Macrospin approximation and quantum effects in models for magnetization reversal

-Spin dynamics in the Kondo impurity model, initiated by suddenly switching the direction of a local magnetic field, is studied by means of the time-dependent density-matrix renormalization group. Quantum effects are identified by systematic computations for different spin quantum numbers S and by comparing with tight-binding spin-dynamics theory for the classical-spin Kondo model. We demonstrate that, besides the conventional precessional motion and relaxation, the quantum-spin dynamics shows nutation, similar to a spinning top. Opposed to semiclassical theory, however, the nutation is efficiently damped on an extremely short time scale. The effect is explained in the large-S limit as quantum dephasing of the eigenmodes in an emergent two-spin model that is weakly entangled with the bulk of the system. We argue that, apart from the Kondo effect, the damping of nutational motion is essentially the only characteristics of the quantum nature of the spin. Qualitative agreement between quantum and semiclassical spin dynamics is found down to S = 1/2.Introduction.-The paradigmatic system to study the real-time dynamics of a spin-1/2 coupled to a Fermi sea is the Kondo model [1]. It is mainly considered as a generic model for the famous Kondo effect [2], namely screening of the impurity spin by a mesoscopically large number of electrons in a thermal state with temperature below the Kondo temperature T K ∼ exp(−1/Jρ), where J is the strength of the exchange coupling and ρ is the density of states. The Kondo effect is a true quantum effect which originates from the two-fold spin degeneracy and is protected by time-reversal symmetry. Longitudinal spin dynamics, such as the time-dependent Kondo screening, has been studied recently [3,4] by starting from an initial state with a fully polarized spin, which can be prepared with the help of local magnetic field. The longitudinal dynamics is initiated by suddenly switching off the field.

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“…= S(S + 1) [39][40][41][42][43]. Indeed, the agreement constantly improves with increasing S, see Fig.…”

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confidence: 71%

Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

Sayad

Rausch

Potthoff

2016

EPL

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“…The present study is performed for a single spin, i.e., we consider a classical-spin Kondo-impurity model with antiferromagnetic local exchange coupling J, while the theory itself is general and can be applied to more than a single or even to a large number of spins as well.As compared to the conventional (quantum-spin) Kondo model, [27,28] the model considered here does not account for the Kondo effect and therefore applies to situations where this is absent or less important, such as for systems with large spin quantum numbers S, strongly anisotropic systems or, as considered here, systems in a strong magnetic field. To estimate the quality of the classical-spin approximation a priori is difficult [29][30][31]. For one-dimensional systems, however, a quantitative study is possible by comparing with full quantum calculations and will be discussed elsewhere [32].There are different questions to be addressed: for dimensional reasons, one should expect that linearresponse theory, even for weak J, must break down at long times.…”

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confidence: 99%

“…As compared to the conventional (quantum-spin) Kondo model, [27,28] the model considered here does not account for the Kondo effect and therefore applies to situations where this is absent or less important, such as for systems with large spin quantum numbers S, strongly anisotropic systems or, as considered here, systems in a strong magnetic field. To estimate the quality of the classical-spin approximation a priori is difficult [29][30][31]. For one-dimensional systems, however, a quantitative study is possible by comparing with full quantum calculations and will be discussed elsewhere [32].…”

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confidence: 99%

Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau–Lifschitz–Gilbert equation

Sayad

Potthoff

2015

New J. Phys.

