Spin Dynamics in the Ferromagnetic Resonance

The LLG equation including the spin-transfer torque term, and the frequency spectrum analysis method are used to study the dynamic process of ferromagnetic resonance. The effects of damping factor α, internal anisotropic field, magnetic field inclination, and spin-transfer torque caused by the spin current are studied. The following results are found as follows. The ferromagnetic resonance spectra as functions of the frequency ω for fixed magnetic field, and functions of magnetic field for fixed frequency are obtained, and it is found that the internal magnetic field also has contribution to the resonance field or frequency, and we know that the resonant frequency ω0≈he + h1 (in unit of γH0). In addition, when the damping factor increases from 0.01 to 0.03, the resonance frequencies increases slightly, and the resonance strength decreases. And the oscillatory waves of mx and my reach their stable values more quickly. Furthermore, the internal field perpendicular to the external field h0 as well as it parallel to h0 also has the effect to the resonant frequency. The positive and negative internal field will have reversed effects to the resonance field or frequency. And in the end when the spin current becomes larger the STT effect becomes stronger, even exceeds the ferromagnetic resonance effect, makes mz reversed, and mx and my decreased.