Acute enhancement of the upper critical field for superconductivity approaching a quantum critical point in URhGe

When a pure material is tuned to the point where a continuous phase-transition line is crossed at zero temperature, known as a quantum critical point (QCP), completely new correlated quantum ordered states can form(1-7). These phases include exotic forms of superconductivity. However, as superconductivity is generally suppressed by a magnetic field, the formation of superconductivity ought not to be possible at extremely high field(8). Here, we report that as we tune the ferromagnet, URhGe, towards a QCP by applying a component of magnetic field in the material's easy magnetic plane, superconductivity survives in progressively higher fields applied simultaneously along the material's magnetic hard axis. Thus, although superconductivity never occurs above a temperature of 0.5 K, we find that it can survive in extremely high magnetic fields, exceeding 28 T.