Enhancing ferromagnetic coupling in CrXY (X = O, S, Se; Y = Cl, Br, I) monolayers by turning the covalent character of Cr-X bonds

The development of two-dimensional (2D) spintronic devices requires materials with strong magnetic exchange interactions and Curie temperatures (TC) at or above room temperature. While intrinsic 2D ferromagnets such as CrI3 and CrGeTe3 have been discovered, their experimental TC values (around 45 K and 20 K, respectively) remain far below room temperature, motivating the search for 2D ferromagnetic semiconductors with higher TC. In transition-metal semiconductors, magnetic cations couple through nonmagnetic anions primarily via kinetic (superexchange) mechanisms, whose sign and magnitude are governed by crystal symmetry and orbital hybridization. Under near-90° cation-anion-cation angles, ferromagnetic (FM) exchange is favored, and the strength of coupling grows with the covalent admixture between cation d and anion p orbitals, which depends on their energy separation. This study investigates 1T-phase chromium chalcogenide-halide monolayers CrXY (X = O, S, Se; Y = Cl, Br, I) in the CrCl2 structure, aiming to identify stable FM semiconductors with enhanced exchange coupling and elevated TC by tuning the covalent character of Cr–X bonds through orbital energy alignment.

The paper situates its work within the context of recent discoveries of intrinsic 2D ferromagnetism (e.g., CrI3) and the broader goals of spintronics (low-power, high-speed, high-density information technologies). Reported 2D ferromagnetic semiconductors have sub-room-temperature TC (CrI3 ~45 K; CrGeTe3 ~20 K). Theoretical frameworks by Goodenough, Kanamori, and Anderson establish that superexchange depends on geometry and orbital symmetry, favoring FM coupling near 90° cation-anion-cation angles. Prior studies emphasize the importance of p–d covalency and orbital energy differences in determining exchange strength. The study builds on these principles to propose enhancing FM coupling in CrXY monolayers by increasing the covalent contribution of Cr–X bonds via reducing p–d energy gaps.

Spin-polarized density functional theory (DFT) calculations were performed using the PAW method within VASP. Exchange-correlation was treated with GGA (PBE) and GGA+U for Cr-3d orbitals with U = 3.0 eV. A plane-wave cutoff of 500 eV was used. Geometry optimizations employed convergence criteria of 1e-5 eV (energy) and 0.01 eV/Å (forces); electronic self-consistent calculations used tighter criteria of 1e-7 eV and 0.001 eV/Å. A vacuum spacing of 15 Å avoided interlayer interactions. Monkhorst-Pack k-point meshes of 10×10×1 (structural optimization) and 15×15×1 (electronic/magnetic properties) were used for unit cells. Phonon dispersions were computed via finite displacements using PHONOPY on 4×4×1 supercells. Thermal stability was assessed by NPT molecular dynamics (Forcite) at 300 K for 20 ps with a 2 fs time step. Mechanical stability was evaluated via elastic constants against Born stability criteria. Magnetic ground states were determined by comparing energies of several spin configurations (FM, AFM-1, AFM-2, AFM-3) and by calculating total energy as a function of magnetic propagation vector q using the generalized Bloch theorem (gBT). Magnetic anisotropy energy (MAE) was obtained by comparing energies for different spin orientations (in-plane vs out-of-plane). Magnetic exchange parameters (nearest J1, second-nearest J2, third-nearest J3) were extracted using the four-state method. The microscopic mechanism of superexchange was analyzed with a minimal Hamiltonian including on-site energies, Coulomb repulsion, and p–d hybridization, identifying allowed hopping channels via Slater–Koster integrals. Wannier projections (Wannier90) provided orbital-resolved energies (Δ1 = Eeg − Ep, Δ2 = Et2g − Ep, ΔCF = Eeg − Et2g) and hopping parameters to interpret trends. Curie temperatures were estimated using Monte Carlo simulations (Metropolis) of a fully anisotropic Heisenberg model on 32×32×1 lattices (mcsolver), extracting TC from peaks in specific heat; methodology was validated by reproducing literature TC for monolayer CrI3 using reported exchange parameters.

