AC Voltages Induced By Spin Pumping In Cirucular Bilayer System

Spintronics is a new field for studying spin-dependent effects and their applications.Its main objective is to investigate how to effectively and precisely manipulate the spin degrees of freedom to carry out the storage,transmission and processing of high-density information.In the article we calculated the dependence of the ferromagnetic resonance on the external magnetic field in the presence of the demagnetizing field when applying a strong external magnetic field perpendicular to the interface of a circular bilayer consisting of a ferreomagnetic material and an paramagnetic metallic material.Moreover,the spin current pumping into the paramagnetic metal from the ferromagnet under the ferromagnetic resonance condition and the diffusion of the spin current in the paramagnetic metal are derived.Finally,we obtained the AC voltages induced by the inverse spin Hall effect and the excitation magnetic field.Main conclusions are outlined as follows.The spin current pumped by an in-plane excitation magnetic field into an adjacent normal metal only can give rise to an AC voltage(current)observed due to the inverse spin Hall effect.We firstly calculated the dependence of the magnitude of the AC voltages induced by the inverse Hall effect and the excitation field on the external magnetic field and found that the former attain the maximum at the ferromagnetic resonance(FMR)and decay quickly away from the FMR,and that the latter always increase with the external magnetic field.Secondly,the magnitude of the total AC voltage perpendicular to the excitation field as a function of the field is investigated for different phase difference between two AC voltages.We obtain that the magnitude of the total AC voltage changes obviously near the FMR and its magnitude attains the maximum at the phase difference 0 and the minimum at the phase difference?.Thirdly,the dependence of the AC voltage on the excitation power is studied and the AC voltages are in scale with _P,different from the dc voltages proportional to P.Finally,for different excitation powers and different paramagnetic metals the dependence of the magnitude of the AC voltages on the sample thickness is investigated.The magnitude of the AC voltage induced by the ISHE decreases with increasing thickness for the paramagnetic metals Pt and Ta from 5nm to 100nm while the magnitude increases firstly,then decreases with increasing thickness in Pd and Au.The magnitude of the total AC voltage induced by the ISHE and the excitation field always increases with increasing thickness of the sample.