Two-dimensional ferromagnetic spin-orbital excitations in the honeycomb VI$_{3}$

Abstract: VI${3}$ is a ferromagnet with planar honeycomb sheets of bonded V$^{3+}$ ions held together by van der Waals forces. We apply neutron spectroscopy to measure the two dimensional ($J/J{c} \approx 17$) magnetic excitations in the ferromagnetic phase, finding two energetically gapped ($\Delta \approx k_{B} T_{c} \approx$ 55 K) and dispersive excitations. We apply a multi-level spin wave formalism to describe the spectra in terms of two coexisting domains hosting differing V$^{3+}$ orbital ground states built from contrasting distorted octahedral environments. This analysis fits a common nearest neighbor in-plane exchange coupling ($J$=-8.6 $\pm$ 0.3 meV) between V$^{3+}$ sites. The distorted local crystalline electric field combined with spin-orbit coupling provides the needed magnetic anisotropy for spatially long-ranged two-dimensional ferromagnetism in VI$_{3}$.