The Influence of s‐d Exchange on Relaxation of Magnons in Metals

Heinrich, B.; Fraítová, D.; Kamberský, V.

doi:10.1002/pssb.19670230209

Cited by 107 publications

(94 citation statements)

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“…It is worthwhile to realize that the s-d exchange relaxation mechanism also applies to bulk ferromagnets, and was evaluated by Heinrich et al 17,18 The Gilbert damping in this case is given by…”

Section: Theoretical Models Of Nonlocal Dampingmentioning

confidence: 98%

“…It should be noted that 1/ sf in metals is proportional to the square of the spin orbit interaction. 17,18 Using P from Kriesman and Callen 19 and sf from the spin diffusion length in current perpendicular to plane giant magnetoresonance measurements one obtains for the bulk Gilbert damping Gϭ5 ϫ10 6 and 1ϫ10 8 s Ϫ1 for Co and permalloy ͑Py͒, respectively, see the details in Ref. 18.…”

Section: Theoretical Models Of Nonlocal Dampingmentioning

confidence: 99%

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Role of dynamic exchange coupling in magnetic relaxations of metallic multilayer films (invited)

Heinrich

Woltersdorf

Urban

et al. 2003

Journal of Applied Physics

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The relaxation processes were investigated by ferromagnetic resonance ͑FMR͒ using magnetic single, Au/Fe/GaAs͑001͒, and double layer, Au/Fe/Au/Fe/GaAs͑001͒, structures prepared by molecular beam epitaxy. These structures provided an excellent opportunity to investigate nonlocal damping which is caused by spin transport across a nonmagnetic spacer. In the double layer structures thin Fe layers F1 were separated from a second thick Fe layer F2 by a Au͑001͒, normal metal spacer. The interface magnetic anisotropies separated the FMR fields of F1 and F2 by a big margin which allowed us to investigate FMR in F1 while F2 had a negligible angle of precession. The main result is that the ultrathin Fe films in magnetic double layers acquire a nonlocal interface Gilbert damping. Several mechanisms have been put forward to explain the nonlocal damping. A brief review of each mechanism will be presented. They will be compared with the experimental results allowing one to critically assess their applicability and strength. It will be shown that the precessing layers act as spin pumps and spin sinks. This concept was tested by investigating the FMR linewidth around an accidental crossover of the resonance fields for the layers F1 and F2.

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Section: Theoretical Models Of Nonlocal Dampingmentioning

confidence: 98%

Section: Theoretical Models Of Nonlocal Dampingmentioning

confidence: 99%

Role of dynamic exchange coupling in magnetic relaxations of metallic multilayer films (invited)

Heinrich

Woltersdorf

Urban

et al. 2003

Journal of Applied Physics

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“…The Gilbert damping in metals is caused by incoherent scattering of electron-hole pair excitations by phonons and magnons. The electron-hole excitations involve three particle scattering ͑see 2 ) can be caused by the exchange interaction between magnons and itinerant electrons ͑s -d exchange interaction 5 ͒. The total angular momentum in the s -d exchange interaction is conserved.…”

Section: Magnetic Relaxation Processes In Single Layersmentioning

confidence: 99%

Magnetic relaxation in metallic films: Single and multilayer structures

Heinrich

Urban

Woltersdorf

2002

Journal of Applied Physics

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The intrinsic magnetic relaxations in metallic films will be discussed. It will be shown that the intrinsic damping mechanism in metals is caused by incoherent scattering of itinerant electron-hole pair excitations by phonons and magnons. Berger ͓L. Berger, Phys. Rev. B 54, 9353 ͑1996͔͒ showed that the interaction between spin waves and itinerant electrons in multilayers can lead to interface Gilbert damping. Ferromagnetic resonance ͑FMR͒ studies were carried out using magnetic single and double layer films. The FMR linewidth of the Fe films in the double layer structures was found to always be larger than the FMR linewidth measured for the single Fe films having the same thickness. The increase in the FMR linewidth scaled inversely with the film thickness, and was found to be linearly dependent on the microwave frequency. These results are in agreement with Berger's predictions.

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“…Mitchell formulated such a model several decades ago to describe the longitudinal relaxation of ferromagnetic metals [23]. A similar description was later employed to describe Gilbert damping in ferromagnets at low frequencies [24,25].…”

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confidence: 99%

Electron-magnon scattering in magnetic heterostructures far out of equilibrium

2015

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We present a theory of out-of-equilibrium ultrafast spin dynamics in magnetic heterostructures based on the s-d model of ferromagnetism. Both in the bulk and across interfaces, the exchange processes between the itinerant s and the localized d electrons are described by kinetic rate equations for electron-magnon spin-flop scattering. The principal channel for dissipation of angular momentum is provided by spin relaxation of the itinerant electrons. Our theory extends interfacial spin phenomena such as torques, pumping, and the Peltier and Seebeck effects to address laser-induced rapid spin dynamics, in which the effective electron temperature may approach or even exceed the Curie temperature.PACS numbers: 72.25. Mk, 72.20.Pa, 75.40.Gb, 72.10.Di Controlling spin flow in magnetic heterostructures at ultrafast time scales using femtosecond (fs) laser pulses opens intriguing possibilities for spintronics [1]. In these experiments the laser-induced perturbations [2] stir up the most extreme regime of spin dynamics, which is governed by the highest energy scale associated with magnetic order: The microscopic spin exchange that controls the ordering temperature (T C ). In contrast, at microwave frequencies the ferromagnetic dynamics in the bulk are well described by the Landau-LifshitzGilbert (LLG) phenomenology [3], which has been successfully applied to the problem of the ferromagnetic resonance (FMR) [4]. At finite temperatures below T C , the spin Seebeck and Peltier effects [5,6] describe the coupled spin and heat currents across interfaces in magnetic heterostructures. These interfacial effects are governed by thermally activated magnetic degrees of freedom with characteristic frequencies that are much higher than the FMR frequency. Despite their different appearances, the microwave, thermal, and ultrafast spin dynamics are all rooted in the exchange interactions between electrons. It is thus natural to try to advance a microscopic understanding of the ultrafast spin dynamics based on the established phenomena at lower energies.Although some attempts have been made [7,8] to extend the LLG phenomenology to describe ultrafast demagnetization in bulk ferromagnets, no firm connection exists between the ultrafast spin generation at interfaces and the microwave spin-transfer and spin-pumping effects [9] or the thermal spin Seebeck and Peltier effects. In this Letter, we unify the energy regimes of microwave, thermal, and ultrafast spin dynamics in magnetic heterostructures from a common microscopic point of view. In the ultrafast regime, rapid heating of itinerant electrons leads to demagnetization of localized spins via electron-magnon spin-flop scattering. The parameters that control the high and low energy limits of spin relaxation originate from the same electronmagnon interactions. In addition to the unified framework, this Letter's unique contributions are the history-dependent, non-thermalized magnon distribution function and the crucial role of the out-of-equilibrium spin accumulation among itinerant electro...

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The Influence of s‐d Exchange on Relaxation of Magnons in Metals

Cited by 107 publications

References 20 publications

Role of dynamic exchange coupling in magnetic relaxations of metallic multilayer films (invited)

Role of dynamic exchange coupling in magnetic relaxations of metallic multilayer films (invited)

Magnetic relaxation in metallic films: Single and multilayer structures

Electron-magnon scattering in magnetic heterostructures far out of equilibrium

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