Engineering spin-wave spectrum via the magnetization inertia tensor

Magnetic inertial dynamics has recently been predicted and experimentally demonstrated in two-sublattice ferromagnets such as CoFeB and NiFe permalloy. In this work, we investigate the spin-wave spectrum of such systems by incorporating the complete magnetic inertia tensor. By decomposing the tensor into symmetric and antisymmetric components, we identify isotropic, anisotropic, and chiral contributions to magnetic inertia. Within linear spin-wave theory, we find that the spectrum comprises two precessional and two inertial magnon bands. Remarkably, the upper precessional band intersects the lower inertial band within the Brillouin zone. Both cross-sublattice and chiral components of the inertia tensor act as effective control parameters for tuning these magnonic band structures. Furthermore, we show that the inertial spin-wave spectrum becomes nonreciprocal along propagation directions where the Dzyaloshinskii-Moriya interaction is finite. Strikingly, a similar nonreciprocity can also arise purely from chiral inertia, even in the absence of Dzyaloshinskii-Moriya interaction. Our findings establish magnetic inertia as a new pathway to engineer nonreciprocal magnon transport and ultrafast spintronic functionalities.