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The real-time dynamics of a classical spin in an external magnetic field and local exchange coupled to an extended one-dimensional system of non-interacting conduction electrons is studied numerically. Retardation effects in the coupled electron-spin dynamics are shown to be the source for the relaxation of the spin in the magnetic field. Total energy and spin is conserved in the non-adiabatic process. Approaching the new local ground state is therefore accompanied by the emission of dispersive wave packets of excitations carrying energy and spin and propagating through the lattice with Fermi velocity. While the spin dynamics in the regime of strong exchange coupling J is rather complex and governed by an emergent new time scale, the motion of the spin for weak J is regular and qualitatively well described by the Landau-Lifschitz-Gilbert (LLG) equation. Quantitatively, however, the full quantum-classical hybrid dynamics differs from the LLG approach. This is understood as a breakdown of weak-coupling perturbation theory in J in the course of time. Furthermore, it is shown that the concept of the Gilbert damping parameter is ill-defined for the case of a one-dimensional system. å å a =´++Í t consists of precession terms coupling the spin at site m to an external magnetic field B and, via exchange couplings J mn , to the spins at sites n. Those precession terms typically have a clear atomistic origin, such as the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction [10-12] which is mediated by the magnetic polarization of conduction electrons. The non-local RKKY couplings J J mn mn 2 c = are given in terms of the elements χ mn of the static conduction-electron spin susceptibility and the local exchange J between the spins and the local magnetic moments of the conduction electrons. Other possibilities comprise direct (Heisenberg) exchange interactions, intra-atomic (Hundʼs) couplings as well as the spin-orbit and other anisotropic interactions. The relaxation term, on the other hand, is often assumed as local, α mn = δ mn α, and represented by purely phenomenological Gilbert damping constant α only. It describes the angular-momentum transfer between the spins and a usually unspecified heat bath.On the atomistic level, the Gilbert damping must be seen as originating from microscopic couplings of the spins to the conduction-electron system (as well as to lattice degrees of freedom which, however, will not be considered here). There are numerous studies where the damping constant, or tensor, α has been computed numerically from a more fundamental model including electron degrees of freedom explicitly [13][14][15] or even from first principles [16][17][18][19][20][21]. All these studies rely on two, partially related, assumptions: (i) the spin-electron coupling J is weak and can be treated perturbatively to lowest order, i.e., the Kubo formula or linear-response theory is employed. (ii) The classical spin dynamics is slow as compared to the electron dynamics. These assumptions appear as well justified but they are also nec...

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“…This macrospin picture is reasoned by the fact that for the coupled spin chain (or cluster, network) in nanoscale ferromagnets with a singledomain state, spins are tightly coupled and thus form an effective coarse-grained macrospin 28 . Microscopically, the spin chain model with exchange interactions can be derived from the tight-binding electron chain model with strong Coulomb interaction.…”

Section: Discussionmentioning

confidence: 99%

“…The central local spin may represent an insulating molecule magnet 26 or a ferromagnetic nanoparticle 27 found in a nanoscale single-domain state and thus is described by the effective macrospin 28 , as:…”

Section: Model and Methodsmentioning

confidence: 99%

Nanoscale Spin Seebeck Rectifier: Controlling Thermal Spin Transport across Insulating Magnetic Junctions with Localized Spin

2014

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The spin Seebeck effect is studied across a charge insulating magnetic junction, in which thermal-spin conjugate transport is assisted by the exchange interactions between the localized spin in the center and electrons in metallic leads. We show that, in contrast with bulk spin Seebeck effect, the figure of merit of such nanoscale thermal-spin conversion can be infinite, leading to the ideal Carnot efficiency in the linear response regime. We also find that in the nonlinear spin Seebeck transport regime, the device possesses the asymmetric and negative differential spin Seebeck effects. In the last, the situations with leaking electron tunneling are also discussed. This nanoscale thermal spin rectifier, by tuning the junction parameters, can act as a spin Seebeck diode, spin Seebeck transistor and spin Seebeck switch, which could have substantial implications for flexible thermal and information control in molecular spin caloritronics.

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Macrospin approximation and quantum effects in models for magnetization reversal

Cited by 10 publications

References 29 publications

Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau–Lifschitz–Gilbert equation

Nanoscale Spin Seebeck Rectifier: Controlling Thermal Spin Transport across Insulating Magnetic Junctions with Localized Spin

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