Water and quantum magnets share critical physics

Under normal conditions, water boils at 100 °C, and its density changes dramatically, making a discontinuous jump from liquid to gas. When a substance changes its state in this way, scientists talk about a phase transition.

If we turn up the pressure, the boiling point of water also increases, until a pressure 221 times atmospheric, where it boils at 374 °C. Here something strange happens: the liquid and gas merge into a single phase. Above this critical point, there is no longer a phase transition at all. By controlling its pressure, water can therefore be steered continuously from liquid to gas without ever crossing such a transition.

Is there a quantum version of the water-like phase diagram? “This question is going to be important in quantum spintronics,” explains Bruce Normand, researcher at PSI and co-author of the study. “The materials that work best for storing and transferring quantum information using quantum spins tend, like water, to have discontinuous phase transitions at the lowest temperatures.”

Previous studies have focused on continuous phase transitions in quantum magnetic materials. Now, in a joint experimental and theoretical project, researchers at EPFL and PSI have studied a discontinuous phase transition to observe the first ever critical point in a quantum magnet, similar to that of water. The study is led by Henrik Rønnow and Frédéric Mila, both professors at the School of Basic Sciences at EPFL.

The scientists used a quantum antiferromagnetic material, known in the field as SCBO from its chemical composition, SrCu₂(BO₃)₂. “Quantum antiferromagnets are especially useful for understanding how the quantum aspects of a material’s structure affect its overall properties – for example, how the spins of its electrons interact to give its magnetic properties,” Normand explains.

SCBO is also a ‘frustrated’ magnet, meaning that its electron spins can’t stabilize in an orderly structure, and instead they adopt some uniquely quantum fluctuating states.

Critical physics in the quantum world

In a complex experiment, the researchers applied both pressure and a magnetic field to milligram pieces of SCBO. “This allowed us to look all around the discontinuous quantum phase transition and that way we found critical-point physics in a pure spin system,” says Rønnow.

The team measured the specific heat of SCBO, which shows how much energy the material can absorb as heat. For example, water absorbs only small amounts of energy at -10 °C, but at 0 °C and 100 °C, it can take up huge amounts as every molecule is driven across the transitions from ice to liquid and liquid to gas. Just like water, the pressure-temperature relationship of SCBO forms a phase diagram with a line of discontinuous transitions separating two quantum magnetic phases, and this line ends at a critical point.

“Now when a magnetic field is applied, things become more complicated than in water,” says Normand. “Neither magnetic phase is strongly affected by a small field, so the line becomes a wall of discontinuities in a three-dimensional phase diagram – but then one of the phases becomes unstable and the field helps push it towards a third phase.”

To explain this macroscopic quantum behaviour, the researchers teamed up with several colleagues, particularly Philippe Corboz at the University of Amsterdam in the Netherlands, who have been developing powerful new computer-based techniques. “Previously it was not possible to calculate the properties of ‘frustrated’ quantum magnets in a realistic two- or three-dimensional model,” says Frédéric Mila. “So SCBO provides a well-timed example where the new numerical methods provide a quantitative explanation of a phenomenon new to quantum magnetism.”

Henrik Rønnow concludes: “Looking forward, the next generation of functional quantum materials will be switched across discontinuous phase transitions, so a proper understanding of their thermal properties will certainly include the critical point, whose classical version has been known to science for two centuries.”

Text: Based on a media release by EPFL with additions from the Paul Scherrer Institute