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

The discovery of monolayer magnetic materials, such as CrI3, has spurred significant interest in two-dimensional (2D) spintronics. A key challenge is enhancing magnetic exchange interaction to enable room-temperature operation (300 K), as current 2D ferromagnetic semiconductors exhibit Curie temperatures (Tc) far below this threshold (e.g., 45 K for CrI3 and 20 K for CrGeTe3). Magnetic cations in transition-metal semiconductors are separated by nonmagnetic anions, with magnetic coupling primarily involving kinetic exchange (superexchange). This interaction depends on the crystal symmetry and the covalent admixture amplitude of p-d bonds, influenced by the energy difference between p- and d-orbitals. This work explores CrXY (X = O, S, Se; Y = Cl, Br, I) monolayers to investigate how adjusting the covalent character of Cr-X bonds affects ferromagnetic coupling strength and Tc.

Existing research highlights the potential of 2D materials for spintronics, but the low Curie temperatures of known materials hinder practical applications. Several studies have explored different 2D materials and strategies to enhance ferromagnetism, including doping and strain engineering. The Goodenough-Kanamori-Anderson rule and the understanding of superexchange interactions are crucial in predicting and designing materials with desired magnetic properties. Previous theoretical work has focused on predicting 2D ferromagnetic semiconductors, however, achieving high Tc at room temperature remains a significant challenge. This paper builds upon this existing research to investigate a new series of CrXY monolayers and explore the relationship between orbital hybridization and ferromagnetic coupling strength.

First-principles calculations based on the projector augmented wave (PAW) pseudopotentials within the Vienna ab initio simulation package (VASP) were employed. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional and the GGA + U method were used to account for the exchange-correlation effect and strong electron correlation of Cr-3d orbitals (U = 3.0 eV). A cutoff energy of 500 eV and a k-point mesh of 10 × 10 × 1 (optimization) and 15 × 15 × 1 (electronic and magnetic properties) were used. Phonon dispersion calculations were performed using a 4 × 4 × 1 supercell with the finite displacement method in PHONOPY. Molecular dynamics (MD) simulations (NPT ensemble at 300 K for 20 ps) using Forcite were conducted to assess thermal stability. Magnetic exchange interaction parameters were calculated using the four-state method. A simple Hamiltonian model was developed to understand the superexchange mechanism and the relationship between the energy difference between orbitals and the exchange coupling. Monte Carlo simulations with the Metropolis algorithm were performed using the mcsolver package to estimate Curie temperature.

Phonon spectra and MD simulations confirmed the dynamic and thermal stability of CrXY monolayers (excluding CrOl). Energetic estimations of various magnetic configurations indicated a ferromagnetic (FM) ground state for all stable monolayers, supported by calculations of the total energy as a function of the magnetic propagation vector. Spin-dependent density of states (DOS) calculations revealed that all stable CrXY monolayers are ferromagnetic semiconductors. Magnetic anisotropy calculations show that long-range FM ordering can emerge at certain temperatures. Analysis of magnetic exchange interaction parameters (J1, J2, J3) showed that J1 is dominant and positive, and significantly enhances with the substitution of O by S/Se. The study explored the superexchange mechanism through a simple Hamiltonian model demonstrating that ferromagnetic coupling is enhanced by reducing the energy difference between p- and d-orbitals, particularly between eg and p-orbitals. The substitution of O by S/Se significantly reduces this energy difference, resulting in a substantial increase in the Curie temperature (Tc). Monte Carlo simulations estimated Tc, reaching or exceeding room temperature for CrSY and CrSeY monolayers. Applying tensile strain further increased Tc.

The findings directly address the research question of enhancing ferromagnetic coupling in 2D materials by manipulating the covalent character of Cr-X bonds. The substantial increase in Tc observed upon substituting O with heavier chalcogens (S, Se) validates the proposed mechanism. The simple Hamiltonian model successfully explains the observed trend, highlighting the crucial role of energy difference between coupled orbitals in determining the strength of ferromagnetic coupling. The high Tc values achieved suggest that these CrXY monolayers are promising candidates for room-temperature 2D spintronic applications. The study provides valuable insights into the design of high-Tc 2D ferromagnetic materials.

This research identifies CrXY (X = S, Se; Y = Cl, Br, I) monolayers as promising 2D ferromagnetic semiconductors with Curie temperatures reaching or exceeding room temperature. The enhanced ferromagnetic coupling is attributed to the increased covalent character of Cr-X bonds, achieved by minimizing the energy difference between the Cr eg and anion p orbitals. This work demonstrates a successful strategy for enhancing Tc in 2D materials and opens up new avenues for exploring and designing high-performance 2D spintronic devices. Future studies could investigate the effects of other substitutional dopants and explore the integration of these materials into functional devices.

The study relies on theoretical calculations and hasn't been experimentally validated. The simple Hamiltonian model, while successfully explaining the trend, involves simplifications and approximations that might affect the quantitative accuracy. The estimated Tc values are based on Monte Carlo simulations using calculated exchange parameters and might deviate from experimental values due to other factors not explicitly considered in the model. Further experimental investigation is necessary to verify the theoretical predictions and explore potential limitations arising from synthesis challenges and environmental factors.