Emerging magnetic nutation

Abstract

Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter of the expansion is the ratio of the colored noise timescale to the precession period. In the process we obtain the Gilbert damping from the same expansion. We recover the known results, when the coefficients of the two terms are proportional to one another, in the white noise limit; and show how colored noise leads to situations where this simple relation breaks down, but what replaces it can be understood by the appropriate generalization of the fluctuation--dissipation theorem. Numerical simulations of the stochastic equations support the analytic approach. In particular we find that the equilibration time is about an order of magnitude longer than the timescale set by the colored noise for a wide range of values of the latter and we can identify the presence of nutation in the non-uniform way the magnetization approaches equilibrium.

arXiv comment7 pages, 2 figures

References in corpus (23)

• Magnetization dynamics in the inertial regime: nutation predicted at short time scales
• Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles
• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Non-Adiabatic Spin Transfer Torque in Real Materials
• Ultra-fast spin dynamics: the effect of colored noise
• Relativistic theory of magnetic inertia in ultrafast spin dynamics
• Relaxation Mechanism for Ordered Magnetic Materials
• Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach
• Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
• Dynamics of magnetization coupled to a thermal bath of elastic modes
• Quantum Landau-Lifshitz-Bloch equation and its comparison with the classical case
• Antiferromagnetic Switching Driven by the Collective Dynamics of a Coexisting Spin Glass
• Non-local Gilbert damping tensor within the torque-torque correlation model
• Nutation Wave as a Platform for Ultrafast Spin Dynamics in Ferromagnets
• Inertial Effects in Non-Equilibrium Thermodynamics
• Gilbert Damping in Conducting Ferromagnets I: Kohn-Sham Theory and Atomic-Scale Inhomogeneity
• Magnetization nutation induced by surface effects in nanomagnets
• Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
• Another view on Gilbert damping in two-dimensional ferromagnets
• A functional calculus for the magnetization dynamics
• Nambu mechanics for stochastic magnetization dynamics
• Finite-dimensional colored fluctuation-dissipation theorem for spin systems
• Origin of intrinsic Gilbert damping