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

The emergent dynamical processes associated with magnetic excitations in heavy-fermion ${\mathrm{SmB}}_6$ 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 nontrivial entanglement between the spin and orbital degree of freedom driven by relativistic couplings.

Figure 1

Electronic structure plots contrasting local-density approximation and Wannier projection. (a) Band structure; (b) density of states.

Figure 2

Schematic magnetic phase diagram of ${\mathrm{SmB}}_6$ obtained by mean-field treatment of first-principles Wannier projection.

Figure 3

Longitudinal spin response spectrum for selected scattering vectors of INS data of Ref. [14]. Note the spectra have been scaled differently.

Figure 4

Top: The sum of the transverse function for $T=1\mathrm{K}, U=1\mathrm{eV}, J=U/10$. Bottom: trace of the transverse function for $T=1\mathrm{K}, U=1\mathrm{eV}, J=U/10$.

Figure 5

Scattering at $q=(0,0.695,0.695)$ as a function of interaction for $T=2\mathrm{K}, J=U/5$. (a) The sum of the longitudinal function. (b) The trace of the longitudinal function.