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Out-of-Plane Spin-Orientation Dependent Magnetotransport Properties in the Anisotropic Helimagnet Cr$_{1/3}$NbS$_2$

Understanding the role of spin-orbit coupling (SOC) has been crucial to controlling magnetic anisotropy in magnetic multilayer films. It has been shown that electronic structure can be altered via interface SOC by varying the superlattice structure, resulting in spontaneous magnetization perpendicular or parallel to the plane. In lieu of magnetic thin films, we study the similarly anisotropic helimagnet Cr$_{1/3}$NbS$_2$, where the spin polarization direction, controlled by the applied magnetic field, can modify the electronic structure. As a result, the direction of spin polarization can modulate the density of states, and in turn affect the in-plane electrical conductivity. In Cr$_{1/3}$NbS$_2$, we found an enhancement of in-plane conductivity when the spin polarization is out-of-plane, as compared to in-plane spin polarization. This is consistent with the increase of density of states near the Fermi energy at the same spin configuration, found from first principles calculations. We also observe unusual field dependence of the Hall signal in the same temperature range. This is unlikely to originate from the non-collinear spin texture, but rather further indicates strong dependence of electronic structure on spin orientation relative to the plane.