Physicists have long theorized the existence of a unique state of matter known as a quantum spin liquid. In this state, magnetic particles do not settle into an orderly pattern, even at absolute zero temperature. Instead, they remain in a constantly fluctuating, entangled state. This unusual behavior is governed by complex quantum rules, leading to emergent properties that resemble fundamental aspects of our universe such as the interactions of light and matter. Despite its intriguing implications, experimentally proving the existence of quantum spin liquids and exploring their distinctive properties has been extremely challenging.
In a paper recently published in Nature Physics , an international group of researchers comprised of an experimental team from Switzerland and France and theoretical physicists in Canada and the U.S., including Rice University, have found evidence of this enigmatic quantum spin liquid in a material known as pyrochlore cerium stannate. They achieved this by combining state-of-the-art experimental techniques, including neutron scattering at extremely low temperatures, with theoretical analysis. By measuring the way in which neutrons interact magnetically with the electron spin in pyrochlore, the researchers observed the collective excitations of spins interacting strongly with lightlike waves.
"Fractional matter quasiparticles, long theorized in quantum spin liquids, required significant advancements in experimental resolution to be convincingly tested in this type of material," said Romain Sibille, the leader of the experimental team at Paul Scherrer Institute in Switzerland. "The actual neutron scattering experiment was performed on a highly specialized spectrometer at the Institut Laue-Langevin in Grenoble, France, allowing us to obtain extremely high-resolution data."
"Neutron scattering is a well-established tool in analyzing the behavior of spins in magnets," added Andriy Nevidomskyy , associate professor of physics and astronomy at Rice who conducted theoretical analysis of the acquired data. "It is very difficult, however, to come up with an unambiguous 'smoking gun' signature that would prove the material harbors a quantum spin liquid."
Indeed, a 2022 study by Nevidomskyy showed that narrowing the theoretical model to dependably describe the experiment is far from easy, requiring numerically sleuthing out the model parameters and fitting it to multiple experiments.
Spinons and fractionalization
In quantum mechanics, electrons possess a property called spin, which behaves like a miniature bar magnet. When many electrons interact, their spins usually align or anti-align (aligning in an opposite direction). However, the arrangement of certain crystal structures such as pyrochlores can disrupt either arrangement. This phenomenon, called "magnetic frustration," prevents spins from stabilizing into a conventional order, creating conditions where quantum mechanics can manifest in extraordinary ways, including the emergence of quantum spin liquids.
"Despite their name, quantum spin liquids exist in solid materials," said Nevidomskyy, who has studied the quantum theory of frustrated magnets for years.
Nevidomskyy explained that the geometric frustration in a quantum spin liquid is so severe that the electrons instead form a quantum mechanical superposition that results in fluidlike correlations between electron spins as if the spins are immersed in a liquid.
"What's more, the elementary excitations are not an individual spin flipping its direction from up to down or vice versa," Nevidomskyy said. "Instead, they are these bizarre, delocalized objects that carry half of one spin degree of freedom; we call them spinons. This phenomenon, when a single spin flip sort of splits into two halves, is called fractionalization."
The concept of fractionalization and understanding how the resulting fractional particles interact with one another was key to the research performed by this experiment-theory collaboration. The spinons can be thought of as having a magnetic charge, and the interaction between two such particles is akin to electrically charged electrons repelling each other.
"At a quantum level, the electrons interact with one another by emitting and reabsorbing quanta of light known as photons. Similarly, in a quantum spin liquid, the interaction between spinons is described in terms of exchanging lightlike quanta," said Nevidomskyy.
This analogy connects the study of quantum spin liquids with quantum electrodynamics (QED), the theory that describes how electrons interact through the exchange of photons and forms the foundation of the Standard Model of particle physics. Similarly, the theory of quantum pyrochlore magnets describes spinons as interacting via emergent "photons." However, unlike QED in our universe, where light travels at a constant speed, the emergent "light" in these magnets is much slower — about 100 times slower than the speed of spinons. This stark difference leads to fascinating phenomena such as Cherenkov radiation and an increased likelihood of particle-antiparticle pair production. When combined with complementary research from a group of physicists at the University of Toronto, these findings offered unambiguous evidence for QED-like interactions in the experimental data.
"It is very exciting to see the difficult experiment and dedicated effort of theorists result in such a conclusion," said Sibille.
Future applications
The study provides some of the clearest experimental evidence yet for quantum spin liquid states and their fractionalized excitations. It confirms that materials like cerium stannate can host these exotic phases of matter, which are not only fascinating for fundamental physics but could also have implications for quantum technologies like quantum computing. The results also suggest that we might be able to tune these materials to explore different quantum phenomena such as the existence of dual particles, opening doors to future research.
Dual particles, known as visons, are unlike spinons in that they carry an electric rather than magnetic charge. They resemble the theoretical magnetic monopoles first proposed nearly a century ago by quantum mechanics pioneer Paul Dirac, who predicted their quantization. Although magnetic monopoles have never been observed and are considered highly unlikely by high-energy theorists, the idea remains a captivating aspect of modern physics.
"After this discovery, it is all the more exciting to search for evidence of monopolelike particles in a toy universe formed out of electron spins in a piece of material," said Nevidomskyy.
The research was supported by the Swiss National Science Foundation (R.S. and V.P., Grant No. 200021_179150), the U.S. National Science Foundation Division of Materials Research under the award DMR-1917511 (H.Y. and A.H.N.) and the Natural Sciences and Engineering Research Council of Canada (F.D. and YB.K.).
