Orbital mixing as key ingredient for magnetic order in a van der Waals ferromagnet

Abstract

Recent years have seen a vast increase in research into van der Waals magnetic materials. In many of these systems, magnetism is introduced via light 3\textit{d}-transition metal elements, combined with chalcogenides or halogens. Despite the high technological promise in the field of spintronics, the connection between the \textit{d}-orbital configuration and the occurrence of low-dimensional magnetic order is currently unclear. Here we address the prototypical two-dimensional ferromagnet CrI\textsubscript{3}, via complementary spectroscopies and density functional theory calculations. We reveal the electronic structure and orbital character of bulk CrI\textsubscript{3} in the paramagnetic and ferromagnetic phases, describing the couplings underpinning its energy diagram, and providing a robust experimental demonstration that the mechanism of stabilization of ferromagnetism is attributable to orbital mixing between I \textit{p} and Cr \textit{e\textsubscript{g}} states. These findings reveal the microscopic connection between orbital and spin degrees of freedom, providing fundamental insights into the behavior of low-dimensional magnetic materials.

Figures (4)

• Figure 1: (a) Top and side hard sphere view of CrI3 crystal structure, where each Cr centre is coordinated by six I atoms. (b) Bulk first Brillouin zone of CrI3 and corresponding surface projection; high-symmetry points are indicated in both cases. (c) Crystal field splitting and nominal electron filling for Oh symmetry. (d) Photoemission intensity (greyscale, darker represents higher electron count) of the isoenergetic ($k_x$, $k_y$) surface at $E-E_{VBM}=-0.1\eV$, at $h\nu=21.7\eV$ photon energy and $T=300K$. The red overlay highlights high-symmetry points and lines. (e) ARPES (E, k) spectrum of CrI3 valence band dispersion along high-symmetry lines in the same experimental conditions as (d). (f) The spectral function $A({\bf k}, E)$ of the paramagnetic state calculated with DFT.
• Figure 2: (a) ARPES (E, k) spectra along the $\bar{\mathrm{K}}-\bar{\Gamma}-\bar{\mathrm{K}}$ direction, at 21.7 (left, out of resonance) and 49 (right, at resonance), at 300. (b) $k$-integrated EDCs of the spectra in (a): out of resonance is teal, at resonance is blue. Arrows mark the two prominent increases in intensity. (c) Cr 3d bands calculated with DFT in the PM state. (d) Atomic-orbital projected density of states in the PM state. Areas shaded in green highlight the local maxima of Cr 3d states, as described in the main text.
• Figure 3: XAS spectra across the Cr L2,3 edges, acquired with left and right circularly polarized photons, and corresponding XMCD, at 90 (top) and at 30 (bottom). The inset shows the experimental geometry.
• Figure 4: (a) ARPES (E, k) spectra along the $\bar{\mathrm{K}}-\bar{\Gamma}-\bar{\mathrm{K}}$ direction, at $T=300\K$ and $T=30\K$. (b) EDCs at $\bar{\Gamma}$ as a function of temperature. The inset enhances the VBM region to highlight the change in slope. (c) EDCs at $\bar{\Gamma}$ at 300 (left) and at 50 (right). The black line is a multipeak fit as described in the main text. The colored Gaussians represent the spectral features splitting below $T_C$. (d) Calculated pDOS of the band structure in the PM (left) and FM (right) phases projected on Cr d and I p orbitals, showing the main contribution in the presented energy range. (e) Collinear DFT calculations highlighting the up- and down-spin projections of the pDOS in the near-Fermi region.