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Measurement of Rashba and Dresselhaus spin–orbit magnetic fields

Nature Physics volume 3, pages 650–654 (2007)Cite this article

A Corrigendum to this article was published on 01 January 2008

Abstract

Spin–orbit coupling is a manifestation of special relativity. In the reference frame of a moving electron, electric fields transform into magnetic fields, which interact with the electron spin and lift the degeneracy of spin-up and spin-down states. In solid-state systems, the resulting spin–orbit fields are referred to as Dresselhaus and Rashba fields, depending on whether the electric fields originate from bulk or structure inversion asymmetry, respectively. Yet, it remains a challenge to determine the absolute value of both contributions in a single sample. Here, we show that both fields can be measured by optically monitoring the angular dependence of the electrons’ spin precession on their direction of motion with respect to the crystal lattice. Furthermore, we demonstrate spin resonance induced by the spin–orbit fields. We apply our method to GaAs/InGaAs quantum-well electrons, but it should be universally useful to characterize spin–orbit interactions in semiconductors, and therefore could facilitate the design of spintronic devices.

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Figure 1: Orientation of the magnetic and electric fields and measurement set-up.
Figure 2: TRFR signal measured at different times and electric-field angles at θ=45∘.
Figure 3: Spin–orbit fields as a function of ϕ for θ=0, 90∘ and 45∘.
Figure 4: Spin resonance induced by an oscillating spin–orbit field.

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Acknowledgements

The authors wish to acknowledge R. Leturcq for help with sample preparation and M. Duckheim, D. Loss, R. Allenspach and T. Ihn for discussions. This work was supported by the Swiss National Science Foundation (NCCR Nanoscale Science).

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Authors and Affiliations

  1. IBM Research, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland

    Lorenz Meier & Gian Salis

  2. Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland

    Lorenz Meier, Ivan Shorubalko & Klaus Ensslin

  3. FIRST Center for Micro- and Nanosciences, ETH Zurich, 8093 Zurich, Switzerland

    Emilio Gini & Silke Schön

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  1. Lorenz Meier
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Contributions

L.M. carried out the experiments and analysed the data in close collaboration with G.S. Samples were fabricated by L.M. and I.S., and grown by E.G. (samples 1 and 2) and S.S. (sample 3). K.E. initiated the collaboration and supported the project in discussions.

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Correspondence to Lorenz Meier or Gian Salis.

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The authors declare no competing financial interests.

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Meier, L., Salis, G., Shorubalko, I. et al. Measurement of Rashba and Dresselhaus spin–orbit magnetic fields. Nature Phys 3, 650–654 (2007). https://doi.org/10.1038/nphys675

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