case of $Ga_{1-x}Mn_{x}As$

TL;DR

This paper develops a theoretical method to calculate magnetic excitation spectra in diluted ferromagnetic systems, specifically applied to $Ga_{1-x}Mn_{x}As$, revealing how dilution affects magnon excitations and matching experimental data.

Contribution

It introduces a general Self-Consistent local Random Phase Approximation approach that accurately accounts for disorder and thermal fluctuations in diluted magnetic semiconductors.

Findings

Dilution drastically reduces the region of well-defined magnon excitations.

Calculated spin stiffness matches experimental measurements in annealed samples.

Provides explanation for small measured values in as-grown samples.

Abstract

We propose a theory which allow to calculate the magnetic excitation spectrum in diluted ferromagnetic systems. The approach is rather general and based on the Self-Consistent local Random Phase Approximation in which disorder (dilution) and thermal fluctuations are properly treated. To illustrate its reliability and accuracy we calculate the magnetic excitation in the diluted III-V magnetic semiconductor $Ga_{1-x}Mn_{x}As$. It is shown that dilution has a drastic effect on the excitation spectrum, indeed well defined magnon excitations exist only in a small region of the Brillouin zone centered around the $\Gamma$ point. We also calculate the spin stiffness in optimally annealed sample as a function of $Mn^{2+}$ concentration. A comparison to available measurements is done. We find a very good agreement for both the Curie temperature and the spin stiffness measured in well annealed samples and provide a plausible explanation for the very small values measured in as grown samples.