Spin-lattice couplings in two-dimensional CrI${}_3$ from first-principles study

Abstract

Since thermal fluctuations become more important as dimensions shrink, it is expected that low-dimensional magnets are more sensitive to lattice distortions and phonons than bulk systems are. Here we present a fully relativistic first-principles study on the spin-lattice coupling, i.e. how the magnetic interactions depend on local lattice distortions, of the prototypical two-dimensional ferromagnet CrI${}_3$. We extract an effective measure of the spin-lattice coupling in CrI${}_3$ which is up to ten times larger than what is found for bcc Fe. The magnetic exchange interactions, including Heisenberg and relativistic Dzyaloshinskii-Moriya interactions, are sensitive both to the in-plane motion of Cr atoms and out-of-plane motion of ligand atoms. We find that significant magnetic pair interactions change sign from ferromagnetic (FM) to anti-ferromagnetic (AFM) for atomic displacements larger than 0.16 Å. We explain the observed strong spin-lattice coupling by analyzing the orbital decomposition of isotropic exchange interactions, involving different crystal-field-split Cr$-3d$ orbitals. The competition between the AFM t${}_{2g}$ - t${}_{2g}$ and FM t${}_{2g}$ - e${}_g$ contributions depends on the bond angle formed by Cr and I atoms as well as Cr-Cr distance. In particular, if a Cr atom is displaced, the FM-AFM sign change when the I-Cr-I bond angle approaches 90${}^{\circ }$. The obtained spin-lattice coupling constants, along with the microscopic orbital analysis can act as a guiding principle for further studies of the thermodynamic properties and combined magnon-phonon excitations in two-dimensional magnets.

References in corpus (5)

• Topological Magnon Insulator in Insulating Ferromagnet
• Relativistic exchange interactions in CrX${}_3$ (X=Cl, Br, I) monolayers
• Microscopic origin of ferromagnetism in trihalides CrCl${}_3$ and CrI${}_3$
• Monolayer CrCl${}_3$ as an ideal Test Bed for the Universality Classes of 2D Magnetism
• Magnetic interactions in strongly correlated systems: spin and orbital contributions

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