On the origin of magnetic anisotropy in two dimensional CrI ₃

Abstract

Abstract.The observation of ferromagnetic order in a monolayer of CrI 3 has been recently reported, with a Curie temperature of 45 Kelvin and off-plane easy axis. Here we study the origin of magnetic anisotropy, a necessary ingredient to have magnetic order in two dimensions, combining two levels of modeling, density functional calculations and spin model Hamiltonians. We find two different contributions to the magnetic anisotropy of the material, favoring off-plane magnetization and opening a gap in the spin wave spectrum. First, ferromagnetic super-exchange across the ≃ 90 degree Cr-I-Cr bonds, are anisotropic, due to the spin orbit interaction of the ligand I atoms. Second, a much smaller contribution that comes from the single ion anisotropy of the S = 3/2 Cr atom. Our results permit to establish the XXZ Hamiltonian, with a very small single ion easy axis anisotropy, as the adequate spin model for this system. Using spin wave theory we estimate the Curie temperature and we highlight the essential role played by the gap that magnetic anisotropy induces on the magnon spectrum.

Magnetic behavior and spin-lattice coupling in cleavable van der Waals layered CrCl3 crystals

“…However, this effect is expected to be weak in trivalent chromium with electronic configuration 3d 3 and nearly octahedral coordination due to quenching of the orbital moment. Thus single ion anisotropy should be weak for Cr, as was demonstrated recently for CrI 3 by Lado and Fernández-Rossier [28]. In that study, spin-orbit coupling on the heavy iodine ions was found to contribute the majority of the anisotropy through Cr-I-Cr superexchange.…”

“…Since the Cr-Cr distances increase with increasing halogen size, the direct exchange is expected to be weakened along this series. This indicates that superexchange, which is expected to favor ferromagnetic alignment, is the more important magnetic interaction [28]. As the electronegativity is decreased from Cl to Br to I, it is expected that the Cr-halogen bonding becomes more covalent, strengthening superexchange interactions and raising ordering temperatures.…”

“…Indeed all three of these chromium trihalides exhibit ferromagnetic ordering of Cr moments within the layers at low temperature [18,24,26,31]. Moving from Cl to Br to I is also expected to increase spin orbit coupling associated with the halogen, which has been identified as a source of magnetic anisotropy in these materials [28].…”

Atomically dispersed tungsten on metal halide monolayer as a ferromagnetic Chern insulator

“…A detailed understanding of the low-temperature magnetic behavior of the W@InI 3 monolayer would be useful for further analyses. We therefore use the quantum mechanical treatment, i.e., the linear spin wave approximation, to study the magnon excitation of this system [40]. This could also allow us to study the spin wave related thermal and topological properties [41][42][43].…”

“…Since the integral is controlled by E − (k), its value is dominated by the integral near the point. Thus, following the spirit of the Debye model, we assume that the integral is within a circular region (within a cutoff radius k c ), which provides good approximation of the main behavior [40]. In order to obtain T c , we need to address when M decreases to an obvious small value.…”