Two-dimensional ferromagnetic spin-orbital excitations in honeycomb VI 3

${\mathrm{VI}}_{3}$ is a ferromagnet with planar honeycomb sheets of bonded ${\mathrm{V}}^{3+}$ ions held together by van der Waals forces. We apply neutron spectroscopy to measure the two-dimensional ($J/{J}_{c}\ensuremath{\approx}17$) magnetic excitations in the ferromagnetic phase, finding two energetically gapped ($\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}{k}_{B}{T}_{c}\ensuremath{\approx}55\phantom{\rule{0.28em}{0ex}}\mathrm{K}$) and dispersive excitations. We apply a multilevel spin-wave formalism to describe the spectra in terms of two coexisting domains hosting differing ${\mathrm{V}}^{3+}$ orbital ground states built from contrasting distorted octahedral environments. This analysis fits a common nearest-neighbor in-plane exchange coupling ($J=\ensuremath{-}8.6\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$) between ${\mathrm{V}}^{3+}$ 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 ${\mathrm{VI}}_{3}$.