Interaction Driven Subgap Spin Exciton in the Kondo Insulator ${\mathrm{SmB}}_6$

Using inelastic neutron scattering, we map a 14 meV coherent resonant mode in the topological Kondo insulator ${\mathrm{SmB}}_6$ and describe its relation to the low energy insulating band structure. The resonant intensity is confined to the $X$ and $R$ high symmetry points, repeating outside the first Brillouin zone and dispersing less than 2 meV, with a $5d$-like magnetic form factor. We present a slave-boson treatment of the Anderson Hamiltonian with a third neighbor dominated hybridized band structure. This approach produces a spin exciton below the charge gap with features that are consistent with the observed neutron scattering. We find that maxima in the wave vector dependence of the inelastic neutron scattering indicate band inversion.

Figure 1

Energy integrated neutron scattering intensity (a),(b),(d) in high symmetry planes. (a) ${}^{154}\mathrm{Sm}{}^{11}{\mathrm{B}}_6$ at 5 K. (b) $\mathrm{La}{}^{11}{\mathrm{B}}_6$ at 5 K. (c) Feynman diagrams illustrating the slave-boson treatment of $f$-electron repulsion within $f\text{−}d$ hybridized bands as described in the main text. (d) Q dependence of ${\chi }_0(\mathbf{Q})|F(\mathbf{Q}){|}^2$, where ${\chi }_0(\mathbf{Q})$ is the Lindhardt susceptibility for the band structure in (e) and $F(Q)$ is the $5d$ electron form factor. (e) Phenomenological band structure within the ($hk0$) plane. Translation from $X$ to $M$ shows the change in band character. Inset: schematic representation of pseudonesting vectors. (f) Smallest unique portion of the Brillouin zone.

Figure 2

Neutron scattering cross section for ${\mathrm{SmB}}_6$ at 5 K along high symmetry directions (inset) (a) from the $\mathrm{\Gamma }$ point and (b) around the Brillouin zone edges. Dashed line shows the dispersion of a slave-boson-mediated exciton.

Figure 3

(a) Dispersion along the high-symmetry path between $X$ and $R$. Vertical lines show bandwidth. (b) Oscillator strength, (c) width and resolution (dashed), and (d) peak energies of the 14 meV mode (line is a lattice-sum fit to guide the eye).

Figure 4

Square of the magnetic form factor of potential scattering centers (lines) and integrated neutron scattering intensity from 12 to 16 meV (symbols) versus $Q$. Each point is integrated over a cubic $Q$-space volume with side lengths of 0.3 rlu. Inset: raw data associated with the three smallest $Q$ points.