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Thermal Properties of Spin Torque Oscillators: Singularity in Effective Energy

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2 Author(s)
Wang, Shuxia ; Dept. of Phys., Univ. of Alabama, Tuscaloosa, AL ; Visscher, P.B.

It is important to be able to calculate steady-state probability distributions in spin torque systems, for such applications as spin-torque oscillators and thermal switching of MRAM. It has been shown using a Fokker-Planck formulation of this problem that the steady state probability can be expressed in terms of an effective energy, which can be calculated analytically for uniaxial systems (including perpendicular-anisotropy thin film elements). For elements with in-plane anisotropy or in-plane fields, the effective energy has been calculated numerically and fit to a polynomial in the energy. The fit was not very good, and in the present paper we show that this is because the effective energy has a logarithmic singularity at the saddle point. Fitting to a form with the singularity built in gives a much better fit, using the same number of parameters. This makes computation of oscillator linewidths and switching rates in spin-torque systems much easier.

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Magnetics, IEEE Transactions on  (Volume:44 ,  Issue: 11 )