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 ($\hat{I}”\approx k_B{T}_c\approx$ 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${}_3$.

(main text - 7 pages, 4 figures; supplementary information - 13 pages, 9 figures, to be published in Phys. Rev. B)