Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions

Abstract

The relaxation time of a classical spin interacting with a large conduction-electron system is computed for a weak magnetic field, which initially drives the spin out of equilibrium. We trace the spin and the conduction-electron dynamics on a time scale, which exceeds the characteristic electronic scale that is set by the inverse nearest-neighbor hopping by more than five orders of magnitude. This is achieved with a novel construction of absorbing boundary conditions, which employs a generalized Lindblad master-equation approach to couple the edge sites of the conduction-electron tight-binding model to an external bath. The failure of the standard Lindblad approach to absorbing boundaries is traced back to artificial excitations initially generated due to the coupling to the bath. This can be cured by introducing Lindblad parameter matrices and by fixing those matrices to perfectly suppress initial-state artifacts as well as reflections of physical excitations propagating to the system boundaries. Numerical results are presented and discussed for generic one-dimensional models of the electronic structure.

arXiv comment12 pages, 9 figures, v2 with minor modifications

References in corpus (22)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Atomistic spin model simulations of magnetic nanomaterials
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Microscopic approach to current-driven domain wall dynamics
• A method for atomistic spin dynamics simulations: implementation and examples
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Ab-initio calculation of the Gilbert damping parameter via linear response formalism
• Gilbert Damping in Magnetic Multilayers
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Linear dynamics of quantum-classical hybrids
• Simple Derivation of the Lindblad Equation
• Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions
• Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
• Many-body open quantum systems beyond Lindblad master equations
• Anomalous spin precession under a geometrical torque
• Absorbing boundary conditions for dynamical many-body quantum systems
• Dynamics of localized spins coupled to the conduction electrons with charge/spin currents
• Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping
• Relaxation of a classical spin coupled to a strongly correlated electron system
• Topological spin torque emerging in classical-spin systems with different time scales

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• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
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• Microscopic theory of spin friction and dissipative spin dynamics
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models
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