Hydrostatic Pressure-Induced Anomalous Hall Effect in Co$_{2}$FeSi Semimetal

Abstract

The Weyl points and nodal line emerge in the momentum space due to symmetry protected state in topological semimetal(TSM) materials and these materials hold significance due to their unusual anomalous transport properties. In this manuscript, we study the topological properties of the electronic band structure of a half-metallic ferromagnet Co$_{2}$FeSi employing the ab-initio DFT method and show that it is a strongly correlated material. The experimentally observed magnetic properties can be explained in terms of the Slater-Pauling (SP) rule and our calculations are consistent with it. We also investigate the band topology of Co$_{2}$FeSi and find that there are three topological nodal lines at 380 meV above Fermi Energy (\textit{E$_F$}). The degeneracy of these nodal lines is perturbed upon introducing spin-orbit coupling with magnetization along [001] direction. However, some points still preserve degeneracy and are identified as Weyl points, each associated with a specific Chern number. At the ambient pressure, the AHC properties of this material have only extrinsic contribution which is consistent with the experimental results. To make the AHC intrinsic, we tune the position of the nodal line close to the Fermi energy by applying the hydrostatic pressure up to 26 GPa. We also discuss crystal symmetries and their relation with nodal lines and Weyl points.