Session N56: Novel Computational Approaches to Coupled Phonon-Magnon Dynamics

Chiral phononics: Controlling magnetic order with phonon angular momentum

Chiral phonons are circularly polarized lattice vibrations, in which the atoms move along circular orbits around their equilibrium positions in a solid. In dielectric materials, the orbital motions of the ions generate atomistic charge currents and therefore a magnetic moment carried by the chiral phonon [1,2]. In this talk, I show that chiral phonons are able to induce giant effective magnetic fields in solids when driven with an ultrashort laser pulse, and I present two examples of how these fields can be utilized to control the magnetic order of materials. First, we demonstrate that chiral phonons in paramagnetic rare-earth trihalides are able to create effective magnetic fields of potentially up to 100 T that polarize the spins in the material [3,4], a prediction that has been successfully verified by a recent experiment [5]. Second, we predict that the effective magnetic field produced by chiral phonons can rectify spin precession in antiferromagnets, leading to a canting of the spins and the generation of a quasistatic magnetization. As a result, a light-induced weak ferromagnetic state is transiently created in the solid [6]. Our results represent a new way of inducing hidden spin configurations that are not accessible in the equilibrium.   

Phonon-induced magnetization and its reciprocity: effects of geometrical phase and nonlinearity

The interaction between phonons and magnetization can significantly influence both the phononic and magnetic properties of materials. Chiral phonons can induce magnetization by generating an effective magnetic field on electrons. Reciprocally, a nonzero magnetization can bestow chirality upon phonons via an effective magnetic field on phonons.

The magnetization has orbital and spin contributions. The first half of this talk focuses on the interplay between phonons and orbital magnetization, closely tied to the electronic geometrical phases. We highlight chiral phonon-induced orbital magnetization, described by a topological second Chern form [1, 2]. We further explore its reciprocity, revealing how orbital magnetization endows optical phonons with chirality [3]. Those geometrical phase effects are overlooked in the traditional Born-Oppenheimer approximation.

This reciprocity extends to phonon-spin-coupled systems, which is the focus of the latter half. Here, we reveal the inherent nonlinearity of the reciprocal processes. Using a paramagnet as an illustration, we demonstrate the nonlinearity by unveiling spontaneous symmetry breaking under a periodic drive [4]. Such bistable behaviors shed light on the exploration of nonlinear phenomena in magnetic materials and present possibilities for on-demand control of magnetization.   

Intrinsic vibrational angular momentum as nonadiabatic effects in noncollinear magnetic molecules

We show that in noncollinear magnetic molecules, nonadiabatic (dynamical) effects due to the electron-vibron coupling are time-reversal symmetry breaking interactions for the vibrational field. Because the electronic wave function cannot be chosen as real in these molecules, a nonzero geometric vector potential (Berry connection) arises. As a result, an intrinsic nonzero vibrational angular momentum occurs even for nondegenerate modes and in the absence of external probes. The vibronic modes can then be seen as elementary quantum particles carrying a sizeable angular momentum. As a proof of concept, we demonstrate the magnitude of this topological effect by performing nonadiabatic first principles calculations on platinum clusters and by showing that these molecules host sizeable intrinsic phonon angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

 

Work done in collaboration with Oliviero Bistoni and Matteo Calandra   

Adiabatic dynamics of coupled spins and phonons in magnetic insulators

In this presentation, we discuss our recent advances in the methodology addressing the coupled adiabatic dynamics of phonons and magnons in magnetic insulators [1,2]. In conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with non-zero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom.  Instead, phonon and spins must be treated on a similar footing [2]. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these [1]. We then solve Lagrange's equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in CrI₃, and the degree of magnetically induced mixing between infrared and Raman modes in Cr₂O₃. The approach is general, and can be applied to determine the adiabatic dynamics of any mixed set of slow variables. We will also discuss the extension of our approach to finite momentum.    

Spin-Orbit induced linear magnon-phonon coupling in 2D van der Waals magnets

Standard ab initio treatments of spin and lattice dynamics neglect the coupling between these two degrees of freedom, which turns out to be often a harsh approximation due to the energy overlapping of the respective normal modes. In the context of localized-spin models, the spin-lattice coupling is normally modelled with a non-linear term ---stemming from the dependence of the exchange couplings on the lattice positions--- whose treatment is demanding even in the case of model Hamiltonians and often restricted to the elastic regime only. However, it is known since the late 40es that a linear spin-lattice coupling may arise in the presence of magnetic anisotropies, whose contribution may become dominant with respect to higher order terms.  By means of a supercell approach within Density-Functional Theory we provided, to the best of our knowledge, the first ab initio computation of the SOC-induced spin-lattice couplings in a real material. Our calculations for the CrI3 van der Waals magnet ---a recently-synthetized 2D material where a large spin-orbit coupling stabilizes 2D long-range magnetic order and is argued to sustain topological magnetic excitations--- show that a polaritonic-like hybridization between the magnon and the phonon modes may induce ~meV gap in its magnetic excitation spectrum close to the K point of the Brillouin Zone.