Dynamically generated spin interactions and nutational spin inertia in normal metal–ferromagnet heterostructures

We consider the spin dynamics of a normal metal--ferromagnet heterostructure, with emphasis on spin-nutation terms arising from a dynamical Ruderman-Kittel-Kasuya-Yosida interaction. We find that the spin-nutation term is anisotropic in spin space due to the broken time-reversal symmetry of the ferromagnet. This contrasts with what one obtains in the paramagnetic state, where the nutation term is isotropic in spin space. We compute the effects this has on the magnetization dynamics derived from a Landau-Lifshitz-Gilbert equation. In particular, due to broken time-reversal symmetry, we predict a qualitative change in the zero-field ferromagnetic resonance spectrum which is present up to the Curie temperature. We propose that this is a strong indicator of the existence of nutation in ferromagnetically ordered spin systems.