Neutrons bridge predictions and reality of quantum spin ice

By linking theoretical predictions with neutron experiments, researchers have found evidence for quantum spin ice in the material Ce₂Sn₂O₇. Their findings could inspire the technology of tomorrow, such as quantum computers. The results have been published in the journal ‘Nature Physics’.

In everyday life, we are surrounded by classical, common states of matter: liquids, solids and gases. But unbeknownst to most of us, much more exotic states can be found in the quantum world. Examples include so-called quantum spin liquids, which, similarly to liquids known in everyday life, are only locally ordered, but remain liquid even at the lowest temperatures. In a physicist's words, they never freeze, but remain in a fluctuating state.

In liquids, "locally ordered" refers to atomic or molecular positions that are only organised with respect to their close neighbours. In the quantum world, electrons in atoms behave like tiny magnets, due to an intrinsic property called spin. The order we are referring to in this case concerns the orientation of these microscopic magnets – that is, their magnetic moments. At low temperatures, they can reach a locally ordered state known as a spin ice.

This occurs famously in the so-called rare-earth pyrochlores – inorganic crystals such as the compound Ce₂Sn₂O₇ (Ce = cerium, Sn = tin, O = oxygen). On an atomic scale, pyrochlores consist of many small pyramids, which are known as tetrahedra. The corners of these tetrahedra are occupied by magnetic ions whose moments follow the "2 in, 2 out" rule: two of them are oriented inwards of the tetrahedron and two point outwards.

While these orientations fluctuate incessantly, thereby preventing a long-range order even at very low temperatures, a phenomenon known as long-range quantum entanglement (LRE) takes place between the magnetic moments. LRE has been described by theoretical models in an idealised system with specific features. But how can we know whether this corresponds to reality in a spin liquid?

Luckily, the LRE gives rise to specific types of magnetic excitations, which can be detected using neutrons. This was exploited in a series of experiments at the Institut Laue-Langevin (ILL), in Grenoble (France) headed by Romain Sibille, from the Paul Scherrer Institute in Switzerland. "We used inelastic neutron scattering on the instruments IN5 and IN16B at the ILL to characterise Ce₂Sn₂O₇ samples", explains Sibille.

For an optimal characterisation of the magnetic fluctuations, the neutron experiments were performed by combining the performances of IN5 and IN16B. The IN5 data allowed for a detailed description of these excitations. "We also captured their temperature dependence to confirm the origin of the signal", adds Jacques Ollivier, ILL scientist and IN5 instrument responsible. "We found the signal to be particularly temperature-sensitive below 1 Kelvin."

At the lowest attained temperature (0.2 K), the team noticed a peculiar signal which needed to be characterised at a higher energy resolution. This was done on IN16B with the help of Markus Appel, ILL researcher and main responsible of this instrument. IN16B also made it possible to obtain particularly high-resolution data of the magnetic excitations in the compound.

The team was delighted to see that the experimental data were well described by recent theoretical models. This is not a given, especially for exotic states such as the ones described here, and is a beautiful example of the power of theoretical physics to describe the world around us. Crucially, clear evidence for a quantum spin ice state was found in Ce₂Sn₂O₇. "To our knowledge, the features we observed are unique descriptors of the quantum spin ice state of this material", says Romain Sibille.

This work paves the way towards future unifications of theory and experiments, which is of particular interest for highly complex areas such as quantum physics and exotic states of matter. The findings also offer a wonderful playground for further exploration of quantum phenomena in materials with potential applications in quantum computing.