We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{\mathrm{c}}$ 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.

• Received 10 July 2015
• Revised 25 February 2016

DOI:https://doi.org/10.1103/PhysRevB.93.134203