Anomalous and spin Hall effects in hcp cobalt from GGA + U calculations

TL;DR

This study uses GGA+U calculations to analyze anomalous and spin Hall effects in hexagonal cobalt, revealing significant anisotropy and spin polarization of Hall currents, aligning well with experimental data.

Contribution

The paper demonstrates that GGA+U calculations with moderate U and J values accurately reproduce Hall conductivities and magnetic moments in cobalt, highlighting the importance of electron correlation effects.

Findings

GGA+U results agree with experimental Hall conductivities and magnetic moments.

Hall conductivities are highly anisotropic with respect to magnetization direction.

Hall current spin polarization can exceed 1, indicating pure spin currents.

Abstract

We have calculated the intrinsic anomalous and spin Hall conductivities, spin and orbital magnetic moments and also spin polarization of Hall currentsin hexagonal cobalt within the density functional theory with the generalized gradient approximation (GGA) plus on-site Coulomb interaction (GGA+$U$). The accurate all-electron full-potential linearized augmented plane wave method is used. We find that the anomalous Hall conductivity (AHC) ($\sigma_{xy}^A$) and orbital magnetic moment ($m_o$) of cobalt with the magnetization being along the c-axis ($m//c$) calculated in the GGA+$U$ scheme with $U = 1.6$ eV and $J = 0.9$ eV agree rather well with the corresponding experimental values while, in contrast, the $\sigma_{xy}^A$ and $m_o$ from the GGA calculations are significantly smaller than the measured ones. This suggests that moderate $U = 1.6$ eV and $J = 0.9$ eV are appropriate for Co metals. The calculated AHC and spin Hall conductivity (SHC) ($\sigma^S$) are highly anisotropic, and the ratio of the Hall conductivity for $m//c$ to that for the magnetization being in-plane ($m//ab$) from the GGA+$U$ calculations, is $\sim$16.0 for the AHC and $\sim$6.0 for the SHC. For $m//c$, the spin-up and spin-down Hall currents are found to flow in the same direction. The magnitude of the calculated Hall current spin polarization ($P^H$) is large and $P^H = -0.61$. Remarkably, for $m//ab$, the spin-up and spin-down Hall currents are predicted to flow in the opposite directions. This indicates that the Hall current contains both spin-polarized charge current and pure spin current, resulting in the magnitude of the Hall current spin polarization ($P^H = -1.59$) being larger than 1.0.