Boundary conditions for and ferromagnetic resonance spectra of magnetic bilayers coupled by interlayer Dzyaloshinskii-Moriya interactions

Interfacial Dzyaloshinskii-Moriya interaction (IFDMI) leads to noncollinear spin configurations within the magnetic layers of multilayer heterostructures, while its interlayer counterpart (ILDMI) minimizes chiral states between the layers. Here, we demonstrate that the symmetries of these interactions are very different, even though both arise from pairwise exchange interactions between magnetic sites mediated by nonmagnetic atoms. By deriving respective boundary conditions for the exchange operator and solving the associated boundary value problem, we show that, unlike IFDMI, which does not contribute to the FMR frequencies, ILDMI alters the frequencies of the fundamental FMR modes and can be separated from other contributions in an FMR experiment.