Electron-magnon scattering in magnetic heterostructures far out of equilibrium

Abstract

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...

Electric current induced ultrafast demagnetization

“…Laser irradiation of magnetic metals can launch precessional modes at frequencies ranging from a few to hundreds of GHz 2,3 , drive ultrafast magnetic phase transitions 4 , and generate enormous pure spin-currents [5][6][7][8][9][10][11] . Optical irradiation of ferrimagnetic systems such as GdFeCo and TbFeCo can result in an ultrafast reversal of the direction of magnetization [12][13][14] .…”

Thermodynamic transport theory of spin waves in ferromagnetic insulators

“…The injection of the magnetization current source into the metallic layer is due to the conversion of the magnetic moment of the magnons at the interface into a spin accumulation in Pt. The microscopic mechanisms involved [12][13][14][15][16][17][18] as well as the role played by imperfect interfaces 46 have been already analyzed in detail. From the point of view of the thermodynamic theory of Johnson and Silsbee 35 the passage of the magnetization current between two layers is described by solving the diffusion problem for the two materials and by imposing the appropriate boundary conditions 29 .…”

“…This effect has been interpreted as the consequence of the presence of a spin current carried by non equilibrium spin waves (or magnons) in the ferrimagnetic insulator which is converted into a spin current carried by electrons in the metal 3,10,11 . The source of this conversion is the interaction between the d electrons in the ferromagnet and the s electrons in the metal which gives rise to an absorption of a magnon in the insulator and the corresponding generation of an electron spin flip in the metal [12][13][14][15][16][17][18] . While the assessment of the interface is well documented in the literature 10,[19][20][21] , the description of the transport of non equilibrium spin waves inside the bulk ferromagnet is still a debated issue [22][23][24][25][26][27][28][29] .…”

Thermoelectric spin transport through ferromagnetic heterostructures

“…Second, spin-transfer torque driven dynamics of n are generally long wavelength and precess at microwave frequencies ( )/ , H K −   thermally activated fluctuations correspond a characteristic (de Broglie) wavelength = / B A k T Λ and precess at frequencies / , B k T   which, in room temperature ferromagnets, are usually much faster than microwave precession. Consequently, the dynamics of the fluctuations may differ considerably from that of n; for example, whereas the long wavelength dynamics of n are captured by the LLG phenomenology, dissipative dynamics of thermal fluctuations may no longer be described by Gilbert damping [30]. We shall, however, extrapolate the LLG phenomenology to thermal energies, with the understanding that results thereby obtained, while capturing key qualitative behavior, may fail to produce accurate quantitative predications.…”