Quantum Criticality in the Ferromagnetic Superconductor UCoGe under Pressure and Magnetic Field

The pressure-temperature phase diagram of the orthorhombic ferromagnetic superconductor UCoGe was determined by resistivity measurements up to $10.5~$GPa. The Curie temperature $T_C$ is suppressed with pressure and vanishes at the critical pressure $p_c\approx1~$GPa. Superconductivity is observed in both the ferromagnetic state at low pressure, and in the paramagnetic state above $p_c$ up to about 4$~$GPa. Non-Fermi liquid behavior appears in a large pressure range. The resistivity varies linearly with temperature around $p_c$ and evolves continuously with pressure to a $T^2$ Fermi-liquid behavior for $p \gtrapprox 5$~GPa. The residual resistivity as a function of pressure shows a maximum far above $p_c$ at $p^\star=7.2~$GPa and the amplitude of the inelastic scattering term of the resistivity decreases by more than one order in magnitude at $p^\star$, which appears to mark the entrance into a weakly correlated regime. The pressure dependence of the upper critical field for magnetic field applied along the $b$ and $c$ axis illustrates the drastic difference in the field dependence of the ferromagnetic superconducting pairing. While for $H\parallel b$ axis $H_{c2}(T)$ is driven by the suppression of the ferromagnetic order, it is dominated by the strong initial suppression of the ferromagnetic fluctuations for a field applied in the easy magnetization axis $c$.