Reinforcement of superconductivity by quantum critical fluctuations of metamagnetism in UTe$_2$

The normal-conducting state of the superconductor UTe$_2$ is studied by entropy analysis for magnetic fields along the $b$-axis, obtained from magnetization using the relation $(\partial M/\partial T)_B=(\partial S/\partial B)_T$. We observe a strong increase in entropy with magnetic field due to metamagnetic fluctuations (spatially uniform, $Q=0$). The field dependence is well described by the Hertz-Millis-Moriya theory for quantum criticality of itinerant metamagnetism. Notably, the lower bound of the quantum-critical region coincides well with the position of the minimum in the superconducting transition temperature $T_c(B)$. Hence, our results suggest that $Q=0$ fluctuations reinforce the superconductivity.