Magnetoelastic honeycomb fragmentation in VI$_{3}$

The discovery of ordered magnetism in two-dimensional van der Waals materials at the monolayer limit challenges the Mermin-Wagner theorem, which forbids spontaneous breaking of continuous symmetries in two dimensions at finite temperatures. The persistence of static magnetism in low-dimensions is fundamentally influenced by magnetic anisotropy and the local single-ion crystalline electric field. Crucially, spin-orbit coupling connects the structural properties with spin degrees of freedom. We investigate the magnetic single-ion properties in the van der Waals magnet VI$_3$. Utilizing neutron and x-ray diffraction, we map out the symmetry breaking phase transitions and argue for a single structural transition at T$_S \sim$ 80 K, driven by an orbital degeneracy, followed by a ferromagnetic transition at a lower temperature, T$_C \sim$ 50 K. Through a comparative analysis of samples prepared under varying conditions, we suggest that lower temperature transitions reported near $\sim$ 30 K are not intrinsic to VI$_{3}$. A group theoretical analysis suggests a structural transition from rhombohedral $R\overline{3}$ to triclinic $P\overline{1}$ or $P1$. This transition is significant as it suggests the formation of two distinct crystallographyically inequivalent V$^{3+}$ sites, each with distinct spin-orbital properties. Neutron spectroscopy provides evidence for dominant magnetic exchange coupling only between symmetry-equivalent sites in the triclinc unit cell. We suggest this breaks up the low-temperature honeycomb VI$_3$ lattice into two interpenetrating approximately hexagonal planes resulting in a fragmentated honeycomb. Our findings highlight the critical role of magnetoelastic coupling in determining the magnetic and structural phases in two-dimensional van der Waals magnets.