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Minimum action paths for spin-torque assisted thermally induced magnetization reversal
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color online) Deterministic flow lines (black) and minimum action paths for the magnetization. The forward (red and above the plane, from m x  = −1 to mx  = +1) and backward (green and below the plane, from mx  = −1 to mx  = -1)) minimum action paths are not only different, but they cannot be obtained from the deterministic trajectories by time reversal under detailed balance except when . Indeed, if is nonzero, the STT term is present and breaks the detailed balance condition: in these cases, the transitions occur out of equilibrium. The shaded area is the basin of attraction of point ; unshaded, of . For finite values of , the transition point moves out of the plane. The external field is T. (Here we set T, , and T for easier visualization.)

Image of FIG. 2.
FIG. 2.

(Color online) Dependence of the minimum of the action (left) and of the effective energy barrier in Eq. (9) (right) on external field and current magnitude . The Zhang–Li theory is expected to be valid for positive fields only.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Minimum action paths for spin-torque assisted thermally induced magnetization reversal