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Interplay of Orbital Degeneracy and Vacancies in Stabilizing Collinear Magnetic Order in Cr$_{1+δ}$Te$_2$

Prasanta Chowdhury, Jyotirmoy Sau, Mohamad Numan, Jhuma Sannigrahi, Matthias Gutmann, Gangadhar Das, D. T. Adroja, Saurav Giri, Manoranjan Kumar, Subham Majumdar

Abstract

Cr$_{1+δ}$Te$_2$, a two-dimensional van der Waals ferromagnet, displays a contested magnetic structure, poised between collinear and non-collinear spin configurations. In this work, we investigate the magnetic structure of Cr$_{1.33}$Te$_2$ at the microscopic level by combining single-crystal neutron diffraction, X-ray absorption spectroscopy, and first-principles calculations. Neutron diffraction measurements reveal a distinct collinear spin alignment, whereas spectroscopic analyses reveal inherent structural vacancies at both Cr and Te sites. These vacancies lead to local symmetry breaking that elevates the orbital degeneracy of the Cr 3$d$ states, as demonstrated by our first-principles analysis. The resulting modification of magnetocrystalline anisotropy emerges as the key mechanism stabilising the collinear magnetic ground state over the non-collinear one in the presence of vacancies. Our findings uncover a vacancy-driven route to control spin anisotropy and magnetic ordering in layered ferromagnets, offering new insights into the design of tunable 2D magnetic materials.

Interplay of Orbital Degeneracy and Vacancies in Stabilizing Collinear Magnetic Order in Cr$_{1+δ}$Te$_2$

Abstract

CrTe, a two-dimensional van der Waals ferromagnet, displays a contested magnetic structure, poised between collinear and non-collinear spin configurations. In this work, we investigate the magnetic structure of CrTe at the microscopic level by combining single-crystal neutron diffraction, X-ray absorption spectroscopy, and first-principles calculations. Neutron diffraction measurements reveal a distinct collinear spin alignment, whereas spectroscopic analyses reveal inherent structural vacancies at both Cr and Te sites. These vacancies lead to local symmetry breaking that elevates the orbital degeneracy of the Cr 3 states, as demonstrated by our first-principles analysis. The resulting modification of magnetocrystalline anisotropy emerges as the key mechanism stabilising the collinear magnetic ground state over the non-collinear one in the presence of vacancies. Our findings uncover a vacancy-driven route to control spin anisotropy and magnetic ordering in layered ferromagnets, offering new insights into the design of tunable 2D magnetic materials.

Paper Structure

This paper contains 17 sections, 23 equations, 12 figures, 7 tables.

Table of Contents

  1. Experimental techniques
  2. Sample characterization
  3. Laue neutron diffraction pattern
  4. Symmetry allowed magnetic structures
  5. Magnetic structure refinement
  6. Temperature dependent magnetic data
  7. Perpendicular magnetic anisotropy
  8. Theoretical study
  9. Computational details
  10. Ground- and Excited-State Energy Landscapes of WoV and WV States
  11. Onsite energy extraction from Wannier functions
  12. Octahedral geometry
  13. Perturbative Spin-Orbit Coupling Formalism for MAE
  14. Hamiltonian Matrix Representation Before and After Spin–Orbit Coupling
  15. WoV system
  16. ...and 2 more sections

Figures (12)

  • Figure 1: Classification of magnetic structures in Cr-Te systems: collinear and non-collinear, based on theoretical and experimental study.
  • Figure 2: (a), (b), and (c) show the $(h~k~0)$ layer of Cr$_{1+\delta}$Te$_2$ measured on SXD at $T = 300$, 140, and 4.5 K, respectively. Laue symmetry $\overline{3}m$ has been applied.
  • Figure 3: (a), (b) Temperature evolution of integrated intensity of some selected Bragg peaks (0 -1 0), (0 0 -1) and (-1 1 0). (c) Calculated (F$_{cal}$) vs observed (F$_{obs}$) structure factors with linear fit at $T=$ 4.5 K (nuclear+magnetic reflections) respectively. (d) Magnetic structure of Cr$_{1+\delta}$Te$_2$ at $T=$ 4.5 K.
  • Figure 4: (a) Normalized XAS spectra of Cr$_{1+\delta}$Te$_2$ and Cr foil measured at the Cr K-edge. The inset (i) shows the enlarge view of the XANES region. (b) Fourier transform of the experimental EXAFS data (black circles) along with the best-fit curve (solid red line). The magnitude ($|FT|$) and imaginary component ($I{\text{mm}}$) have been labeled and vertically shifted for clarity. (c) $k^3$-weighted Cr K-edge EXAFS spectra in $k$-space (black circles) together with the corresponding best-fit curve (solid red line). The contributions from individual single-scattering paths, labeled by the scattering atom and its distance from the absorber.
  • Figure 5: (a) Magnetic configurations of Cr$_{10}$Te$_{16}$ (Cr$_{1.25}$Te$_2$) and vacancy-containing Cr$_8$Te$_{12}$ (Cr$_{1.33}$Te$_2$). The upper-right panel shows the zoomed layer of the vacancy-free system, while the lower panel depicts the favorable configuration with vacancy. (b) Partial density of states (PDOS) of Cr $d$ orbitals for spin-up and spin-down channels. (c) Occupancy of different $d$ orbitals for spin-up and spin-down channels. (d) Normalized magnetocrystalline anisotropy energy (MAE) in spherical polar coordinate space. (e) MAE in different planes as a function of the polar angle, along with the experimental data presented with black symbols and dotted line. (f) Orbital-pair resolved contributions to the MAE in the presence of SOC.
  • ...and 7 more figures