Thermal spin current and spin accumulation at ferromagnetic insulator/nonmagnetic metal interface

Abstract

Spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. Using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering because of the imbalance between magnon emission and absorption caused by either non-equilibrium distribution of magnons or non-equilibrium between magnons and electrons. A temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current which carries angular momenta parallel to the magnetization of FI from the hotter side to the colder one. Interestingly, the spin current induced by a temperature gradient in NM is negligibly small due to the nonmagnetic nature of the non-equilibrium electron distributions. The results agree well with all existing experiments.

Interplay of wave localization and turbulence in spin Seebeck effect

“…However, as we illustrate later, as far as spin waves with long enough localized length (ξ ∼ L for spread spin waves), the magnons can still sense a mean temperature of the YIG. In the opposite limit, however, highly-localized magnons (P nk ∼ δ nk ) inherit the same local temperature as the itinerant electrons in the Pt contact, and therefore cannot generate a net spin current, consistent with the second law of thermodynamics [41]. Our arguments are qualitatively applicable to 2D, although the corresponding localization length is longer by a factor from 1 to 3 than 1D (see below).…”

Magnon hybridization in ferrimagnetic heterostructures

“…Note that α 2 -type magnons are also found at these two wavevectors in the high-frequency regime (not shown here). With the hybrid magnon spectra and wave functions, one can analyze the consequences of hybrid modes in the transport properties, e.g., LSSE, in which the nonequilibrium between the phonons and magnons near the magnetic insulator-normal metal (NM) interface is considered as the driving force [40][41][42][43][44]. During the measurement of LSSE, the magnons accumulated at the GdIG-NM interface are mainly α 1 -type and β 2 -type while the contributions from β 1 -type and α 2 -type modes are far lesser due to the blockage by GdIG and the high excitation frequency, respectively.…”

“…Within the linear-response regime, the spin currents generated in YIG-GdIG-NM trilayer are proportional to the temperature differences between magnons and electrons [36,41,45], i.e.,…”

Temperature dependence of the magnon-phonon energy relaxation time in a ferromagnetic insulator

“…Here α is the probability of transmission through, and β = 1 − α is the probability of reflection of the phonon from the interface with the substrate. The condition (18) means that phonons that are specularly reflected from the interface with the substrate and phonons from the substrate that have passed this interface fall into a state with the wave vector q.…”

“…In this area, the spin Seebeck effect (SSE), which consists in generating a spin current by a heat flux, is of great interest [5][6][7][8][9][10][11][12][13]. The theoretical description of the SSE is based either on the Landau-Lifshitz-Gilbert equation, on the formalism of the kinetic equation, or on the technique of Green functions [14][15][16][17][18][19][20]. In these studies, however, the case of stationary heating is considered.…”