Suppression of magnetic excitations near the surface of the topological Kondo insulator ${\mathrm{SmB}}_6$

We present a detailed investigation of the temperature and depth dependence of the magnetic properties of the three-dimensional topological Kondo insulator ${\mathrm{SmB}}_6$, in particular, near its surface. We find that local magnetic field fluctuations detected in the bulk are suppressed rapidly with decreasing depths, disappearing almost completely at the surface. We attribute the magnetic excitations to spin excitons in bulk ${\mathrm{SmB}}_6$, which produce local magnetic fields of about $\sim 1.8\mathrm{mT}$ fluctuating on a time scale of $\sim 60\mathrm{ns}$. We find that the excitonic fluctuations are suppressed when approaching the surface on a length scale of $\sim 40–90\mathrm{nm}$, accompanied by a small enhancement in static magnetic fields. We associate this length scale to the size of the excitonic state.

Figure 1

ZF-$\mu \mathrm{SR}$ spectra obtained at different temperatures and implantation energies. The solid lines are fits to Eq. (1).

Figure 2

Muon implantation profiles in ${\mathrm{SmB}}_6$, calculated using trim.sp for various implantation energies.

Figure 3

Temperature dependence of the dynamic muon spin relaxation rate $\lambda$ for different muon implantation energies. The solid lines are guides to the eye.

Figure 4

The relaxation rates $\lambda$ at $\sim 4.5\mathrm{K}$ (red, left axis) and $\sigma$ (blue, right axis) as a function of muon implantation depth in ${\mathrm{SmB}}_6$. The dashed lines are guides to the eye and the dotted vertical lines indicate the different $E$ values.

Figure 5

The relaxation rate $\lambda$ at $1.8\mathrm{K}$ as a function of applied field [32]. The solid line is the fit described in the text.