Anomalous Hall effect and current spin polarization inCo2FeXHeusler compounds (X=Al, Ga, In, Si, Ge, and Sn): A systematicab initiostudy

Abstract

Co-based Heusler compounds are ferromagnetic with a high Curie temperature and a large magnetization density, and thus are promising for spintronic applications. In this paper, we perform a systematic ab initio study of two principal spin-related phenomena, namely, anomalous Hall effect and current spin polarization, in ${\mathrm{Co}}_{2}$-based Heusler compounds ${\mathrm{Co}}_{2}\mathrm{Fe}X$ ($X=\mathrm{Al}, \mathrm{Ga}, \mathrm{In}, \mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}$) in the cubic ${\mathrm{L}2}_{1}$ structure within the density functional theory with the generalized gradient approximation (GGA). The accurate all-electron full-potential linearized augmented plane-wave method is used. First, we find that the spin polarization of the longitudinal current (${P}^{L}$) in ${\mathrm{Co}}_{2}\mathrm{Fe}X$ ($X=\mathrm{Al}, \mathrm{Ga}, \mathrm{In}, {\mathrm{Al}}_{0.5}{\mathrm{Si}}_{0.5}, \text{and} \mathrm{Sn}$) is $\ensuremath{\sim}100$% even though that of the electronic states at the Fermi level (${P}^{D}$) is not. Further, the other compounds also have a high current spin polarization with ${P}^{L}>85$%. This indicates that all the ${\mathrm{Co}}_{2}\mathrm{Fe}X$ compounds considered are promising for spin-transport devices. Interestingly, ${P}^{D}$ is negative in ${\mathrm{Co}}_{2}\mathrm{Fe}X$ ($X=\mathrm{Si}, \mathrm{Ge}, \text{and} \mathrm{Sn}$), differing in sign from the ${P}^{L}$ as well as that from the transport experiments. Second, the calculated anomalous Hall conductivities (AHCs) are moderate, being within 200 S/cm, and agree well with the available experiments on a highly ${\mathrm{L}2}_{1}$ ordered ${\mathrm{Co}}_{2}\mathrm{FeSi}$ specimen although they differ significantly from the reported experiments on other compounds where the B2 antisite disorders were present. Surprisingly, the AHC in ${\mathrm{Co}}_{2}\mathrm{FeSi}$ decreases and then changes sign when Si is replaced by Ge and finally by Sn. Third, the calculated total magnetic moments agree well with the corresponding experimental ones in all the studied compounds except ${\mathrm{Co}}_{2}\mathrm{FeSi}$ where a difference of 0.3 ${\ensuremath{\mu}}_{B}/\mathrm{f}.\mathrm{u}.$ exists. We also perform the GGA plus on-site Coulomb interaction $U$ calculations in the $\mathrm{GGA}+U$ scheme. We find that including the $U$ affects the calculated total magnetic moment, spin polarization and AHC significantly, and in most cases, unfortunately, results in a disagreement with the available experimental results. All these interesting findings are discussed in terms of the underlying band structures.