Quantum Brownian Motion for Magnets

Abstract

Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized spin+environment Hamiltonian, we here derive a general spin operator equation of motion that describes three-dimensional precession and damping and consistently accounts for effects arising from memory, coloured noise and quantum statistics. The LLG equation is recovered as its classical, Ohmic approximation. We further introduce resonant Lorentzian system--reservoir couplings that allow a systematic comparison of dynamics between Ohmic and non--Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a spin in the semi--classical limit. At low temperatures, our numerical results demonstrate a characteristic reduction and flattening of the steady state spin alignment with an external field, caused by the quantum statistics of the environment. The results provide a powerful framework to explore general three-dimensional dissipation in quantum thermodynamics.

substantially updated version, 5 figures, 12 pages+refs+appendix, comments welcome (previous title: Versatile three-dimensional quantum spin dynamics equation with guaranteed fluctuation-dissipation link)

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Cited by in corpus (8)

• Inertial spin dynamics in epitaxial cobalt films
• Coupling function from bath density of states
• The fractional Landau-Lifshitz-Gilbert equation
• Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check
• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Inertial dynamics and equilibrium correlation functions of magnetization at short times
• Derivation of Interacting Two-Qubit Dynamics from Spin-Boson Model
• Magnetization switching in the inertial regime