### Abstract

According to Noethers theorem, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electrons spin, or SU(2) symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin-orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be achieved in a two-dimensional electron gas, despite the presence of spin-orbit coupling. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the persistent spin helix. SU(2) is realized, in principle, when the strengths of two dominant spin-orbit interactions, the Rashba (strength parameterized by α) and linear Dresselhaus (Β 1) interactions, are equal. This symmetry is predicted to be robust against all forms of spin-independent scattering, including electron-electron interactions, but is broken by the cubic Dresselhaus term (Β 3) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as α approaches Β 1. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning α and Β 1. Using transient spin-grating spectroscopy, we find a spin-lifetime enhancement of two orders of magnitude near the symmetry point. Excellent quantitative agreement with theory across a wide range of sample parameters allows us to obtain an absolute measure of all relevant spin-orbit terms, identifying Β 3 as the main SU(2)-violating term in our samples. The tunable suppression of spin relaxation demonstrated in this work is well suited for application to spintronics.

Original language | English (US) |
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Pages (from-to) | 610-613 |

Number of pages | 4 |

Journal | Nature |

Volume | 458 |

Issue number | 7238 |

DOIs | |

State | Published - Apr 2 2009 |

### All Science Journal Classification (ASJC) codes

- General

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## Cite this

*Nature*,

*458*(7238), 610-613. https://doi.org/10.1038/nature07871