Interplay between Fermi surface topology and ordering in URu${}_2$Si${}_2$ revealed through abrupt Hall coefficient changes in strong magnetic fields

Temperature- and field-dependent measurements of the Hall effect of pure and 4 % Rh-doped URu${}_2$Si${}_2$ reveal low density (0.03 hole/U) high mobility carriers to be unique to the hidden order' phase and consistent with an itinerant density-wave order parameter. The Fermi surface undergoes a series of abrupt changes as the magnetic field is increased. When combined with existing de Haas-van Alphen data, the Hall data expose a strong interplay between the stability of the hidden order,’ the degree of polarization of the Fermi liquid and the Fermi surface topology.