Inertial dynamics and equilibrium correlation functions of magnetization at short times

The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series expansion of the correlation functions and the estimation of the expansion coefficients. This method significantly reduces the complexity of analysis of equilibrium correlation functions. Analytical expressions are derived for the first three coefficients for the longitudinal and transverse correlation functions for the uniaxial magnetocrystalline anisotropy of ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting cases of very strong and negligibly weak external longitudinal fields are considered. The Gordon sum rule for inertial magnetization dynamics is discussed. In addition, we show that finite analytic series can be used as a simple and satisfactory approximation for the numerical calculation of correlation functions at short times

Inertial effects in ultrafast spin dynamics

The dynamics of magnetic moments consist of a precession around the magnetic field direction and a relaxation towards the field to minimize the energy. While the magnetic moment and the angular momentum are conventionally assumed to be parallel to each other, at ultrafast time scales their directions become separated due to inertial effects. The inertial dynamics give rise to additional high-frequency modes in the excitation spectrum of magnetic materials. Here, we review the recent theoretical and experimental advances in this emerging topic and discuss the open challenges and opportunities in the detection and the potential applications of inertial spin dynamics.Comment: 11 pages, 8 figure

Chiral phonons and phononic birefringence in ferromagnetic metal - bulk acoustic resonator hybrids

Magnomechanical devices, in which magnetic excitations couple to mechanical vibrations, have been discussed as efficient and broadband microwave signal transducers in the classical and quantum limit. We experimentally investigate the magnetoelastic coupling between the ferromagnetic resonance (FMR) modes in a metallic Co$_{25}$Fe$_{75}$ thin film, featuring ultra-low magnetic damping as well as sizable magnetostriction, and standing transverse elastic phonon modes in sapphire, silicon and gadolinium gallium garnet by performing broadband FMR spectroscopy at cryogenic temperatures. For all these substrate materials, we observe an interaction between the resonant acoustic and magnetic modes, which can be tailored by the propagation direction of the acoustic mode with respect to the crystallographic axes. We identify these phonon modes as transverse shear waves propagating with slightly different velocities with relative magnitudes of $\Delta v/v\simeq10^{-5}$, i.e., all substrates show phononic birefringence. Upon appropriately choosing the phononic mode, the hybrid magnomechanical system enters the Purcell enhanced coupling regime.Comment: 7 oages, 4 figure