Symmetry-Selective Topological Magnon Engineering by Phonon Angular Momentum

Abstract: Dynamical control of Berry curvature remains an outstanding challenge in the engineering of topological phases. Here, we demonstrate control of magnon band structures via coherently driven phonons, based on \textit{ab initio} spin-lattice coupling and Floquet theory. We show that this control is symmetry selective: linearly polarized phonons leave the spectrum unchanged, whereas circular and elliptical phonons carrying finite phonon angular momentum (PAM) induce chiral interactions that open and tune gaps at Dirac points, generating and reversing topological magnon phases. The gap magnitude and Chern numbers are directly governed by the PAM, enabling handedness-selective topology control. Applied to monolayer CrI$_3$, and supported by symmetry analysis, our results establish driven lattice dynamics as a general route to engineering topological bosonic excitations and a versatile platform for Floquet control of magnetism.