No Arabic abstract
The crystal-field (CF) splitting of the $^6H_{5/2}$ Hunds rule ground state of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been determined with high resolution resonant inelastic x-ray scattering (RIXS) at the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large energy range of RIXS allows the crystal-field analysis of a high lying multiplet at about 2.4,eV that has the same total angular momentum $J$ as the ground state so that ambiguities due to the elastic tail can be avoided. We find that the $Gamma_7$ doublet and $Gamma_8$ quartet of the $^6H_{5/2}$ Hunds rule ground state are split by $Delta^{CF}_{^6H_{5/2}}$,=,20$pm$10,meV which sets an upper limit for the 4$f$ band width. This indicates an extremely large mass renormalization from the band structure value, pointing out the need to consider the coefficients of fractional parentage for the hopping of the 4$f$ electrons.
Samarium hexaboride is a topological Kondo insulator, with metallic surface states manifesting from its insulating band structure. Since the insulating bulk itself is driven by strong correlations, both the bulk and surface host compelling magnetic and electronic phenomena. We employed X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) at the Sm M$_{4,5}$ edges to measure surface and bulk magnetic properties of Sm$^{2+}$ and Sm$^{3+}$ within SmB$_6$. We observed anti-alignment to the applied field of the Sm$^{3+}$ magnetic dipole moment below $T = 75$ K and of the total orbital moment of samarium below 30 K. The induced Sm$^{3+}$ moment at the cleaved surface at 8 K and 6 T implies 1.5% of the total Sm as magnetized Sm$^{3+}$. The field dependence of the Sm$^{3+}$ XMCD dichorism at 8 K is diamagnetic and approximately linear. The bulk magnetization at 2 K is however driven by Sm$^{2+}$ Van Vleck susceptibility as well as 1% paramagnetic impurities with $mu_{rm Eff} = 5.2(1)~mu_{rm B}$. This indicates diamagnetic Sm$^{3+}$ is compensated within the bulk. The XAS and XMCD spectra are weakly affected by Sm vacancies and carbon doping while XAS is strongly affected by polishing.
We investigated the crystal-electric field ground state of the 4$f$ manifold in the strongly correlated topological insulator SmB$_6$ using core level non-resonant inelastic x-ray scattering (NIXS). The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the $Gamma_8$ quartet state of the Sm $f^5$ $J$=$5/2$ configuration governs the ground-state symmetry and hence the topological properties of SmB$_6$. Our findings contradict the results of density functional calculations reported so far.
The true topological nature of the Kondo insulator SmB$_6$ remains to be unveiled. Our previous tunneling study not only found evidence for the existence of surface Dirac fermions, but it also uncovered that they inherently interact with the spin excitons, collective excitations in the bulk. We have extended such a spectroscopic investigation into crystals containing a Sm deficiency. The bulk hybridization gap is found to be insensitive to the deficiency up to 1% studied here, but the surface states in Sm-deficient crystals exhibit quite different temperature evolutions from those in stoichiometric ones. We attribute this to the topological surface states remaining incoherent down to the lowest measurement temperature due to their continued interaction with the spin excitons that remain uncondensed. This result shows that the detailed topological nature of SmB$_6$ could vary drastically in the presence of disorder in the lattice. This sensitiveness to disorder is seemingly contradictory to the celebrated topological protection, but it can be understood as being due to the intimate interplay between strong correlations and topological effects.
A necessary element for the predicted topological state in Kondo insulator SmB$_6$ is the hybridization gap which opens in this compound at low temperatures. In this work, we present a comparative study of the in-gap density of states due to Sm vacancies by Raman scattering spectroscopy and heat capacity for samples where the number of Sm vacancies is equal to or below 1 %. We demonstrate that hybridization gap is very sensitive to the presence of Sm vacancies. At the amount of vacancies above 1 % the gap fills in with impurity states and low temperature heat capacity is enhanced.
We report a systematic study of Sm valence in the prototypical intermediate valence compound SmB$_6$. Sm mean valence, $v_{rm Sm}$, was measured by X-ray absorption spectroscopy as functions of pressure ($1<P<13$ GPa) and temperature ($3<T<300$ K). Pressure induced magnetic order (MO) was detected above $P_c = 10$ GPa by resistivity measurements. A shift toward localized $4f$ state with increasing $P$ and/or $T$ is evident from an increase in $v_{rm Sm}$. However $v_{rm Sm}$ at $P_c$ is anomalously far below 3, which differs from the general case of nonmagnetic-magnetic transition in Yb and Ce compounds. From the $T$ dependence of $v_{rm Sm}(P,T)$, we found that $v_{rm Sm}(P,T)$ consists of two different characteristic components: one is associated with low-energy electronic correlations involving Kondo like behavior, and the other with high-energy valence fluctuations.