The influence of the spin-orbit interaction on the thermodynamical properties of SmB$_6$

Strong electron correlations occur very often in the modern solid-state physics The compound SmB$_6$, studied for more than 50 years, is now emerging as a strong candidate for a three-dimensional Kondo topological insulator (TKI) with a well-defined energy gap. The value of the energy gap depends on the experimental method and amounts approximately to 20 meV (=232 K).

On the other hand, the experimentally measured specific heat of SmB$_6$ contains a substantial additional contribution, when we compare it with the experimental results for isostructural LaB6 (the reference system). This excess heat in SmB$_6$ is large because the entropy associated with this excess, up to 300 K, is 19-23 J/K mol f.u. It corresponds to 2.3-2.9 R (where the gas constant R = 8.314 J/(K mol f.u.)). This additional entropy would indicate a number of additional degrees of freedom on the order of 10 to 16, which we interpret as localized energy states. Such large numbers are not at all expected for the Sm$^{2+}$ and Sm$^{3+}$ ions in the classical description of the crystal field states in the $|J, J_z>$ basis. We have noticed that such description somehow assumes the infinite value of the spin-orbit coupling, what we think is incorrect.
In this contribution, we reanalyze experimentally measured specific heat considering a finite value of the spin- orbit coupling. It means that we have changed the description of the Sm ions from the $|J, J_z>$ basis to the description in the $|LSL_zS_z>$ space. The obtained results shown in the figure describes the experimental temperature dependence of the specific heat very well confirming the physical adequacy of the description that has been used. Moreover, we think that our theoretical description is in agreement with inelastic-neutron-scattering (INS) experiments which reveals some in-gap states observing a wide hump of INS intensity below 20 meV.