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  • Review Article
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Rashba-like physics in condensed matter

Nature Reviews Physics volume 4, pages 642–659 (2022)Cite this article

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Abstract

Spin–orbit coupling induces a unique form of Zeeman interaction in momentum space in materials that lack inversion symmetry: the electron’s spin is locked on an effective magnetic field that is odd in momentum. The resulting interconnection between the electron’s momentum and its spin leads to various effects such as electric dipole spin resonance, anisotropic spin relaxation and the Aharonov–Casher effect, but also to electrically driven and optically driven spin galvanic effects. Over the past 15 years, the emergence of topological materials has widened this research field by introducing complex forms of spin textures and orbital hybridization. The vast field of Rashba-like physics is now blooming, with great attention paid to non-equilibrium mechanisms such as spin-to-charge conversion, but also to nonlinear transport effects. This Review aims to offer an overview of recent progress in the development of condensed matter research that exploits the unique properties of spin–orbit coupling in non-centrosymmetric heterostructures.

Key points

  • The Rashba effect is a mechanism that locks the spin of a charge carrier to its momentum and stems from the coexistence of inversion symmetry breaking and spin–orbit coupling.

  • The Rashba effect is ubiquitous in condensed matter and exists in a wide variety of systems and heterostructures, including semiconductors, metals, superconductors and correlated materials.

  • The physics of the Rashba effect is at the origin of several important phenomena in condensed matter, including spin-to-charge interconversion, non-reciprocal magnetoelectric and magnetoptical response, and anomalous nonlinear effects.

  • Depending on the crystal and magnetic symmetries of the system under consideration, complex forms of spin–momentum locking and dispersion can be obtained, leading to a rich zoo of phenomena.

  • The impact of the Rashba effect extends far beyond spin transport and is at the basis of several key concepts in topological insulators, semimetals and superconductors.

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Fig. 1: Electrostatic and geometric symmetry breaking giving rise to k-antisymmetric orbital momentum and Rashba-like spin–orbit coupling.
Fig. 2: Schematics of the interplay between inversion symmetry breaking and spin–orbit coupling.
Fig. 3: Spin and orbital textures in momentum space.
Fig. 4: Cubic Rashba effect and emergence of 2D ferromagnetism at iridium silicide surface of valence-fluctuating EuIr2Si2.
Fig. 5: Spin–charge interconversion using the Rashba effect.

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Acknowledgements

The authors thank F. Nasr for her critical reading of the manuscript. P.N. acknowledges the support of the ETH Zurich Postdoctoral Fellowship Program 19-2 FEL-61. A.M. acknowledges support from the Excellence Initiative of Aix-Marseille Université–A*Midex, a French ‘Investissements d’Avenir’ program.

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Authors and Affiliations

  1. Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich, Germany

    Gustav Bihlmayer

  2. Department of Materials, ETH Zurich, Zurich, Switzerland

    Paul Noël

  3. Donostia International Physics Center (DIPC), Donostia–San Sebastián, Spain

    Denis V. Vyalikh & Evgueni V. Chulkov

  4. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    Denis V. Vyalikh

  5. Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU, Donostia–San Sebastián, Spain

    Evgueni V. Chulkov

  6. Aix-Marseille Université, CNRS, CINaM, Marseille, France

    Aurélien Manchon

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Supplementary information

Glossary

Floquet engineering

Modification of the electronic band structure on shining off-resonant light on a material.

Bloch states

Solutions of the Schrödinger equation in the presence of a periodic potential, which characterize electrons in crystals.

Neumann’s principle

The physical properties of a crystal should possess at least the same symmetries as the crystal itself.

Orbital Hall effect

Generation of a pure orbital current transverse to an injected charge current.

Photogalvanic effect

Generation of a DC charge current on shining linearly or circularly polarized light on a material.

Quantum spin Hall effect

Transport mechanism associated with insulating bulk states and topologically protected spin-current carrying edges or surface states.

Quantum anomalous Hall effect

Transport mechanism associated with insulating bulk states and topologically protected charge-carrying edges or surface states.

Fermi arcs

Disconnected arcs in momentum space appearing at the surface of certain materials such as Weyl semimetals.

Topological magnetoelectric effect

Generation of a quantized contribution to the magnetization by applying an external electric field.

Pairing parity

Symmetry property describing the behaviour of the wavefunction of a Cooper pair under permutation of the paired electrons.

Non-reciprocal transport

Inequivalence of the conductivity of a material or a heterostructure upon changing the current polarity.

Nonlinear anomalous Hall effect

Charge current flowing transverse to the injected current in the absence of time-reversal symmetry breaking and at second order in the electric field.

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Bihlmayer, G., Noël, P., Vyalikh, D.V. et al. Rashba-like physics in condensed matter. Nat Rev Phys 4, 642–659 (2022). https://doi.org/10.1038/s42254-022-00490-y

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