Gilbert-like damping caused by time retardation in atomistic magnetization dynamics

Thonig, Danny; Henk, J.; Eriksson, Olle

doi:10.1103/physrevb.92.104403

Cited by 16 publications

(18 citation statements)

References 39 publications

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“…On the other hand, it is well-known that even infinitely slow dynamics of M i (t) can pump spin currents [58,59], as well as charge current if additional conditions are satisfied [59][60][61]. Therefore, using NEGF+LLG approach precludes taking into account self-consistent feedback [55,62] where the dynamics of M i (t) leads to pumped spin currents which, in turn, can exert additional torque and timeretarded damping (with microscopically [63,64] rather than phenomenologically [65,66] determined memory kernel) on M i (t) thereby modifying its dynamics. Finally, time-dependent quantum treatment of electrons is required to describe pulse-current-induced dynamics of M i (t) which is of paramount importance in basic research experiments [8] and, e.g., racetrack memory applications [17,18] where usage of current pulses [67] or their trains [68] reduces threshold current density to move the DW while precise control of the DW position can be achieved by tailoring pulse duration and shape [38,[69][70][71][72].…”

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confidence: 99%

Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach

et al. 2018

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We introduce a multiscale framework which combines time-dependent nonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in the number of time steps and describing quantummechanically conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces dynamics of magnetic moments as the key resource for next generation spintronics. Previous approaches to such nonequilibrium many-body system (like steady-state-NEGF+LLG framework) neglect noncommutativity of a quantum Hamiltonian of conduction electrons at different times and, therefore, the impact of time-dependent magnetic moments on electrons leading to pumping of spin and charge currents. The pumped currents can, in turn, self-consistently affect the dynamics of magnetic moments themselves. Using magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on the top of unpolarized DC charge current injected through normal metal leads to drive the DW motion), where the latter can be viewed as a realization of quantum charge pumping due to time-dependence of the Hamiltonian and left-right symmetry breaking of the two-terminal device structure. The conversion of AC components of spin current, whose amplitude increases (decreases) as the DW approaches (distances from) the normal metal lead, into AC voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures-the perturbative analytical formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed 10 • . arXiv:1802.05682v3 [cond-mat.mes-hall] 9 Aug 2018 x y z Electron Flow J t t J sd

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confidence: 99%

Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach

et al. 2018

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“…A plausible explanation for this shift of the maximum in Ref. [6] is the influence of high-frequency oscillations imposed on top of the dominant precession, e.g., nutations [23,31,126]. These higher order oscillations emerge in the dynamics for intermediate and strong J sd 4 [14,31], as discussed in Appendix A, and are long-lived [14].…”

Section: A Analysis Of Classical Spin Relaxation Ratesmentioning

confidence: 92%

Spin Dynamics in Magnetic Nano-Junctions

Smorka¹,

Žonda²,

Thoss³

2021

Preprint

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We investigate nonequilibrium processes in magnetic nano-junctions employing a numerical approach, which combines classical spin dynamics with the hierarchical equations of motion technique for the quantum dynamics of the conduction electrons. Focusing on the spin dynamics, we find that the spin relaxation rates depend in a non-monotonous way on the coupling between the localized spin and conduction electrons, with a pronounced maximum at intermediate coupling strength. This result can be understood by analyzing the local density of states. In the case of a magnetic junction subject to an external dc-voltage, spin relaxation exhibits resonant features reflecting the electronic spectrum of the system. In addition, in multi-site junctions, spin relaxation is also influenced by electron localization.

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“…where B eff , Ĝ and Î is the effective magnetic field, Gilbert damping and the moment of inertia tensor, respectively. The moment of inertia term, Î, has here been added in comparison to the conventional LLG equation, as there has been suggestions of its importance to short-time dynamics [35,62]. The shortcomings of the conventional LLG equation is that its parameters are both constant and local.…”

Section: B Spin Equation Of Motionmentioning

confidence: 99%

“…This has successfully been applied to describe the magnetization dynamics of different materials [34]. The LLG equation has been extended to take into account temperature, moment of inertia, and stochastic forces [35][36][37][38][39][40][41][42]. Due to the large interest in the field of ultra-fast spin dynamics [43], further investigations has been done of the LLG equation in the ultra-fast regime [36,37] and on dynamic exchange interactions [44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Transient spin dynamics in a single-molecule magnet

Hammar

Fransson

2017

Phys. Rev. B

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We explore the limitations and validity of semi-classically formulated spin equations of motion. Using a single-molecule magnet as a test model, we employ three qualitatively different approximation schemes. From a microscopic model, we derive a generalized spin equation of motion in which the parameters have a non-local time-dependence. This dynamical equation is simplified to the Landau-Lifshitz-Gilbert equation with i) timedependent, and ii) time-independent parameters. We show that transient dynamics is essentially non-existing in the latter approximation, while the former breaks down in the regime of strong coupling between the spin and the itinerant electrons.

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Gilbert-like damping caused by time retardation in atomistic magnetization dynamics

Cited by 16 publications

References 39 publications

Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach

Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach

Spin Dynamics in Magnetic Nano-Junctions

Transient spin dynamics in a single-molecule magnet

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