It is expected that there will be one magnetic octapole and three peaks of decreasing intensity in the inelastic neutron scattering of the π flux QSI. Image courtesy of Desrochers & Kim
Quantum spin liquids are fascinating quantum systems that have recently attracted a great deal of research attention. These systems are characterized by intense competition between interactions, which prevents the establishment of long-range magnetic sequences, such as those observed in conventional magnets, in which all spins are aligned in the same direction to produce a net magnetic field.
Researchers at the University of Toronto recently introduced a framework that could facilitate experimental observations of a new 3D quantum spin liquid, known as π-flux eight-pole quantum spin ice (π-O-QSI). Their paper, published in Physical Review Letters, predicts the system's unique spectral signature that can be measured in future experiments.
"Interestingly, quantum spin liquids can carry fractionation excitation," Félix Desrochers, a co-author of the paper, told Phys.org. That is, the electrons in these materials appear to dissociate into multiple components. For example, while electrons carry both spin and charge, emergent quasiparticles can carry spin but no charge.
"These excitations are not produced by the splitting of electrons into several pieces, but are the result of a highly non-trivial form of collective movement caused by their strong interactions.
For decades, physicists have been searching for clear examples of quantum spin liquid states. Still, progress in this area of research has been slow so far due to two main factors.
First, it has proven challenging to design theoretical models that can realistically describe the ground state of spin liquids and can be used to derive accurate predictions. Second, detecting and characterizing the physical properties of these systems in real materials has also proven difficult.
"Quantum spin ice (QSI) is a rare model example with the well-known quantum spin liquid ground state, which can also be found in real materials such as the rare earth thermogreenstone family," Desrochers explained.
"QSI is remarkable because it achieves the lattice equivalent of quantum electrodynamics: it possesses emergent photon-like modes (i.e., excitation similar to light particles), electrostatically charged particles, with reciprocal Coulomb interactions, called spins, and even magnetic monopoles.
Based on theoretical predictions, the quantum electrodynamics that emerge in QSI are very different from those of conventional electrodynamics. For example, the speed of the so-called "emerging light" should be on the order of 1 m/s, not the 3x108 m/s light that we encounter in our daily lives.
"Recent experiments with Ce2Zr2O7, Ce2Sn2O7 and Ce2Hf2O7 have been very exciting," Desrochers said. "The materials do not show any signs of ordering to the minimum usable temperature.
The momentum integral dynamic spin structure factor of the 0 flux and π flux QSI as a function of the lateral coupling. The π flux QSI shows three sharp peaks of decreasing intensity, while the 0 flux QSI shows one peak. Image courtesy of Desrochers & Kim
"Further analysis identified microscopic parameters that describe its behavior. They found that the system is located in a region of the parameter space that theoretically suggests a specific flavor that hosts a QSI called π flux quantum spin ice (π-QSI).
While recent studies have gathered encouraging findings, reliably identifying quantum spin liquids is a very complex task, as even a faint disorder can disrupt these states. To unambiguously detect these states, researchers first need to identify unique features unique to quantum spin liquids that remain stable.
"Prior to our work, there were no clear recommendations to study the smoking gun characteristics of spin dynamics in π flux QSI," Desrochers explained. "Therefore, our work aims to highlight potentially different features that can help determine whether π flux QSI is achieved in Ce, 2, Zr, 2, O, 7, and other similar compounds. We pay particular attention to the characteristics that can be measured with the currently available experimental equipment.
As part of their research, Desrochers and his PhD supervisor, Yong Baek Kim, began using a theoretical framework introduced by Lucile Savary and Leon Balents in 2012, called Gauge Mean Field Theory (GMFT), to predict the unique spectral characteristics of π flux QSI states. The framework essentially rewrites the initial spin operator based on the emergent excitation (i.e., photons and spinons) present in the quantum spin ice.
"This framework has been used to study some of the earliest π flux QSIs using GMFT," Desrochers said. "So we expanded this work with the aim of making experimental predictions. To ensure that our predictions are reliable, we also make extensive comparisons with previous numerical results from our group and literature.
This recent study by Desrochers and Kim makes meaningful predictions of the unique spectral signature of the spin liquid π flux QSI. These features could guide future experimental studies and help physicists confirm the existence of this singular state.
"We emphasize that the π flux QSI should produce three peaks of decreasing intensity in the inelastic neutron scattering," Desrochers said. "This is a unique and distinctive sign. If measured, these three peaks will provide convincing evidence for the experimental realization of such a three-dimensional QSL.
Desrochers and Kim hope their predictions will help researchers determine what to measure when confronted with an elusive π flux QSI state. Notably, the spectral signatures they identified should be detectable at the currently achievable experimental resolutions, so they may soon be observed.
At the same time, the researchers plan to build on their recent research and collect increasingly detailed predictions. For example, they want to study how the peaks they predict evolve at different temperatures and estimate at what temperature they disappear.
"The most exciting future developments will certainly come from the experimental side," Desrochers adds. "Confirming the existence of these peaks will provide very convincing evidence for the realization of this long-sought new state of matter. There are already some encouraging signs: recent measurements of Ce2Sn2O7 studies have shown signs of three peaks of declining intensity.
More information: Félix Desrochers et al., Spectral characterization of fractionation in eight-pole quantum spin ice, Physical Review Letters (2024). DOI: 10.1103/PhysRevLett.132.066502
期刊信息：Physical Review Letters arXiv