Enigmatic pathways of heat in quantum materials

What if heat didn’t simply propagate from a hot side to a cold one but also followed a diverted path, bending under the influence of invisible magnetic forces exerted by an externally applied magnetic field? The team of Louis Taillefer at the Institut Quantique (Quantum Institute) of Université de Sherbrooke has found evidence for such an effect in insulating quantum materials—a surprising phenomenon that caught the scientific community off guard. In search of answers and armed with the precision of the finest jewelers, the group conducted a series of experiments whose results, recently published in Nature Physics and featured by the renowned Nature news & views, Physics today and phys.org, now illuminate the path towards understanding this mysterious process.

To dive into the heart of this enigma, we start with the thermal Hall effect. In a metal, electrons move freely and can transport heat across the material. When the metal is exposed to a magnetic field, electrons are deflected from their path by the Lorentz force (because they are electrically charged), and the heat is similarly diverted. In insulators, however, electrons are tightly bound to their atoms, so no thermal Hall effect, right? Against all odds, a thermal Hall effect signal was measured in several magnetic insulators. The research team led by Louis Taillefer has shown in the past that phonons—the elementary quasi-particles associated with vibrations in solids—generate this effect. But since phonons carry no charge, the cause of the phenomenon remains obscure. “Why does the magnetic field have a grip on these neutral particles?” says Louis Taillefer. The question has spread worldwide, drawing the interest of theoretical physicists like Steven Kivelson from Stanford University and Subir Sachdev from Harvard University. “Now, what path can we follow to guide us towards a theoretical explanation?” wonders Taillefer.

At the Heart of Strontium Iridate

In search of an explanation, the team turned to strontium iridate, Sr2IrO4. The researchers devised a strategic plan to unravel the secrets of phonons: by introducing impurities, such as small gems, into the Sr2IrO4 network—i.e., by controlled replacement of some iridium atoms with rhodium atoms—they altered the environment in which phonons move. If the sample has no defects, virtually no thermal Hall effect is observed, whereas adding impurities causes a dramatic increase in thermal Hall conductivity. Moreover, the introduction of lanthanum impurities, which substitute for strontium atoms outside the magnetic planes, induces a lesser effect, suggesting that the location of impurities within the magnetic environment is decisive. “This confirms the theory that impurities are at the heart of the mechanism,” concludes Taillefer, referring to the theories proposed by Kivelson and Sachdev, according to which phonons are scattered by defects in the crystal lattice.

The experimental journey to achieve such a result is anything but simple. Working with crystals at the micrometer scale requires a level of precision and care that Louis Taillefer compares to that of a jeweler. “This time, the samples that we studied were particularly small! It was very difficult to handle them in order to make reliable measurements,” recalls Amirreza Ataei, a PhD student in the group and the lead author of the paper. The delicate task of manually placing six silver or gold wires, each thinner than a human hair, on a crystal less than one millimeter, or even half a millimeter, in size illustrates the extent to which the seasoned team of physicists must exhibit both sophisticated knowledge and meticulous craftsmanship. Moreover, the measurement of thermal Hall conductivity in dozens of samples for this study had to be performed with milli-degree Celsius resolution down to temperatures close to absolute zero (-273 °C), in the presence of an applied magnetic field over 200,000 times stronger than the Earth’s magnetic field!

The researchers at Sherbrooke are also grateful to have been able to collaborate with Véronique Brouet from the Solid State Physics Laboratory at the University of Paris-Saclay, whose expertise in crystal growth was crucial to the success of the study. Thanks to the many high-quality samples with precisely controlled impurity content, Amirreza Ataei was able to systematically study the impact of different types of impurities on thermal Hall conductivity. “If we were to grow this type of samples here in Sherbrooke, it would have taken years,” acknowledges Ataei, highlighting the acceleration of research that such international collaborations can bring.

“This Sherbrooke-France collaboration is part of the mission of the new IRL Quantum Frontiers, an International Research Lab created by the French CNRS in 2022 to stimulate collaboration in quantum sciences between the University of Sherbrooke and laboratories in France,” explains Louis Taillefer, director of the IRL initiative.

Prospects of an Enigmatic Phenomenon and the Impact of Phonons on Quantum Properties

The team is eager to explore new dimensions of this phenomenon, including how the effect varies with the relative directions of the field and current and the possibility of using nanofabrication to work with even smaller samples.

It is important to understand the behavior of phonons in materials, as well as their interaction with other quantum particles, such as electrons and magnons. For example, phonons can generate superconductivity in certain metals by acting as a glue between two electrons, thereby forming pairs capable of perfectly transmitting electricity without any energy loss – a fascinating property that, among other things, enables magnetic resonance imaging (MRI). The numerous quantum materials studied by the Taillefer group in Sherbrooke, such as the iridates in the current study, have new and astonishing thermal, electrical, and magnetic properties at the frontier of the materials research, some of which could pave the way for innovative future technologies.