Correlation induced magnetic topological phases in the mixed-valence compound SmB_{6}

SmB_{6} is a mixed-valence compound with flat f-electron bands that have a propensity to magnetism. Here, using a realistic Γ_{8} quartet model, we investigate the dynamical spin susceptibility and describe the in-gap collective mode observed in neutron scattering experiments. We show that as the Sm valence increases with pressure, the magnetic correlations enhance and SmB_{6} undergoes a first-order phase transition into a metallic antiferromagnetic state, whose symmetry depends on the model parameters. The magnetic orderings give rise to distinct band topologies: while the A-type order leads to an overlap between valence and conduction bands in the form of Dirac nodal lines, the G-type order has a negative indirect gap with weak Z_{2} indices. We also consider the spin polarized phase under a strong magnetic field, and find that it exhibits Weyl points as well as nodal lines close to the Fermi level. The magnetic phases show markedly different surface states and tunable bulk transport properties, with important implications for experiments. Our theory predicts that a magnetic order can be stabilized also by lifting the Γ_{8} cubic symmetry, thus explaining the surface magnetism reported in SmB_{6}.