Gate voltage dependent Rashba spin splitting in hole transverse magnetic focusing

Magnetic focusing of charge carriers in two-dimensional systems provides a solid state version of a mass spectrometer. In the presence of a spin-orbit interaction, the first focusing peak splits into two spin dependent peaks, allowing focusing to be used to measure spin polarization and the strength of the spin-orbit interaction. In hole systems, the ${k}³$ dependence of the Rashba spin-orbit term allows the spatial separation of spins to be changed in situ using a voltage applied to an overall top gate. Here, we demonstrate that this can be used to control the splitting of the magnetic focusing peaks. Additionally, we compare the focusing peak splitting to that predicted by Shubnikov--de Haas oscillations and $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ band-structure calculations. We find that the focusing peak splitting is consistently larger than expected, suggesting further work is needed on understanding spin dependent magnetic focusing.