When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states

Abstract

Experiments in spintronics and magnonics operate with macroscopically large number of localized spins within ferromagnetic (F) or antiferromagnetic (AF) materials, so that their nonequilibrium dynamics is standardly described by the Landau-Lifshitz (LL) equation treating localized spins as classical vectors of fixed length. However, spin is a genuine quantum degree of freedom, and even though quantum effects become progressively less important for spin value $S>1$, they exist for all $S<\infty$. While this has motivated exploration of limitations/breakdown of the LL equation, by using examples of F insulators, analogous comparison of fully quantum many-body vs. quantum (for electrons)-classical (for localized spins) dynamics in systems where nonequilibrium conduction electrons are present is lacking. Here we employ quantum Heisenberg F or AF chains of $N=4$ sites, whose localized spins interact with conduction electrons via $sd$ exchange interaction, to perform such comparison by starting from unentangled pure (at zero temperature) or mixed (at finite temperature) quantum state of localized spins as the initial condition. This reveals that quantum-classical dynamics can faithfully reproduce fully quantum dynamics in the F metallic case, but only when spin $S$, Heisenberg exchange between localized spins and $sd$ exchange are sufficiently small. Increasing any of these three parameters can lead to substantial deviations, which are explained by the dynamical buildup of entanglement between localized spins and/or between them and electrons. In the AF metallic case, substantial deviations appear even at early times, despite starting from unentangled Néel state, which therefore poses a challenge on how to rigorously justify wide usage of the LL equation in phenomenological modeling of antiferromagnetic spintronics experiments.

11 pages, 7 figures

References in corpus (17)

• Spin Transfer Torques
• Phenomenology of Current-Induced Dynamics in Antiferromagnets
• Spin-Torque Driven Magnetization Dynamics: Micromagnetic Modelling
• Scattering theory of current-induced forces in mesoscopic systems
• Quantum dynamics and entanglement of spins on a square lattice
• Current-induced atomic dynamics, instabilities, and Raman signals: Quasi-classical Langevin equation approach
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Experimental realisation of multipartite entanglement via quantum Fisher information in a uniform antiferromagnetic quantum spin chain
• Scattering theory of adiabatic reaction forces due to out-of-equilibrium quantum environments
• Hybrid classical-quantum formulations ask for hybrid notions
• Effective temperature and Gilbert damping of a current-driven localized spin
• Multi-scale modelling of current-induced switching in magnetic tunnel junctions using ab initio spin transfer torques
• Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons
• Chiral Spin Order in Kondo-Heisenberg systems
• Pulse-noise approach for classical spin systems
• Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions
• Internal environment: What is it like to be a Schrodinger cat?

Cited by in corpus (8)

• Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics
• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Dynamics of spin relaxation in nonequilibrium magnetic nanojunctions
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Birth and Early Growth of Entanglement by sd Exchange with Gate-Voltage-Controllable Destiny
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• Quantum wake dynamics in Heisenberg antiferromagnetic chains