Spin-Lattice Interaction in Two-Dimensional CrI3 Computed from First Principles

Introduction and motivation: We recently developed a computationally efficient and general first-principles based method for atomistic spin-lattice simulations. In this talk I will present our recent results for the two-dimensional (2D) magnet CrI3. This system is of special interest in the context of spin-lattice interactions due to the presence of topological edge magnons (TEM) in combination with the fact that phonons and magnons in this class of materials have similar energies, i.e., significant hybridization between these two types of quasiparticles can be expected. On a more general note, our new computational method opens the door for a quantitative description and understanding of the microscopic origin of many fundamental phenomena of contemporary interest in which the spin and lattice motions interact, such as, e.g., ultrafast demagnetization, magnetocalorics, spincaloritronics, or magnetic polaron formation.<br/><br/>Topological edge magnons have, from general arguments, been predicted to exist in systems in which the magnetic atoms form a honeycomb lattice. The existence of TEM in CrI3 has been indirectly confirmed in inelastic neutron scattering experiments. Previous computations based on density functional theory (DFT) -- including spin-orbit coupling and corrections for strong electron-electron correlations -- do indeed reproduce the TEM, but the computed gap is much smaller than the experimentally observed gap. The reason for this discrepancy is unclear but lattice effects could be one possible mechanism. In graphene, phonon-induced intervalley scattering can led to a dynamical gap opening up in the electron spectrum, and it has been speculated that a similar effect may occur in magnetic honeycomb lattices as well.<br/><br/>Method: The computational method is based on a coupling of atomistic spin dynamics and molecular dynamics simulations, expressed through a spin-lattice Hamiltonian, where the bilinear magnetic term is expanded up to second order in displacement. The Heisenberg as well as Dzyaloshinskii-Moriya (DM) magnetic interaction parameters to enter the spin-lattice Hamiltonian are computed from first principles using Density Functional Theory (DFT) using a Green’s function formalism. In short, our approach to computing the magnetic interaction parameters is based on a linear-response theory formulated for second order perturbation in the deviations of spins from an equilibrium magnetic configuration, generalized to take relativistic effects into account. To further compute the actual spin-lattice interaction parameters, this scheme is combined with symmetry-adapted displacements of individual atoms using a super-cell approach.<br/><br/>Results: We extract an effective measure of the spin-lattice coupling in CrI3 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 the out-of-plane motion of ligand atoms. Furthermore, we find that some magnetic pair interactions change sign from ferromagnetic (FM) to anti-ferromagnetic (AFM) for certain atomic displacements. 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 t2g - t2g and FM t2g - eg contributions depends on the bond angle between the Cr and I atoms, as well as the Cr-Cr distance. In particular, if a Cr atom is displaced, the FM-AFM sign changes when the I-Cr-I bond angle approaches 90 degrees.