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Precession states in planar spin-transfer devices: The effective one-dimensional approximation

Ya. B. Bazaliy
Phys. Rev. B 76, 140402(R) – Published 4 October 2007
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    Abstract

    Current induced precession states in spin-transfer devices are studied in the case of large easy plane anisotropy (present in most experimental setups). It is shown that the effective one-dimensional planar description provides a simple qualitative understanding of the emergence and evolution of such states. Switching boundaries are found analytically for the collinear device and the spin-flip transistor. The latter can generate microwave oscillations at zero external magnetic field without either special functional form of spin-transfer torque, or “fieldlike” terms, if the Gilbert constant corresponds to the overdamped planar regime.

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    • Received 24 May 2007

    DOI:https://doi.org/10.1103/PhysRevB.76.140402

    ©2007 American Physical Society

    Authors & Affiliations

    Ya. B. Bazaliy

    • Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands; Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA; and Institute of Magnetism, National Academy of Science, 36-b Vernadsky Boulevard, Kyiv 03142, Ukraine

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    Issue

    Vol. 76, Iss. 14 — 1 October 2007

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    Images

    • Figure 1
      Figure 1
      Planar spin-transfer devices. Hashed parts of the devices are ferromagnetic; white parts are made from a nonmagnetic metal.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) Evolution of effective energy profile and stable solutions with spin-transfer strength (graphs are shifted up as u becomes more negative) for a device with collinear polarizer. Left: Low field regime, 0<h<ω̃∣∣. Right: High field regime, h>ω̃∣∣. Evolution stage (3) is missing in the high field regime due to the absence of the second energy minimum. The dashed red (gray) parts of the energy profile graphs mark the αeff<0 regions. Filled and empty circles represent the effective particle.Reuse & Permissions
    • Figure 3
      Figure 3
      Switching diagram of a device with collinear polarizer. The u-axis direction is reversed for the purpose of comparison with Refs. 7, 26. The parts of the diagram not shown can be recovered by a 180° rotation of the picture. Stable in-plane directions in each region are given by small arrows; the precession states are marked as PS1,2. The large arrow shows the fixed in-plane polarizer direction. Inset: Schematic PS1 (gray) and PS2 (dashed) trajectories on the unit sphere.Reuse & Permissions
    • Figure 4
      Figure 4
      (Color online) Switching diagram of a spin-flip transistor. The u<0 part of the diagram can be obtained by reflection with respect to the horizontal axis. In each region stable directions are given by small arrows; precession state is marked by PS1. The large arrow shows the polarizer direction. Threshold u¯3(α) is sketched as a dashed line where approximation (13) is not valid. Lower panels: the evolution of effective energy and trajectories (graphs are shifted up with growing u) at α≪α* (left) and α>α* (right). The dashed red (gray) parts of the energy profiles correspond to αeff<0. Effective particle is shown by filled and empty circles.Reuse & Permissions
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