Topology-induced symmetry breaking demonstrated in antiferromagnetic magnons on a M\"obius strip

Abstract

We propose a mechanism of topology-induced symmetry breaking, where certain local symmetry preserved by the Hamiltonian is explicitly broken in the eigenmodes of excitation due to nontrivial real-space topology. We demonstrate this phenomenon by studying magnonic excitations on a M\"obius strip comprising two antiferromagnetically coupled spin chains. Even with a simple Hamiltonian respecting local rotational symmetry, with all local curvature effects ignored, magnons exhibit linear polarization of the N\'eel vector devoid of chirality, forming two non-degenerate branches that cannot be smoothly connected to nor globally decomposed into, the circularly-polarized magnons. Correspondingly, one branch undergoes a spectral shift and only admits standing waves of half-integer wavelength, whereas the other only affords standing waves of integer wavelength. Under the M\"obius boundary condition, we further identify an exotic phase hosting spontaneous antiferromagnetic order whilst all exchange couplings are ferromagnetic. The suppression of chirality in the order parameter dynamics, hence the pattern of standing waves, can be generalized to other elementary excitations on non-orientable surfaces. Our findings showcase the profound influence of real-space topology on the physical nature of not just the ground state but also the quasiparticles.