Superconductivity and the high field ordered phase in the heavy fermion compound PrOs$_4$Sb$_{12}$

Superconductivity is observed in the filled skutterudite compound \PrOsSb{} below a critical temperature temperature $T_\mathrm{c} = 1.85$ K and appears to develop out of a nonmagnetic heavy Fermi liquid with an effective mass $m^{*} \approx 50 m_\mathrm{e}$, where $m_\mathrm{e}$ is the free electron mass. Features associated with a cubic crystalline electric field are present in magnetic susceptibility, specific heat, electrical resistivity, and inelastic neutron scattering measurements, yielding a Pr$^{3+}$ energy level scheme consisting of a $\Gamma_{3}$ nonmagnetic doublet ground state, a low lying $\Gamma_{5}$ triplet excitied state at $\sim 10$ K, and much higher temperature $\Gamma_{4}$ triplet and $\Gamma_{1}$ singlet excited states. Measurements also indicate that the superconducting state is unconventional and consists of two distinct superconducting phases. At high fields and low temperatures, an ordered phase of magnetic or quadrupolar origin is observed, suggesting that the superconductivity may occur in the vicinity of a magnetic or quadrupolar quantum critical point.