Fermi volume as a probe of hidden order

We demonstrate that the volume of the Fermi surface, measured very precisely using de Haas-van Alphen oscillations, can be used to probe changes in the nature and occupancy of localized electronic states. In systems with unconventional ordered states, this allows an underlying electronic order parameter to be followed to very low temperatures. We describe this effect in the field-induced antiferroquadrupolar (AFQ) ordered phase of PrOs ⁴Sb¹², a heavy fermion intermetallic compound. We find that the phase of de Haas-van Alphen oscillations is sensitively coupled, through the Fermi volume, to the configuration of the Pr f-electron states that are responsible for AFQ order. In particular, the β sheet of the Fermi surface expands or shrinks as the occupancy of two competing localized Pr crystal field states changes. Our results are in good agreement with previous measurements, above 300 mK, of the AFQ order parameter by other methods. In addition, the low-temperature sensitivity of our measurement technique reveals a strong and previously unrecognized influence of hyperfine coupling on the order parameter below 300 mK within the AFQ phase. Such hyperfine couplings could provide insight into the nature of hidden order states in other systems.