The emergence of superconductivity at high magnetic fields in URhGe is regarded as a paradigm for new state formation approaching a quantum critical point. Until now, a divergence of the quasiparticle mass at the metamagnetic transition was considered essential for superconductivity to survive at magnetic fields above 30 tesla. Here we report the observation of quantum oscillations in URhGe revealing a tiny pocket of heavy quasiparticles that shrinks continuously with increasing magnetic field, and finally disappears at a topological Fermi surface transition close to or at the metamagnetic field. The quasiparticle mass decreases and remains finite, implying that the Fermi velocity vanishes due to the collapse of the Fermi wavevector. This offers a novel explanation for the re-emergence of superconductivity at extreme magnetic fields and makes URhGe the first proven example of a material where magnetic field-tuning of the Fermi surface, rather than quantum criticality alone, governs quantum phase formation.The discovery and understanding of new quantum phases is a central theme of research in strongly correlated electron systems. Metals with narrow bandwidths including the felectron heavy fermion (HF) materials show rich behaviour because their high density of states (DOS) promotes correlation effects and the energy scale for navigating the phase diagram is accessible with realistic magnetic fields and pressures. The HF metals UGe 2 [1], URhGe [2] and UCoGe [3] attract particular interest because they show microscopic coexistence of superconductivity (SC) and ferromagnetism (FM), which are competing orders in conventional SC theories with opposite-spin pairs. They therefore offer the prospect of realizing the long-predicted metallic analogue of the A1 superfluid phase in 3 He [4] in which magnetic fluctuations bind together quasiparticles with equal spin. Strong experimental evidence that the Cooper pairs are indeed equal-spin states in URhGe is provided by the sensitivity of SC to disorder and the magnitude and T dependence of the critical field for destruction of SC [5].The phase diagram of URhGe is shown schematically in Fig. 1. Ferromagnetism exists below T = 9.5 K with a spontaneous magnetic moment M c = 0.4 µ B parallel to the crystal c-axis. Bulk SC forms deep within the FM state [2] at T c = 275 mK in the cleanest crystals. A magnetic field applied along b first destroys SC but remarkably it reappears between 8 T and ≈ 12.5 T with a higher T c than at zero field [6]. Measurements with B tilted by an angle θ away from b within the easy b, c-plane [6] suggest the surface of first order transitions separating M c > 0 from M c < 0 bifurcates at a tricritical point around 12 T giving two surfaces B R (±θ, T ) across which the moment rotates discontinuously towards B. These surfaces extend to angles a few degrees away from b, beyond which the transition is replaced by a cross-over. It has not been established if fluctuations associated with possible quantum critical points at the end of the first order lines pr...

We performed laser-heated diamond anvil cell experiments on bulk compositions in the systems MgO-SiO 2 -H 2 O (MSH) and MgO-Al 2 O 3 -SiO 2 -H 2 O (MASH) that constrain the stability of hydrous phases in Earth's lower mantle. Phase identification by synchrotron powder diffraction reveals a consistent set of stability relations for the high-pressure, dense hydrous silicate phases D and H. In the MSH system phase D is stable to ~ 50 GPa, independent of temperature from ~ 1300 to 1700 K. Phase H becomes stable between 35 and 40 GPa, and the phase H out reaction occurs at ~ 55 GPa at 1600 K with a negative dT/dP slope of ~ -75 K/GPa.Between ~ 30 and 50 GPa dehydration melting occurs at ~ 1800K with a flat dT/dP slope. A cusp along the solidus at ~ 50 GPa corresponds with the intersection of the subsolidus phase H out reaction, and the dT/dP melting slope steepens to ~15 K/GPa up to ~ 85 GPa. In the MASH system phase H is stable in experiments between ~ 45 and 115 GPa in all bulkcompositions studied, and we expect aluminous phase H to be stable throughout the lower mantle depth range beneath ~ 1200 km in both peridotitic and basaltic lithologies. In the subsolidus, aluminous Phase D is stable to ~ 55 GPa, whereas at higher pressures aluminous phase H is the stable hydrous phase. The presence of hydrogen may sharpen the bridgmanite to post-perovskite transition. The ambient unit cell volume of bridgmanite increases systematically with pressure above ~ 55 GPa, possibly representing an increase in alumina content, and potentially hydrogen content, with depth. Bridgmanite in equilibrium with phases D and H has a relatively low alumina content, and alumina partitions preferentially into the hydrous phases.The melting curves of MASH compositions are shallower than in the MSH system, with dT/dP of ~ 6K/GPa. Phase D and H solid solutions are stable in cold, hydrated subducting slabs and can deliver water to the deepest lower mantle. However, hydrated lithologies in the lower mantle are likely to be partially molten at all depths along an ambient mantle geotherm.

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We have developed a miniature diamond anvil cell for magnetization measurements in a widely used magnetic property measurement system commercial magnetometer built around a superconducting quantum interference device. The design of the pressure cell is based on the turnbuckle principle in which force can be created and maintained by rotating the body of the device while restricting the counterthreaded end-nuts to translational movement. The load on the opposed diamond anvils and the sample between them is generated using a hydraulic press. The load is then locked by rotating the body of the cell with respect to the end-nuts. The dimensions of the pressure cell have been optimized by use of finite element analysis. The cell is approximately a cylinder 7 mm long and 7 mm in diameter and weighs only 1.5 g. Due to its small size the cell thermalizes rapidly. It is capable of achieving pressures in excess of 10 GPa while allowing measurements to be performed with the maximum sensitivity of the magnetometer. The performance of the pressure cell is illustrated by a high pressure magnetic study of Mn(3)[Cr(CN)(6)](2) x xH(2)O Prussian blue analog up to 10.3 GPa.