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...
Herein, we study the spin-wave dispersion and dissipation in a ferromagnetic insulator-normal metal-ferromagnetic insulator system. Long-range dynamic coupling because of spin pumping and spin transfer lead to collective magnetic excitations in the two thin-film ferromagnets. In addition, the dynamic dipolar field contributes to the interlayer coupling. By solving the Landau-LifshitzGilbert-Slonczewski equation for macrospin excitations and the exchange-dipole volume as well as surface spin waves, we compute the effect of the dynamic coupling on the resonance frequencies and linewidths of the various modes. The long-wavelength modes may couple acoustically or optically. In the absence of spin-memory loss in the normal metal, the spin-pumping-induced Gilbert damping enhancement of the acoustic mode vanishes, whereas the optical mode acquires a significant Gilbert damping enhancement, comparable to that of a system attached to a perfect spin sink. The dynamic coupling is reduced for short-wavelength spin waves, and there is no synchronization. For intermediate wavelengths, the coupling can be increased by the dipolar field such that the modes in the two ferromagnetic insulators can couple despite possible small frequency asymmetries. The surface waves induced by an easy-axis surface anisotropy exhibit much greater Gilbert damping enhancement. These modes also may acoustically or optically couple, but they are unaffected by thickness asymmetries.
We theoretically consider the spin-wave mode-and wavelength-dependent enhancement of the Gilbert damping in magnetic insulator-normal metal bilayers due to spin pumping as well as the enhancement's relation to direct and alternating inverse spin Hall voltages in the normal metal. In the long-wavelength limit, including long-range dipole interactions, the ratio of the enhancement for transverse volume modes to that of the macrospin mode is equal to two. With an out-of-plane magnetization, this ratio decreases with both an increasing surface anisotropic energy and mode number. If the surface anisotropy induces a surface state, the enhancement can be an order of magnitude larger than for the macrospin. With an in-plane magnetization, the induced dissipation enhancement can be understood by mapping the anisotropy parameter to the out-of-plane case with anisotropy. For shorter wavelengths, we compute the enhancement numerically and find good agreement with the analytical results in the applicable limits. We also compute the induced direct-and alternating-current inverse spin Hall voltages and relate these to the magnetic energy stored in the ferromagnet. Because the magnitude of the direct spin Hall voltage is a measure of spin dissipation, it is directly proportional to the enhancement of Gilbert damping. The alternating spin Hall voltage exhibits a similar in-plane wave-number dependence, and we demonstrate that it is greatest for surface-localized modes.
Training and recovery of exchange bias in FeNi/Cu/Co/FeMn spin valves have been studied by magnetoresistance curves with field sweep rates from 1000 to 4800 Oe/s. It is found that training and recovery of exchange field are proportional to the logarithm of the training cycles and recovery time, respectively. These behaviours are explained within the model based on thermal activation. For the field sweep rates of 1000, 2000 and 4000 Oe/s, the relaxation time of antiferromagnet spins are 61.4, 27.6, and 11.5 in the unit of ms respectively, much shorter than the long relaxation time (∼ 10 2 s) in conventional magnetometry measurements.
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