Comprehensive magnetic-field-orientation dependent studies of the susceptibility and de Haas-van Alphen effect have been carried out on single crystals of the filled skutterudites PrOs$_4$As$_{12}$ and LaOs$_4$As$_{12}$ using magnetic fields of up to 40~T. Several peaks are observed in the low-field susceptibility of PrOs$_4$As$_{12}$, corresponding to cascades of metamagnetic transitions separating the low-field antiferromagnetic and high-field paramagnetic metal (PMM) phases. The de Haas-van Alphen experiments show that the Fermi-surface topologies of PrOs$_4$As$_{12}$ in its PMM phase and LaOs$_4$As$_{12}$ are very similar. In addition, they are in reasonable agreement with the predictions of bandstructure calculations for LaOs$_4$As$_{12}$ on the PrOs$_4$As$_{12}$ lattice. Both observations suggest that the Pr 4$f$ electrons contribute little to the number of itinerant quasiparticles in the PMM phase. However, whilst the properties of LaOs$_4$As$_{12}$ suggest a conventional nonmagnetic Fermi liquid, the effects of direct exchange and electron correlations are detected in the PMM phase of PrOs$_4$As$_{12}$. For example, the quasiparticle effective masses in PrOs$_4$As$_{12}$ are found to decrease with increasing field, probably reflecting the gradual suppression of magnetic fluctuations associated with proximity to the low-temperature, low-field antiferromagnetic state.
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