Antiferromagnetic magnons on a M\"obius strip: topology-induced symmetry breaking

We study a M\"obius strip comprising of two antiferromagnetically coupled spin chains. To satisfy the boundary condition, magnon excitations feature linear polarization of the N\'eel vector devoid of chirality, forming two non-degenerate branches of modes that can neither be smoothly connected to nor be decomposed by the circularly-polarized magnons of opposite chirality commonly found in antiferromagnets. Only one branch supports standing-wave formation on the M\"obius strip while the other does not, owing to its spectral shift incurred by the boundary condition. Our findings unravel the profound impact of topology-induced symmetry breaking on magnons.