Possible surface magnetism in the topological Kondo insulator candidate FeSi

Our group has previously reported the existence of a conducting surface state (CSS) in FeSi, a candidate for a $d$-electron topological Kondo insulator (TKI), at low temperature. In this paper, we present the electrical transport properties of single crystals of FeSi studied in the phase space of temperature ($T$), magnetic field ($B$), and the angle (\ensuremath{\theta}) between the electrical current and $B$. The normalized $T$-dependent electrical resistance ($R$) of a successively thinned FeSi crystal provides further confirmation of the existence of a CSS. We report that, in the CSS, the magnetoresistance (MR) exhibits a hysteresis loop bounded within $\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.28em}{0ex}}\mathrm{T}$, suggesting two-dimensional magnetic ordering. The hysteretic MR is asymmetric in $B$ and anisotropic with respect to \ensuremath{\theta}. Further exploration of $R(\ensuremath{\theta})$ at a fixed field of 9 T reveals an initial progressive rotation of the axis for twofold rotational symmetry from 2 to 10 K, then a stabilized axis for twofold symmetry until, at $T>40\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, the anisotropy vanishes, coincident with the disappearance of the CSS. These observations point to a possible magnetically ordered surface state that has been reported in similar systems such as FeSi nanofilms and bulk ${\mathrm{SmB}}₆$.