Magnetic-field-dependence of the YbRh$_2$Si$_2$ Fermi surface

Magnetic-field-induced changes of the Fermi surface play a central role in theories of the exotic quantum criticality of YbRh$_2$Si$_2$. We have carried out de Haas--van Alphen measurements in the magnetic field range 8 T~$\leq H \leq$~16~T, and directly observe field-dependence of the extremal Fermi surface areas. Our data support the theory that a low-field ``large'' Fermi surface, including the Yb 4$f$ quasi-hole, is increasingly spin-split until a majority-spin branch undergoes a Lifshitz transition and disappears at $H_0 \approx 10$~T, without requiring 4$f$-localization at $H_0$.