Emergent Electrodynamics in Frustrated Magnets

Emergence describes the process in which a collection of small interacting components governed by simple rules can combine to form larger, more complex systems with new behaviors that are not expressed individually by the constituent components. Emergence appears to be a ubiquitous phenomenon throughout the universe. It is found on the cosmological scale with the formation of galactic structures, to the microscopic scale in the formation of atoms and molecules. As biology is considered an emergent property of chemistry, emergence is thought to play an important role in describing living processes. Studying emergent systems thus has broad implications across all of science. Emergence in magnetism can be seen when a collection of magnetic atoms is brought together to form a crystal, the magnetic components may interact stabilizing a collective magnetic state, a so-called magnet is formed. In some cases, geometric and energetic constraints of the crystal structure can cause competition between the magnetic interactions inhibiting the stabilization of a traditional magnet. This is known as a frustrated magnet. In the frustrated magnets known as rare earth pyrochlores, these constraints produce a set of simple rules that dictate the magnetic arrangement causing the magnetism to freeze in a disordered way similar to how water freezes into ice. This is known as a spin ice. A remarkable consequence of these rules is that new forms of conductivity based on magnetic monopole excitations within the spin ice can emerge from the electrodynamics that governs the frustrated magnetic interactions. While the theoretical basis for such phenomena has been established, experimental evidence has been elusive despite a significant research effort. In this project, we aim to investigate these emergent electrodynamics and the associated conductive properties of frustrated magnets in the context of rare-earth pyrochlores.

Our research aimed to uncover unexpected "magnetic electricity" effects in spin-ice crystals-materials whose atomic magnets mimic the disordered arrangement of water ice. Right from the outset, we observed a novel feature in the terahertz-frequency absorption and phase shift that may be consistent with magnetic monopole dynamics, owing to its extreme sensitivity to sample temperature. Early on, delays in receiving a specialised cryostat for terahertz measurements forced us to pivot. We reallocated funds to support our PhD students and turned to a diverse group of international collaborators for key data. When our improved spin-ice samples finally arrived late in the project, their behaviour confirmed that sample quality-and potentially lattice vibrations-play crucial roles in the magnetic dynamics we measure. To broaden our understanding, we also explored related materials. In a spin-liquid candidate (TbTiO) and in compounds like francisite and langasite, we studied how magnetic, electric, and vibrational motions interact. These complementary studies enriched our insights into spin-ice behaviour and revealed new avenues for future investigation. Looking ahead, our lab has just acquired a broadband terahertz time-domain spectrometer, which will allow us to map the full frequency-and-field "fingerprint" of these effects at low temperatures. Moreover, advanced X-ray imaging may help clarify how subtle variations in sample quality influence magnetic behaviour under thermal cycling. The principal investigator will join the Australian Synchrotron in 2025, where these imaging techniques will be applied to resolve the remaining puzzles. Together, these findings shed light on the complex interplay of magnetic charges, electric polarization, and lattice motion in exotic crystals. Understanding these effects could one day inform new technologies-such as high-speed magnetic sensors or data-storage devices-that harness "magnetic electricity" at terahertz frequencies.