Acoustic signatures of the field-induced electronic-topological transitions in YbNi$_4$P$_2$

We investigated the magnetoelastic properties of an YbNi$_4$P$_2$ single crystal at low temperatures under magnetic fields directed along the crystallographic [001] axis. We report a series of strong anomalies in the sound velocity, which is consistent with the cascade of electronic-topological transitions reported previously for this compound. In particular, we identify the vanishing of a small orbit on the Fermi surface, associated with a quantum-oscillation frequency of 34 T. Furthermore, the different transitions are better resolved with acoustic modes of particular symmetry. Using a microscopic model adapted to the strongly correlated electronic structure of YbNi$_4$P$_2$, we describe our results by inspecting realistic electron-phonon couplings in reciprocal space for each acoustic mode. This shows how the $k$ selectivity of ultrasound experiments allows to investigate Fermi-surface reconstructions in strongly correlated electronic systems.