Enhancement of the anomalous Hall effect in ternary alloys

We consider ternary alloys of the composition Cu(Mn1−wTw), where T corresponds to different nonmagnetic impurities. As was discovered by Fert et al. [J. Magn. Magn. Mater. 24, 231 (1981)], the anomalous Hall effect (AHE) in the binary Cu(Mn) alloy can be significantly enhanced by means of codoping using 5d impurities. Moreover, they attempted to quantify the spin Hall effect (SHE) in Cu(T) binary alloys via the AHE measured in the related ternary alloys. Here, we present a theoretical study serving as a detailed background of the experimental findings by clarifying the conditions required for a maximal enhancement of the AHE as well as the relations between both Hall effects. Based on the proposed approach, we perform first-principles calculations for several Cu(Mn1−wTw)[T = Au, Bi, Ir, Lu, Sb, or Ta] alloys, which are underpinned by theoretical investigations via Matthiessen's rule.