## Abstract

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 spincurrent 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.

Original language | English (US) |
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Title of host publication | Fluctuating Nonlinear Oscillators |

Subtitle of host publication | From Nanomechanics to Quantum Superconducting Circuits |

Publisher | Oxford University Press |

Volume | 9780199691388 |

ISBN (Electronic) | 9780191742255 |

ISBN (Print) | 9780199691388 |

DOIs | |

State | Published - Sep 20 2012 |

## Keywords

- Magnetic tunnel junction
- Nano magnets
- Nonlinear oscillator
- Spin torque
- Spin torque oscillator
- Spin transfer torque
- Spintronics
- Stochastic dynamics