Anatomy of inertial magnons in ferromagnetic nanostructures

We analyze dispersion relations of magnons in ferromagnetic nanostructures with uniaxial anisotropy taking into account inertial terms, i.e. magnetic nutation. Inertial effects are parametrized by damping-independent parameter $\beta$, which allows for an unambiguous discrimination from Gilbert damping $\alpha$. The analysis magnon relation shows its two branches modified the effect, albeit different ways. upper nutation branch starts at $\omega=1/ \beta$, lower coincides FMR long-wavelength limit and deviates zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ exchange magnon. Taking a realistic experimental geometry thin films, nanowires nanodiscs, eigenfrequencies, eigenvectors $Q$-factors found to depend on shape anisotropy. possibility phase-matched magneto-elastic excitation is discussed condition was stiffness $D$ acoustic velocity.