A quantum magnetic analogue to the critical point of water

Abstract

At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point [1], a concept ubiquitous in statistical thermodynamics [2]. In correlated quantum materials, a critical point was predicted [3] and measured [4, 5] terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) [6] have been investigated extensively [7-11], but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu2(BO3)2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model [12-14] and displays exotic phenomena including magnetization plateaux [15], anomalous thermodynamics [16] and discontinuous QPTs [17]. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu2(BO3)2 has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite temperature tensor-network methods [16, 18-20]. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties [21, 22] for spintronic applications drive an increasing focus on first-order QPTs.