Thermodynamic signatures of a nearby quantum critical endpoint in UTe$_2$ under intense magnetic field

Several unconventional superconducting phases have been discovered in the vicinity of metamagnetism in the heavy-fermion paramagnet UTe$_2$ under magnetic field. To describe the mechanism of magnetic-field-induced superconductivity, a challenge is to characterize the quantum critical magnetic properties at the metamagnetic transition. In this work, we investigate the thermodynamic properties of UTe$_2$ under magnetic fields up to 60~T applied in the crystallographic $\mathbf{b}-\mathbf{c}$ plane. Magnetization and magnetostriction experiments have been performed under magnetic fields tilted by an angle $θ\lesssim42^\circ$ from $\mathbf{b}$ toward $\mathbf{c}$. They support that a quantum critical endpoint at the field angle $θ_{QCEP}\simeq(70\pm10)^\circ$ and magnetic field $μ_0H_{QCEP}\simeq(75\pm10)$~T terminates the metamagnetic transition line. A pseudo-gap in the magnetic susceptibility is related with the metamagnetic transition observed in magnetic fields for $θ<θ_{QCEP}$. The possible relation between the quantum critical endpoint and the development of magnetic-field-induced superconductivity is discussed.