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(Color online) The schematics of experimental geometries and wave-vector selection rules for (a) perpendicular and (b) parallel parametric excitations. Arrows in the schematics indicate directions of the static and dynamic magnetic fields for each of geometries. As the spin current created by the spin pumping flows in to the Pt layer, spin Hall voltage VISHE is generated in its plane and measured in the experiment. Dashed lines in graphs show spin-wave dispersion characteristics for different angles θ and ϕ defined by the orientation of the wave vector with respect to the film plane and the static magnetic field, respectively. Solid curves show the states available for the parametrically excited spin waves as a function of the pumping frequency f p. f 0 is the FMR frequency.
(Color online) Field dependences of (a) the absorbed microwave power P abs and (b) the inverse spin-Hall voltage V ISHE obtained at different powers P applied to the microstrip. The data were recorded in the perpendicular pumping geometry for f p = 3.5 GHz. (c)–(f) show the excitation power dependences of P abs and V ISHE for linear and parametric excitation as labeled. For the linear case, we plot the measured P abs and V ISHE at H 0 = 640 Oe and both plots are fitted by linear functions. For the parametric case, we plot the measured P abs and V ISHE at H 0 = 300 Oe and both plots are fitted by a function of , where is a fitting parameter and P thr = 50 mW is used.
(Color online) (a) and (b) show the field dependences of measured inverse spin-Hall voltage V ISHE (solid curves) and of the calculated number of excited magnons n k (dashed curves) for different pumping powers P, as labelled, for parallel and perpendicular pumping, respectively. (c) and (d) measured the field dependences of the threshold power P thr for parallel and perpendicular pumping, respectively. The pumping frequency is 8.2 GHz.
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