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Gate-controllable spin-orbit coupling is often one requisite for spintronic devices. For practical spin field-effect transistors, another essential requirement is ballistic spin transport, where the spin precession length is shorter than the mean free path such that the gate-controlled spin precession is not randomized by disorder. In this letter, we report the observation of a gate-induced crossover from weak localization to weak anti-localization in the magneto-resistance of a high-mobility two-dimensional hole gas in a strained germanium quantum well. From the magneto-resistance, we extract the phase-coherence time, spin-orbit precession time, spin-orbit energy splitting, and cubic Rashba coefficient over a wide density range. The mobility and the mean free path increase with increasing hole density, while the spin precession length decreases due to increasingly stronger spin-orbit coupling. As the density becomes larger than ∼6 × 1011 cm-2, the spin precession length becomes shorter than the mean free path, and the system enters the ballistic spin transport regime. We also report here the numerical methods and code developed for calculating the magneto-resistance in the ballistic regime, where the commonly used HLN and ILP models for analyzing weak localization and anti-localization are not valid. These results pave the way toward silicon-compatible spintronic devices.

A demonstration of 2D hole gases in GeSn/Ge heterostructures with a mobility as high as 20 000 cm2 V−1 s−1 is given. Both the Shubnikov–de Haas oscillations and integer quantum Hall effect are observed, indicating high sample quality. The Rashba spin‐orbit coupling (SOC) is investigated via magneto‐transport. Further, a transition from weak localization to weak anti‐localization is observed, which shows the tunability of the SOC strength by gating. The magneto‐transport data are fitted to the Hikami–Larkin–Nagaoka formula. The phase‐coherence and spin‐relaxation times, as well as spin‐splitting energy and Rashba coefficient of the k‐cubic term, are extracted. The analysis reveals that the effects of strain and confinement potential at a high fraction of Sn suppress the Rashba SOC caused by the GeSn/Ge heterostructures.

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