As 2025 marks the International Year of Quantum Technology, the ESRF contributes to the global exploration of quantum phenomena by delving into the mysteries of novel quantum magnets. These materials offer a fascinating window into the fundamental interactions of matter, yet their behaviour remains highly mysterious. To unravel them, ESRF users have had to push the boundaries of an X-ray technique. This article was first published in the March 2025 issue of the ESRFnews magazine, dedicated to quantum technology.
It is one of the most famous experiments in physics. Light illuminates a pair of slits in a wall, generating an array of bright and dark patches on a screen. The British physicist Thomas Young first performed the experiment at the turn of the 19th century to demonstrate that light can interfere with itself, behaving as a wave. Much later, quantum versions of the experiment would demonstrate something far more mysterious: that photons, electrons and other particles can exhibit wave-like interference patterns, but apparently only when no-one is watching. The experiment “has in it the heart of quantum mechanics”, wrote the American physicist and Nobel laureate Richard Feynman. “In reality, it contains the only mystery.”
Today, few scientists doubt the merits of quantum mechanics. It has proved itself through mind-boggling predictive power, not to mention a host of practical applications: semiconductor electronics, lasers, superconducting magnets, quantum cryptography and quantum computing, to name but a few. Yet it is still a subject ripe with puzzles, both in its basic interpretation and in its role in condensed matter, where each material can serve as a quantum playground.
One puzzle is the existence of peculiar types of magnetism, as studied by ESRF users such as Markus Grüninger from the University of Cologne in Germany. Unravelling these phenomena has led Grüninger and his colleagues to shift the boundaries of an X-ray technique – amazingly, in such a way as to recall Young’s famous experiment once again. “Our experiments rely on the excellent beam quality at the ESRF, the outstanding performance of the set-up at beamline ID20, and the fruitful collaboration with the beamline staff,” says Grüninger.
The technique in question is resonant inelastic X-ray scattering (RIXS). This begins with an X-ray photon knocking a tightly bound electron up to a higher atomic energy level. Almost instantaneously an electron from another high energy level relaxes into the resultant hole, releasing a new photon. By measuring the difference in energy between the incoming and outgoing photons, users can learn how the process has changed the solid in collective excitations of electron charge and spin – the latter being the basis of magnetism. The ESRF has helped develop RIXS since the 1990s, and currently offers it at two dedicated, world-leading beamlines: ID32 with soft X-rays, and ID20 with hard X-rays.
Hard X-ray photons can transfer a lot of momentum to a sample. In 2019, an international team led by Grüninger wanted to push ID20’s capabilities, and record an even greater range of momentum transfer than usual. Drawing on theory by Jeroen van den Brink at IFW Dresden in Germany, and making use of new ID20 instrumentation developed by beamline scientists Giulio Monaco (now at the University of Padova in Italy) and Marco Moretti (now at the Polytechnic University of Milan, also in Italy), the team studied the effect of large changes in momentum transfer on the intensity of the outgoing X-rays. Their sample was a crystal of an iridium oxide containing pairs or “dimers” of iridium ions. To their delight, the researchers found an interference pattern, demonstrating that the X-ray photons were exciting electrons at both iridium sites in the dimers at once – similar to light passing through Young’s double-slit, although in this case putting the dimer in an excited state
The experiment marked the beginning of RIXS interferometry, a technique that was predicted as far back as the mid 1990s. By demonstrating that the electrons in the iridium dimers experience a quantum, wave-like delocalization over a quasi-molecular dimer orbital, RIXS interferometry opened the door to the study of materials with novel magnetic properties, which physicists have been trying to understand for decades.
The most familiar type of magnetism – the sort that exists in a common fridge magnet – is ferromagnetism. In metals such as iron, it results from conduction electrons that are delocalized over an entire crystal, with spins able to align parallel to one another, producing a net magnetic moment. This is very different to one type of material with novel magnetism, the Mott insulator. Conduction in this type of material is forbidden due to strong electron repulsion, but it still has magnetism because its spins, while localized on individual ions, can interact with each other. Even more intriguing is the cluster Mott insulator, an emerging new class of material that exhibits what could be called a “local delocalization”. Here, electrons are fully delocalized over a dimer (or another small collection of ions), but they cannot propagate from one dimer to another. This results in local magnetic moments, residing not on individual ions but on quasi-molecular clusters. “In contrast to the usual electron spin, these cluster moments are something that we can tailor, by choosing the ionic species, cluster geometry, electron count, pressure and so on,” says Grüninger.
In 2022, Grüninger and colleagues used their new RIXS interferometry to unambiguously identify a cluster Mott insulator for the first time. The ID20 data could directly reveal the presence of three electron spins delocalized over an iridium dimer, creating a cluster magnetic moment [2] in a compound that is a candidate for a quantum spin liquid. The data also paved the way for a systematic exploration of more complex compounds, for example with trimers [3] or tetramers, rather than dimers. “Our results show that the trimers reside in an unexpected parameter regime that promises non-trivial magnetic moments,” says Grüninger. “They challenge previous views on trimer physics, highlighting the strength of RIXS interferometry.”
Cluster Mott insulators are exciting because of their potential as microscopic, fine-tuned magnets, as well as for their still-unexplored quantum properties. They also have potential to realize quantum “spin liquids”. First predicted by the US physicist and Nobel laureate Philip Anderson back in the 1970s, though experimentally elusive, spin liquids excel by the quantum-driven absence of magnetic order – even at temperatures close to absolute zero – that defines more conventional magnets. They are characterized by a quantum-entangled network of strongly fluctuating spins, driven by competing interactions that cannot be satisfied simultaneously. A simplified example of the situation is three spins on the vertices of a triangle: they may all want to align antiparallel to each other, but this is possible only for a pair of them, not all three simultaneously.
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