Nonreciprocal Phonons in PT-Symmetric Antiferromagnets.

Phonon nonreciprocity, indicating different transport properties along opposite directions, has been observed in experiments under a magnetic field. We show that nonreciprocal acoustic phonons can also exist without a magnetic field or net magnetization. We identify crucial contributions in phenomenological elastic theory. In PT symmetric antiferromagnets, we find two terms, dubbed flexo viscosity and flexo torque, that induce phonon nonreciprocity. The microscopic origin of these terms is attributed to the derivatives of molecular Berry curvature, manifested as emergent nonlocal magnetic fields on phonons. The symmetry breaking that originated from spin order is transferred to the phonon system through spin-orbit coupling, where the orbital degree of freedom affects the lattice dynamics directly. By electrically breaking inversion symmetry and modifying the spin-orbit coupling, we find extra contributions and show that both the phonon nonreciprocity and helicity can be controlled and enhanced. Importantly, the phonon nonreciprocity is an odd function of the Néel vector, serving as an indicator of the order parameter.