Intrinsic anomalous Hall effect in nickel: An GGA+U study

TL;DR

This study uses GGA+U calculations to accurately determine the intrinsic anomalous Hall conductivity in nickel, highlighting the importance of electron-electron correlations for matching experimental results.

Contribution

It demonstrates that including on-site Coulomb interactions (U) in GGA calculations yields results consistent with experiments, unlike standard GGA, and predicts sign changes in Hall conductivity.

Findings

GGA+U results match experimental Hall conductivity in nickel.

On-site Coulomb interaction shifts d-bands, affecting Fermi surface features.

Predicted sign change of Hall conductivity at specific Fermi energy.

Abstract

The electronic structure and intrinsic anomalous Hall conductivity of nickel have been calculated based on the generalized gradient approximation (GGA) plus on-site Coulomb interaction (GGA+U) scheme. It is found that the intrinsic anomalous Hall conductivity ($\sigma_{xy}^H$) obtained from the GGA+U calculations with $U = 1.9$ eV and $J=1.2$ eV, is in nearly perfect agreement with that measured recently at low temperatures while, in contrast, the $\sigma_{xy}^H$ from the GGA calculations is about 100% larger than the measured one. This indicates that, as for the other spin-orbit interaction (SOI)-induced phenomena in 3$d$ itinerant magnets such as the orbital magnetic magnetization and magnetocrystalline anisotropy, the on-site electron-electron correlation, though moderate only, should be taken into account properly in order to get the correct anomalous Hall conductivity. The intrinsic $\sigma_{xy}^H$ and the number of valence electrons ($N_e$) have also been calculated as a function of the Fermi energy ($E_F$). A sign change is predicted at $E_F = -0.38$ eV ($N_e = 9.57$), and this explain qualitatively why the theoretical and experimental $\sigma_{xy}^H$ values for Fe and Co are positive. It is also predicted that fcc Ni$_{(1-x)}$Co(Fe,Cu)$_x$ alloys with $x$ being small, would also have the negative $\sigma_{xy}^H$ with the magnitude being in the range of $500\sim 1400$ $\Omega^{-1}$cm$^{-1}$. The most pronounced effect of including the on-site Coulomb interaction is that all the $d$-dominant bands are lowered in energy relative to the $E_F$ by about 0.3 eV, and consequently, the small minority spin X$_2$ hole pocket disappears. The presence of the small X$_2$ hole pocket in the GGA calculations is attributed to be responsible for the large discrepancy in the $\sigma_{xy}^H$ between theory and experiment.