Analytical investigation of modulated spin-torque oscillators in the framework of coupled differential equations with variable coefficients

Ezio Iacocca, Johan Akerman

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Modulation of spin torque oscillators (STOs) is investigated by analytically solving the time-dependent coupled equations of an auto-oscillator. A Fourier-series solution is proposed, leading to the coefficients being determined with a linear set of equations, from which a nonlinear amplitude and frequency modulation (NFAM) scheme is obtained. In this framework, the NFAM features are related to the intrinsic STO parameters, revealing a frequency dependence of the harmonic-dependent modulation index that allows a modulation bandwidth to be defined for these devices. The presented results expose a rich parameter space, where the modulation and the STO's operation conditions define the observed modulation features. The Fourier-series representation of the time signal is suitable for studying periodic perturbations on the auto-oscillator equation.
Original languageEnglish
Article number184420
JournalPhysical Review B
Issue number18
Publication statusPublished - 22 May 2012
Externally publishedYes

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