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Generalized magnetoelectronic circuit theory and spin relaxation at interfaces in magnetic multilayers

G. G. Baez Flores, Alexey A. Kovalev, M. van Schilfgaarde, and K. D. Belashchenko
Phys. Rev. B 101, 224405 – Published 3 June 2020
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  • INTRODUCTION
  • GENERALIZED CIRCUIT THEORY
  • SPIN LOSS AT INTERFACES
  • SPIN-ORBIT TORQUE
  • COMPUTATIONAL DETAILS AND INTERFACE…
  • ADIABATIC EMBEDDING
  • RESULTS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Spin transport at metallic interfaces is an essential ingredient of various spintronic device concepts, such as giant magnetoresistance, spin-transfer torque, and spin pumping. Spin-orbit coupling plays an important role in many such devices. In particular, spin current is partially absorbed at the interface due to spin-orbit coupling. We develop a general magnetoelectronic circuit theory and generalize the concept of spin-mixing conductance, accounting for various mechanisms responsible for spin-flip scattering. For the special case when exchange interactions dominate, we give a simple expression for the spin-mixing conductance in terms of the contributions responsible for spin relaxation (i.e., spin memory loss), spin torque, and spin precession. The spin memory loss parameter δ is related to spin-flip transmission and reflection probabilities. There is no straightforward relation between spin torque and spin memory loss. We calculate the spin-flip scattering rates for N|N, F|N, and F|F interfaces using the Landauer-Büttiker method within the linear muffin-tin orbital method and determine the values of δ using circuit theory.

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    • Received 30 March 2020
    • Accepted 14 May 2020

    DOI:https://doi.org/10.1103/PhysRevB.101.224405

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Giant magnetoresistanceSpin currentSpin diffusionSpin relaxationSpin torqueSpin-orbit couplingSpintronics
    1. Physical Systems
    Magnetic multilayers
    1. Techniques
    First-principles calculationsGreen's function methodsNonequilibrium Green's function
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    G. G. Baez Flores1, Alexey A. Kovalev1, M. van Schilfgaarde2,3, and K. D. Belashchenko1

    • 1Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska–Lincoln, Lincoln, Nebraska 68588, USA
    • 2Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
    • 3National Renewable Energy Laboratory, Golden, Colorado 80401, USA

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    Issue

    Vol. 101, Iss. 22 — 1 June 2020

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    Images

    • Figure 1
      Figure 1

      Crossing of the electronic bands in a ferromagnetic lead near an intersection of two Fermi surface sheets of opposite spin. The parallel component of the quasimomentum, k∥, is fixed. (a)–(b) and (c)–(d): Cases where the normal component of the group velocity v⊥ has the same or opposite sign on the two sheets, resulting in resonant spin-flip reflection or transmission, respectively. (a) and (c): No SOC. (b) and (d): Avoided crossings induced by SOC.

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    • Figure 2
      Figure 2

      Spin-flip scattering mechanisms induced by a crossing of two Fermi sheets of opposite spin in an adiabatically embedded interface with no disorder. Dashed vertical lines show the interface; the label F specifies that the given metal must be ferromagnetic. Blue and red lines schematically show the trajectory of an electron before and after the spin flip. Crosses show physical spin-flip scattering processes, while circles denote those that occur solely due to adiabatic embedding.

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    • Figure 3
      Figure 3

      k-resolved spin-flip reflection functions for adiabatically embedded Pt|Pt, Pd|Pd, and Pt|Pd interfaces with and without k-point filtering. (a) R↓↑ in Pt|Pt; (b) RL↓↑ in Pt|Pd; (c) RR↓↑ in Pt|Pd; (d) R↓↑ in Pd|Pd; (e) R↓↑ in Pt|Pt, filtered; (f) RL↓↑ in Pt|Pd, filtered; (g) RR↓↑ in Pt|Pd, filtered; (h) R↓↑ in Pd|Pd, filtered.

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    • Figure 4
      Figure 4

      k-resolved spin-flip transmission and reflection functions for Ni|Ni, Co|Co, and Ni|Co, and an illustration of k-point filtering. (a) R↓↑ in Ni|Ni; (b) R↓↑ in Co∣Co; (c) T↓↑ in Ni|Ni; (d) T↓↑ in Co|Co; (e) T↓↑ in Ni|Co; (f) T↑↓ in Ni|Co; (g) R↓↑L in Ni|Co; (h) R↓↑R in Ni|Co; (i) T↓↑ in Ni|Co, filtered; (j) T↑↓ in Ni|Co, filtered; (k) R↓↑L in Ni|Co, filtered; (l) R↓↑R in Ni|Co, filtered.

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