Chiral Magnons and Cycloidal Phonons in Altermagnetic CuF${}_2$ Monolayer

Abstract

Altermagnetism establishes momentum-dependent spin splitting through non-symmorphic crystal symmetries, yet whether these same symmetries simultaneously govern spin and lattice collective excitations remains open. Here we show, using first-principles calculations and linear spin-wave theory, that monolayer CuF${}_2$ hosts both chirality-split magnons and cycloidal phonons controlled by the same $P{2}_1/c$ symmetry operations. The altermagnetic order drives strongly anisotropic magnon chirality via symmetric anisotropic exchange, with Dzyaloshinskii--Moriya interactions acting as a weak secondary modulation. Crucially, the phonon and magnon chiral responses are directionally complementary: cycloidal phonon angular momentum emerges precisely where magnon chirality is symmetry-suppressed, and vice versa. The magnon bands further carry quantized Chern numbers $C^M=\pm 2$, confirming non-trivial altermagnetic topology. These results establish monolayer CuF${}_2$ as a platform where a single symmetry framework engineers magnonic, phononic, and topological responses, providing a direct connection between altermagnetism and spin-lattice chirality in two-dimensional materials.

6 pages