Electronic Energy Scales of Cr$X_3$ ($X$ = Cl, Br, and I) using High-resolution X-ray Scattering

TL;DR

This work addresses the challenge of obtaining precise electronic-energy scales that govern magnetism in Cr$X_3$ 2D magnets. It combines ultra-high-resolution Cr $L$-edge RIXS with ligand-field multiplet theory in a distorted $C_3$ octahedral framework to extract $10Dq$, Racah parameters ($B$, $C$), and crystal-field distortions ($D\\sigma$, $D\\tau$), including spin-orbit effects. The authors report the first clear energy separation between spin-quartet and spin-doublet states in Cr$X_3$, demonstrate halogen-dependent trends (CrCl$_3$ to CrI$_3$) in these energy scales, and show that SOC in Cr $2p$ is essential to access spin-flip excitations. These results provide energy-design principles for spintronic devices based on 2D Cr$X_3$ and establish a rigorous spectroscopic route to refine electronic structure parameters in TM halides.

Abstract

Chromium tri-halides Cr$X_3$ ($X$ = Cl, Br, and I) have recently become a focal point of research due to their intriguing low-temperature,layer-dependent magnetism that can be manipulated by an electric field. This makes them essential candidates for spintronics applications. These magnetic orders are often related to the electronic structure parameters, such as spin-orbit coupling (SOC), Hund's coupling ($J_H$), $p-d$ covalency, and inter-orbital Coulomb interactions. Accurately determining such parameters is paramount for understanding Cr$X_3$ physics. We have used ultra high-resolution resonant inelastic x-ray scattering (RIXS) spectroscopy to study Cr$X_3$ across phase transition temperatures. Ligand field multiplet calculations were used to determine the electronic structure parameters by incorporating the crystal field interactions in a distorted octahedral with $C_3$ symmetry. These methods provide the most detailed description of Cr$X_3$ magneto-optical and electronic energetic (terms) to date. For the first time, the crystal field distortion parameters $Dσ$ and $Dτ$ were calculated, and the energies of $d$ orbitals have been reported. Our RIXS spectroscopic measurements reveal a clear energy separation between spin-allowed quartet states and spin-forbidden doublet states in Cr$X_3$. The role of SOC in Cr $2p$ orbitals for the spin-flip excitations has been demonstrated. The determined 10$Dq$ values are in good agreement with the spectrochemical series, and Racah B follows the Nephelauxetic effect. Such precise measurements offer insights into the energy design of spintronic devices that utilize quantum state tuning within 2D magnetic materials.

Figures (7)

• Figure 1: (a) Lattice structure of Cr$X_3$. The metal Cr and halide ions (X = Cl, Br, and I) are shown in green and red, respectively. (b) The schematic diagram illustrates the experimental setup for RIXS measurements. $k_{in}$ and $k_{out}$ are the incident and scattered photon beam wave vectors. (c) Cr $L$-edge XAS measurements on Cr$X_3$ ($X$ = Cl, Br, and I). The photon energies labeled a, b and c were used as the excitation energies in the RIXS measurements.
• Figure 2: (a) Cr $L_3$-edge RIXS data measured in Cr$X_3$ at 300 K and (b) at 24 K. The RIXS data have been collected at three different excitation energies: a, b, and c (see Figure \ref{['fig: Experimental_setup']}(c)). The three regions, I, II, and III, show different spectral features in RIXS spectra. (c) Temperature comparison of the RIXS data at Cr $L_3$ edge. Solid (dashed) lines indicate the 300 K (24 K) RIXS data.
• Figure 3: (a) valence $d$ orbital electron distribution in Cr$^{3+}$ metal ion. (b) Lifting of degeneracy of the $d^{3+}$ spectroscopic term (free $F^{4+}$ ion) due to $O_h$ symmetry. This configuration’s 5 $d$ orbitals are divided into two energy levels $t_{2g}$ and $e_g$. (c) Lifting of the degeneracy of the $d^{3+}$ electrons due to $C_3$ symmetry. The five $d$ orbitals are divided into one $a$ state and two $e$ states within the $C_3$ symmetry.
• Figure 4: (a) Energy level diagrams as a function of crystal field $Dq$ (b) Racah B and (c) Racah C in CrI$_3$. The quartet and doublet states in Cr$^{3+}$ metal are shown by solid red and dashed blue lines, respectively. The black, green, and purple stars indicate the extracted $Dq$, Racah B, and Racah C values by comparing the ELDs with experimental RIXS spectra. (d) Calculated RIXS map recorded at 300 K. A broadening of 30 meV was considered, similar to the experimental resolution.
• Figure 5: Comparison of experimental and simulated RIXS spectra at Cr $L_3$ edge (a)-(c) at 300 K and (d) - (f) at 24 K in CrCl$_3$, CrBr$_3$, and CrI$_3$, respectively. In each figure, the top panel and the middle panels show the experimental and simulated RIXS spectra at the Cr $L_3$ edge. Bottom panel indicates the spectroscopic term labels given in $C_3$ symmetry, analogous to the middle panel.