Nuclear magnetic resonance (NMR) experiments have confirmed the presence of higher order interactions and lattice distortions in the quantum ferromagnetic phase transition in the double perovskite, Ba₂NaOsO_6­, in work published recently in Nature Communications. 

Phase transitions have been understood from a classical perspective for many years, and manipulating them forms the basis for many applications and devices used today. Classical magnetism has been driven by the understanding of the ordering of unpaired electron spins at low temperatures or in the presence of magnetic fields. This is exploited in traditional magnetic hard drives for memory storage. Condensed matter physicists have sought to identify suitable “order parameters” (such as spins in magnetic materials) that could be used to predict the bulk property effects of phase transitions.

Some materials, however, either lack observable order parameters or possess properties that seem to defy the predictions of classical theory. Called quantum materials, this broad class of matter includes high-temperature superconductors, topological states, and Mott insulators, to name a few. These materials present interesting challenges for theoreticians, who wish to establish a quantum mechanical framework to explain their properties. From an experimental standpoint, the focus lies not only in discovering novel phases but also finding ways to probe the underlying mechanisms that give rise to these emergent phenomena. These materials are of great interest because their properties could be utilized in future devices such as quantum computers.  

Ba₂NaOsO₆­ is one such quantum material that possesses a ferromagnetic phase transition that is interesting from both experimental and theoretical perspectives. In this transition in Ba₂NaOsO_6, the low-temperature ferromagnetic phase orders along the [110] direction ­(see Physical Review Letters) that cannot be explained by classical theory. According to Vesna Mitrović, associate professor of physics at Brown University and corresponding author on the work in Nature Communications, this unusual orientation made it “very clear for us that something was happening for this [type of] magnetism to onset.” To explain this anomaly, theoreticians devised a quantum model based on competing electron correlations and spin orbit coupling, and Mitrović’s team used NMR to confirm this model.

“Spin orbit coupling and strong correlation lead to more complicated physics,” Mitrović says. The theory specifically indicated that the ferromagnetic state in Ba₂NaOsO₆ was dependent on quadrupolar interactions between four or six different spins. The theory also predicted that the transition to this ferromagnetic phase would be preceded by a tetragonal distortion of the cubic symmetry state (see Physical Review B.)

“These are all predictions that NMR is ideally suited to test,” says Leon Balents, professor of physics at the University of California, Santa Barbara. Ba₂NaOsO₆­ has a canted ferromagnetic (cFM) phase, where the local spin orientation is staggered along alternating planes in the crystal. NMR measures the local spin environment, which is necessary to observe this staggering. Additionally, the researchers were able to observe the onset of the broken local symmetry phase (BLSP) at temperatures between the cFM and paramagnetic states. Through additional calculations, the research team found that the BLSP was consistent with a general transition from cubic to tetragonal symmetry, as initially predicted by the quantum theory. This symmetry breaking had never before been observed.

More exciting are the future directions suggested by this work. “The same [quantum] theory…would predict different [properties]” for a material with a different composition, says Mitrović. Beyond Mott insulators, Mitrović says that “spin orbit coupling is very important” in matter with “any sort of topological phase.” According to Balents, these experiments confirm that spin orbit coupling interactions are important “in materials regime[s] that go beyond topology, which is quite exciting!”

Read the article in Nature Communications.