Anisotropy of Skyrmion Lattice in Mn$_{0.9}$Fe$_{0.1}$Si probed by magnetic field orientation dependence of the topological Hall effect and magnetoresistance

We report the magnetic field orientation dependence of the topological Hall effect (THE) and magnetoresistance (MR) of Mn$_{0.9}$Fe$_{0.1}$Si in the $A$-phase within the applied magnetic field ($H$) – temperature ($T$) phase diagram. In the $A$-phase a two dimensional Skyrmion lattice is formed in the plane perpendicular to the direction of $H$, which is responsible for the observed THE signal. At a given $T$ within the $A$-phase, we investigated the angular dependence of THE and MR at a fixed $H$ to probe the boundaries of the $A$-phase region. We find the MR signal exhibits a unique $H$-direction dependence at the entering and exiting of the $A$-phase, whereas, in the middle $H$ range, i.e. in the core of $A$-phase, the angular dependence is consistent with what is expected from a perfect 2D Skyrmion lattice. However, THE signals show extreme sensitivity upon entering the $A$-phase and unexpected angular dependence, yet did not leave any trace through exiting. The discrepancy between the angular dependence of MR and THE signals at the $A$-phase boundaries indicates a crucial role of Fe impurities as pinning centers for the Skyrmions. We will discuss further our $H$-orientation dependence of the THE, compared to sweeping $H$ at a fixed angle in Fe doped MnSi.