Chapter

Dynamics of nano‐magnetic oscillators

T. Dunn, A. L. Chudnovskiy and A. Kamenev

in Fluctuating Nonlinear Oscillators

Published in print July 2012 | ISBN: 9780199691388
Published online September 2012 | e-ISBN: 9780191742255 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199691388.003.0006
Dynamics of nano‐magnetic oscillators

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This chapter explores how non-equilibrium noise affects spin-torque switching elements and oscillators. It first discusses the deterministic dynamics of magnetic tunnel junctions, introducing a convenient set of slow and fast degrees of freedom. It then derives an effective Langevin equation for the slowly varying energy of precessional orbit and introduces the corresponding energy noise and energy diffusion coefficient. This allows for the formulation of a Fokker–Planck equation for the energy density distribution, which is used to analyze switching time distribution as well as the shape of the optimal spin-current pulse, which minimizes Joule losses of a switch. Finally, the chapter derives a generic expression for the linewidth of a spin-torque oscillator and discusses its dependence on temperature, spin-current amplitude, and other parameters.

Keywords: spin torque; spin transfer torque; spin torque oscillator; nano magnets; spintronics; magnetic tunnel junction; stochastic dynamics; nonlinear oscillator

Chapter.  11383 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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