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Spin transfer exchange torque in ferromagnet/ferromagnet structures made of half-metals with large exchange gaps

V. Shablenko and Ya. B. Bazaliy
Phys. Rev. B 108, 174446 – Published 30 November 2023
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  • INTRODUCTION
  • MODEL OF FERROMAGNETS
  • SINGLE-ELECTRON CONTRIBUTIONS TO…
  • EXCHANGE INTERACTION IN EQUILIBRIUM
  • BOUNDARY CONDUCTANCE
  • CONCLUSIONS AND DISCUSSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Spin torques in magnetic multilayers are produced by spin polarization P of ferromagnetic (F) layers, and increase with growing P. The latter, however, cannot exceed the P=1 value found in half-metals. We study the P=1 case to find what other parameters still influence spin torques in this extreme limit. It is found that the ratio of the exchange gap to Fermi energy strongly affects the properties of the torque. For large values of the gap, the magnitude of exchange spin torque exhibits a sharp peak at very small misalignment angles between magnetizations. This behavior is found to be linked to a transition between Ohmic and tunneling transport regimes through the F/F boundary.

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    • Received 6 September 2023
    • Accepted 7 November 2023

    DOI:https://doi.org/10.1103/PhysRevB.108.174446

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    MagnetismSpin currentSpin polarizationSpin torqueSpintronics
    1. Physical Systems
    Half-metalsHeusler alloy
    1. Techniques
    Boltzmann theoryLandauer formula
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    V. Shablenko* and Ya. B. Bazaliy†

    • Department of Physics & Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA

    • *shablenv@email.sc.edu
    • †Corresponding author: bazaliy@mailbox.sc.edu

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    Issue

    Vol. 108, Iss. 17 — 1 November 2023

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    Images

    • Figure 1
      Figure 1

      (a) F/F device and (b) coordinates in spin space.

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    • Figure 2
      Figure 2

      Energy diagram for electrons crossing the F/F boundary. Ferromagnets on both sides of the structure are assumed to be identical.

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    • Figure 3
      Figure 3

      Angular dependence of normalized exchange torque TLY(β)/kF4. Numbers near curves give the values of kF/kΔ.

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    • Figure 4
      Figure 4

      Model for electric current calculation. (a) Electron distribution in k-space. Distributions on both sides of the boundary are shown. Filled electron states of the “shifted Fermi spheres” are shown in red color; equilibrium Fermi spheres are shown by dashed lines. Vertical dashed lines separate the k states of right-moving and left-moving electrons. Current produced by L→R moving electrons is partially compensated by R→L moving electrons. (b) Energy diagram. Electrons contained in energy intervals I, II, and III are uncompensated and contribute to the total current.

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    • Figure 5
      Figure 5

      Exact and approximate single-electron particle currents jn(1)(β) for kL/kΔ=0.1, kV/kL=0.1.

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    • Figure 6
      Figure 6

      Exact and approximate single-electron spin currents jsY(1)(β) for kL/kΔ=0.1.

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    • Figure 7
      Figure 7

      Dynamic behavior of ML is governed by the equation L̇=TL for the angular momentum of the left layer, where L↑↓ML. The sense of rotation is determined by L̇Y=TLY>0. Similar logic works for the dynamics of MR.

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    • Figure 8
      Figure 8

      Distributions of electrons on both sides of F/F boundary. Fermi surface shift by Δk translates into the energy shift Δε. (a) Three intervals of energy contributing to electric current. (b) Regions in the k space of the left F layer, corresponding to the three energy intervals in (a). Dashed semicircles with radii kF and k(−) define region I. Crescent-shaped regions II and III have widths Δk and δk, see text.

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    • Figure 9
      Figure 9

      Impurity at the boundary enables conductance by flipping electron spins.

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