Magnetoelastic honeycomb fragmentation in VI$_{3}$

TL;DR

This work investigates the magnetoelastic coupling and spin–orbit–driven magnetism in the two-dimensional van der Waals magnet VI$_3$. By combining neutron and x-ray diffraction with a Green's function (RPA) treatment of spin–orbit–entangled single-ion states, the authors show a single structural transition at $T_S\sim80$ K from rhombohedral $R\overline{3}$ to a triclinic phase ($P\overline{1}$ or $P1$), followed by a ferromagnetic transition at $T_C\sim50$ K, accompanied by notable magnetostriction. The symmetry breaking yields two crystallographically inequivalent V$^{3+}$ sites, effectively fragmenting the honeycomb lattice into two interpenetrating hexagonal planes; this fragmentation provides a natural explanation for the two observed magnetic modes and highlights the central role of magnetoelastic coupling and orbital degrees of freedom in 2D VI$_3$. While a subset of powders shows additional features near $\sim30$ K, the authors argue these arise from stacking motifs rather than intrinsic symmetry changes, offering a stacking-dependent perspective on low-temperature behavior. Overall, the study establishes a magnetoelastic, two-site framework that reconciles diffraction, spectroscopy, and theory for VI$_3$ and points to rich stack-related physics in 2D magnets.

Abstract

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.

Figures (10)

• Figure 1: The $(a)$, crystal structure of VI$_3$ in the $a-b$ plane together with the $(b)$, unit cell of VI$_3$ emphasizing the stacking of the honeycomb sheets. A plot of the $(c)$ single-ion splitting due to spin-orbit coupling, tetragonal distortion and the molecular field is also presented. The lowest energy dipole allowed transitions are indicated by the arrow.
• Figure 2: The temperature dependence of the the $\vec{Q}$=(1,1,0) Bragg peak taken on $(a)$ MACS and $(b)$ SPINS with scans in A3. The ferromagnetic transition T$_{c}$ and the structural transition are denoted by dashed lines.
• Figure 3: Structural transition in crushed VI$_3$ single crystals. $(a-b)$ Temperature evolution of the (3,0,0) Bragg peak showing the $R\overline{3}$ to $P\overline{1}$ transition at $\sim$ 80 K (Smartlab) and $\sim$ 70 K (ESRF). $(c-e)$ Representative diffraction patterns showing: $(c)$ high-temperature R$\overline{3}$ phase, $(d)$ intermediate $P\overline{1}$ phase, and $(e)$ fully split low-temperature $P\overline{1}$ pattern. The $\sim$ 50 K anomaly corresponds to magnetostriction at T$_C$.
• Figure 4: Structural characterization of VI$_{3}$ powder samples. $(a-b)$ Le Bail refinements confirming $R\overline{3}$ to $P\overline{1}$ transition. $(c-h)$ Sample-dependent behavior: Sample A (400°C quench): $\sim$ 80 K transition to $P\overline{1}$. Sample B (500°C slow-cool): $\sim$ 30 K transition with weak splitting. Sample C (400°C slow-cool): Coexistence of both transitions ($\sim$ 80 K main + $\sim$ 30 K secondary splitting). The variable transition temperatures suggest stacking-dependent polymorphism.
• Figure 5: Diffraction patterns revealing sample-specific structural features. $(a)$ Comparative 100 K patterns showing overall phase consistency, with red boxes highlighting distinctive features in Sample B. $(b)$ Two characteristic peaks at (1 0 1) and (1 0 -2) unique to Sample B, suggesting possible stacking faults. $(c)$ The (0 0 12) reflection appearing exclusively in Sample B.