Spin Pumping and Enhanced Gilbert Damping in Thin Magnetic Insulator Films

Abstract

Precessing magnetization in a thin film magnetic insulator pumps spins into adjacent metals; however, this phenomenon is not quantitatively understood. We present a theory for the dependence of spin-pumping on the transverse mode number and in-plane wave vector. For long-wavelength spin waves, the enhanced Gilbert damping for the transverse mode volume waves is twice that of the macrospin mode, and for surface modes, the enhancement can be ten or more times stronger. Spinpumping is negligible for short-wavelength exchange spin waves. We corroborate our analytical theory with numerical calculations in agreement with recent experimental results. PACS numbers: 76.50.+g, 75.30.Ds, 75.76.+j, Metallic spintronics have been tremendously successful in creating devices that both fulfill significant market needs and challenge our understanding of spin transport in materials. Topics that are currently of great interest are spin transfer and spin-pumping [1][2][3], spin Hall effects [4], and combinations thereof for use in non-volatile memory, oscillator circuits, and spin wave logic devices. A recent experimental demonstration that spin transfer and spin-pumping can be as effective in magnetic insulators as in metallic ferromagnetic systems was surprising and has initiated a new field of inquiry [5].In magnetic insulators, no moving charges are present, and in some cases, the dissipative losses associated with the magnetization dynamics are exceptionally low. Nevertheless, when a magnetic insulator is placed in contact with a normal metal, magnetization dynamics induce spin-pumping, which in turn causes angular momentum to be dumped to the metal's itinerant electron system. Due to this non-local interaction, the magnetization losses become enhanced. Careful experimental investigations of spin-pumping and the associated enhanced magnetization dissipation were recently performed, demonstrating that the dynamic coupling between the magnetization dynamics in magnetic insulators and spin currents in adjacent normal metals is strong. Importantly, in magnetic insulators, an exceptionally low intrinsic damping combined with good material control has enabled the study of spin-pumping for a much larger range of wave vectors than has previously been obtained in metallic ferromagnets [5][6][7][8][9][10][11][12][13][14].In thin film ferromagnets, the magnetization dynamics are strongly affected by the long-range dipolar interaction, which has both static and spatiotemporal contributions. This yields different types of spin waves. When the in-plane wavelength is comparable to the film thickness or greater, the long-range dipolar interaction causes the separation of the spin-wave modes into three classes depending on the relative orientation of the applied external field, in relation to the film normal, and the spinwave propagation direction [15][16][17][18][19][20]. These spin waves are classified according to their dispersion and transverse magnetization distribution as forward volume magnetostatic spin waves (FVMSWs) when the external...

Spin pumping, dissipation, and direct and alternating inverse spin Hall effects in magnetic-insulator/normal-metal bilayers

“…These results are consistent with our previous findings [18]: in the long-wavelength limit, the ratio between the enhanced Gilbert damping for the higher volume modes and that of the macrospin mode is equal to two. When there is significant surface anisotropy, the uniform mode can be altered to become a pure localized surface mode (in the out-of-plane geometry and with EP surface anisotropy), a blend between a uniform mode and a localized mode (in-plane geometries and EA surface anisotropy), or quenched uniform modes (out-of-plane field configuration and EA surface anisotropy, or in-plane field configuration and EP surface anisotropy).…”

“…In this paper, we extend our previous findings [18] in the following four aspects. (i) We compute the influence of the spin backflow on the enhanced spin dissipation.…”

“…Next, we will obtain analytical results beyond the description in Ref. [18] for the enhancement of the Gilbert damping in the presence of surface anisotropy.…”

Electrically driven Bose-Einstein condensation of magnons in antiferromagnets

“…We assume that the exchange energy, Jh 2 , and the Fermi energy are large compared to the other energy scales of the problem. In Appendix C, we calculate the coefficients V ± q,k,k for the modes that are uniform in the direction of transport and the modes with finite longitudinal momenta q separately, and we find that they differ by a factor [36] of √ 2:…”

“…(7) is the reason why the enhanced Gilbert damping for the longitudinal finite wavelength modes is twice that of the longitudinal homogeneous mode [36].…”