Critical role of magnetic moments in heavy-fermion materials: revisiting mysteries of SmB$_{6}$

Heavy-fermion family exhibits fascinating and often puzzling properties due to the presence of open-shell $f$ ions and the complexity of the associated charge, orbital, and spin degrees of freedom. SmB$_6 $ is a prototypical heavy-fermion compound that is electrically insulating but yet it displays quantum oscillations, which are a telltale signature of the metallic state. Adding to the enigma is the possibility that SmB$_6$ is a topological Kondo insulator. Here, by treating the spin degree of freedom on an equal footing with other degrees of freedom using the parameter-free strongly-constrained and appropriately-normed (SCAN) density functional, we explore the ground-state electronic structure of SmB$_{6}$. A number of competing magnetic phases lying very closely in energy are found, indicating the key role of spin fluctuations in the material. The computed band structure, crystal-field splittings in the $f$-electron complex, the heavy effective electron mass at the Fermi energy, and the large specific heat are all in good agreement with the corresponding experimental results. In particular, our predicted FS explains the experimentally observed bulk quantum oscillations as well as the low electrical conductivity of SmB$_{6}$. The topological Kondo state of SmB$_6$ is shown to be robust regardless of its magnetic configuration. The excellent performance of SCAN in heavy-fermion systems is explained in terms of its ability to treat self-interaction errors and symmetry breaking within the framework of the density functional theory. Our study provides a new approach for modeling heavy-fermion materials.Comment: 14 pages, 7 figures and 1 tabl