Importance of orbital fluctuations for the magnetic dynamics in heavy-fermion compound SmB${}_6$

The emergent dynamical processes associated with magnetic excitations in heavy-fermion SmB${}_6$ are investigated. By imposing multiorbital interactions on a first-principles model, we find the interplay between spin and orbital fluctuations in the $f$ manifold is highly sensitive to local correlations. The magnetic phase diagram constructed at zero temperature reveals quantum critical features with the existence of several competing phases. Within the random phase approximation, we perform a comprehensive study of the spin-spin correlation function, and our results agree with neutron scattering experiments. Spectral weight analysis shows the low energy spin excitations are selectively accompanied by orbital fluctuations, indicating a non-trivial entanglement between the spin and orbital degree of freedom driven by relativistic couplings.