- Structural and thermal stability: Phonon spectra show no imaginary modes for all CrXY monolayers except CrOI, indicating dynamical stability; MD at 300 K for 20 ps shows stable morphologies; elastic constants satisfy Born criteria, confirming mechanical stability. - Magnetic ground state: For all dynamically stable CrXY monolayers, FM is the lowest-energy state. Relative energies (meV/Cr) of AFM states above FM span from ~1.36 meV (e.g., AFM-3 in CrOBr) up to ~204 meV (AFM-1 in CrSCl), confirming robust FM preferences across compositions. - Electronic structure: All stable CrXY monolayers are ferromagnetic semiconductors. Cr-3d splits into t2g (lower, half-occupied) and eg (higher, partially occupied/empty) levels in an octahedral crystal field. Net moment ≈ 3 μB per formula unit, consistent with high-spin d3 Cr3+. - Magnetic anisotropy: All systems exhibit finite MAE enabling long-range FM order; easy axis is out-of-plane for most compounds, while CrSeCl and CrSeBr favor in-plane magnetization. - Exchange interactions: Nearest-neighbor J1 is dominant and positive, driving FM order; J2 is small positive; J3 is small negative. Representative values (meV): J1 increases from ~1.43 (CrOBr)–3.11 (CrOCl) to ~11–13 for S/Se-based compounds (e.g., CrSCl 11.64; CrSBr 11.66; CrSI 11.05; CrSeCl 11.33; CrSeBr 12.53; CrSeI 13.12). J2 ranges ~0.05–0.51 meV; J3 ranges about −0.60 to −1.63 meV. - Mechanism: FM superexchange arises via eg–p–t2g hopping under near-90° Cr–X/Y–Cr angles and three-fold rotational symmetry; AFM channels (t2g–p–t2g or eg–p–eg) are suppressed for two-step hopping. Exchange polarization via the anion pσ orbital stabilizes FM alignment of neighboring Cr spins. - Covalency tuning: Decreasing the energy separations Δ1 (Eeg − Ep), Δ2 (Et2g − Ep), and ΔCF (Eeg − Et2g) enhances p–d covalency and strengthens J. Substituting O with S/Se significantly reduces Δ1 (from ~2 eV to ≲1 eV), markedly increasing J1; changes from Cl→Br→I are comparatively minor. Charge-density differences show increased interstitial density between Cr and S/Se vs Cr–O, evidencing stronger covalency. - Curie temperatures: Predicted TC values for CrSY and CrSeY monolayers approach or exceed room temperature due to larger exchange; the highest TC is 334 K for CrSeI. Applying ~10% tensile strain further raises TC of CrSeI to 409 K. For CrOI and CrOBr, TC was extracted from specific heat peaks within the MC framework. - Robustness checks: Varying U (1–2.5 eV) qualitatively preserves trends in exchange parameters; model–DFT discrepancies in absolute J are reconciled by including interorbital Coulomb repulsion (Uinter) in an effective Δeff.

The study addresses the challenge of achieving room-temperature 2D ferromagnetism by identifying a symmetry- and chemistry-driven pathway to enhance FM superexchange in CrXY monolayers. The three-fold rotational symmetry and near-90° Cr–X/Y–Cr bond angle enable an eg–p–t2g superexchange channel that intrinsically favors FM coupling. By reducing the energy mismatch between anion p and Cr eg/t2g orbitals—primarily via substituting O with heavier chalcogens (S, Se)—the covalent hybridization is strengthened, leading to larger J1 and elevated TC. The analysis of orbital energy differences (Δ1, Δ2, ΔCF) and charge-density redistribution corroborates the mechanism. The dominant contribution of the Cr–X–Cr path over Cr–Y–Cr explains why chalcogen substitution is more effective than halogen substitution in boosting FM interactions. The combination of DFT, Wannier analysis, model Hamiltonian, and classical MC simulations consistently supports the conclusion that tuning covalency is a viable strategy to achieve room-temperature ferromagnetism in 2D semiconductors, with CrSeI reaching 334 K and further enhanced under tensile strain.

This work predicts and rationalizes a family of 1T-phase chromium chalcogenide-halide monolayers, CrXY (X = O, S, Se; Y = Cl, Br, I), as ferromagnetic semiconductors with robust stability (except CrOI) and tunable Curie temperatures. A symmetry-selected eg–p–t2g superexchange mechanism underpins FM order, and enhancing the covalent character of Cr–X bonds—achieved by reducing p–d energy separations via O→S/Se substitution—substantially strengthens exchange interactions. As a result, TC is elevated to room temperature and beyond, with CrSeI achieving 334 K (and up to 409 K under 10% tensile strain). These findings provide a general strategy for engineering high-TC 2D ferromagnets for spintronic applications. Future research could include experimental synthesis and characterization of predicted monolayers, precise determination of magnetic anisotropy and exchange parameters, exploration of external stimuli (strain, gating, doping), and extension of the covalency-tuning approach to other 2D magnetic material families.

- The dynamic instability of CrOI precludes its inclusion among stable candidates. - DFT results rely on the GGA+U approach with a chosen U value (3.0 eV); while trends are robust to U variations, absolute values of exchange parameters may vary with electronic correlation treatment. - The minimal superexchange model initially neglects interorbital Coulomb repulsion (Uinter), leading to overestimation of J unless an effective Δeff = Δ1 + Uinter is used. - Monte Carlo simulations use a classical Heisenberg model on finite lattices; quantum effects and finite-size effects may influence TC estimates. - Thermal stability tests (MD at 300 K, 20 ps) and elastic criteria indicate stability but do not replace long-term experimental stability assessments. - Effects of defects, substrates, and environmental interactions are not explicitly modeled; strain-enhanced TC is a theoretical prediction pending experimental validation.