Quantum Supercritical Regime with Universal Magnetocaloric Scaling in Ising Magnets

Abstract: Quantum critical points (QCPs) ubiquitously emerge in strongly correlated systems, with their influence extending beyond zero temperature. There exist extended quantum critical regimes (QCRs) at finite temperatures and external fields. A paradigmatic example exhibiting QCP is quantum Ising magnets like \cno, where critical quantum fluctuations and robust universal scaling behavior provide crucial insights into the quantum material. In this work, we discover a fundamentally distinct quantum supercritical regime (QSR) emerging also from the QCP but controlled by symmetry-breaking fields ($h$) coupled to the order parameter. The QSR is enclosed by the crossover boundaries $T \propto h^{{z\nu}/\Delta}$, where $z$, $\nu$ and $\Delta\equiv\beta+\gamma$ are critical exponents. Amongst other intriguing phenomena, there exists an enhanced magnetocaloric effect (MCE) in QSR, characterized by a universally diverging magnetic Gr\"uneisen ratio $\Gamma_h \equiv \frac{1}{T} (\frac{\partial T}{\partial h})_{S} \propto T^{-\Delta/{z\nu}}$. Even small symmetry-breaking fields generate dramatic temperature variations. The supercritical scaling can be comprehended via thermal data collapse based on the derived scaling form. We propose to observe the QSR and related supercritical MCE in \cno~and other quantum Ising magnets, which may enable cryogenic technologies capable of reaching the millikelvin regime without relying on helium-3.