Anderson Metal-Insulator Transitions With Classical Magnetic Impurities

TL;DR

This study numerically investigates how classical magnetic impurities influence the Anderson metal-insulator transition, revealing modifications in critical disorder, correlation length exponent, and multifractality, aligning with experimental observations.

Contribution

It demonstrates that magnetic impurities alter critical parameters of the Anderson transition and introduces a numerical approach combining finite-size scaling and kernel polynomial method for critical property analysis.

Findings

Magnetic impurities increase the critical disorder amplitude $W_c$.

Presence of impurities lowers the correlation length exponent $ u$.

Impurities enhance the multifractality parameter $eta_0$.

Abstract

We study effects of classical magnetic impurities on the Anderson metal-insulator transition numerically. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{\rm c}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\nu$ and enhances the multifractality parameter $\alpha_0$. The new value of $\nu$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.