Intrinsic Low-Temperature Magnetism in ${\mathrm{SmB}}_6$

By means of new muon spin relaxation experiments, we disentangle extrinsic and intrinsic sources of low-temperature bulk magnetism in the candidate topological Kondo insulator (TKI) ${\mathrm{SmB}}_6$. Results on Al-flux-grown ${\mathrm{SmB}}_6$ single crystals are compared to those on a large floating-zone-grown ${}^{154}\mathrm{Sm}$ ${{}^{11}\mathrm{B}}_6$ single crystal in which a 14 meV bulk spin exciton has been detected by inelastic neutron scattering. Below $\sim 10\mathrm{K}$, we detect the gradual development of quasistatic magnetism due to rare-earth impurities and Sm vacancies. Our measurements also reveal two additional forms of intrinsic magnetism: (1) underlying low-energy ($\sim 100\mathrm{meV}$) weak magnetic moment ($\sim {10}^{-2}{\mu }_B$) fluctuations similar to those detected in the related candidate TKI ${\mathrm{YbB}}_{12}$ that persist down to millikelvin temperatures, and (2) magnetic fluctuations consistent with a 2.6 meV bulk magnetic excitation at zero magnetic field that appears to hinder surface conductivity above $\sim 4.5\mathrm{K}$. We discuss potential origins of the magnetism.

Figure 1

Temperature dependence of the bulk magnetic susceptibility at $H=1\mathrm{kOe}$ for a piece of the FZ-grown ${}^{154}\mathrm{Sm}$ ${{}^{11}\mathrm{B}}_6$ single crystal, a mosaic of 16 of the Al-flux-grown ${\mathrm{SmB}}_6$ single crystals, and one of the Al-flux-grown single crystals studied in Ref. [24].

Figure 2

Representative (a) ZF- and (b) LF-$\mu \mathrm{SR}$ asymmetry spectra recorded on the ${}^{154}\mathrm{Sm}$ ${{}^{11}\mathrm{B}}_6$ single crystal. The LF-$\mu \mathrm{SR}$ spectra were recorded for a field $H_{\mathrm{LF}}=100\mathrm{Oe}$ applied parallel to the initial muon spin polarization. The solid curves through the data points are fits to Eq. (1).

Figure 3

Temperature dependence of the ZF-$\mu \mathrm{SR}$ (solid symbols) and 100 Oe LF-$\mu \mathrm{SR}$ (open symbols) relaxation rate $\lambda$ for the FZ-grown ${}^{154}\mathrm{Sm}$ ${{}^{11}\mathrm{B}}_6$ and Al-flux-grown ${\mathrm{SmB}}_6$ single crystals. (Inset) Temperature dependence of the ZF data for the Al-flux-grown sample at $T\ge 10\mathrm{K}$, shown as an Arrhenius plot in the form $T\ln \lambda$ vs $T$. The green line is a linear fit with intercept $E_a/k_b$.

Figure 4

Field dependence of the relaxation rate $\lambda$ obtained from fits of the LF-$\mu \mathrm{SR}$ asymmetry spectra at (a) 50, (b) 4.5, and (c) 2 K. Note that $\lambda$ is a “pure” exponential relaxation rate in (a), but a stretched-exponential relaxation rate in (b) and (c). The solid green circles and open brown squares in (c) are from fits assuming the ZF values $\beta =0.562$ and $\beta =0.699$, respectively. The open green triangles are results for the ${}^{154}\mathrm{Sm}$ ${{}^{11}\mathrm{B}}_6$ single crystal from fits assuming the ZF value $\beta =0.562$ for the Al-flux-grown sample. The solid red curves in (b) and (c) are fits of the $H_{\mathrm{LF}}>100\mathrm{Oe}$ data for the Al-flux-grown single crystals to Eq. (2).