The Effect of Cr Substitution on the Anomalous Hall Effect of Co3−xCrxAl (x = 0, 1, 2, 3) Heusler Compounds: An Ab Initio Study

Based on density functional theory, we studied the electronic, magnetic, and mechanical properties of Co3−xCrxAl (x = 0, 1, 2, 3) Heusler compounds with the generalized gradient approximation (GGA) for the exchange-correlation potential. In this study, we report two principal spin-related phenomena, namely, the anomalous Hall effect and current spin polarization of the Co3−xCrxAl Heusler compounds in the L21 crystal structure. Heusler compounds, both ideally and inversely ordered, were considered. We found that the calculated magnetic moment of Co3−xCrxAl decreased with an increase in the Cr concentration for both ideally and inversely ordered structures, except for Cr3Al. We also found that the spin polarization for all Co3−xCrxAl was larger than 50%, except for Cr2CoAl in the inverse structure. All the considered Heusler compounds were mechanically stable except for the regular Cr2CoAl. The Hall current spin polarization was also calculated. We found that Co2CrAl in the XA structure had the largest spin Hall conductivity of 370 (ℏS/e cm), and the spin polarization of the induced Hall current was high.