Lozano-Gómez, D.; Noculak, V.; Oitmaa, J.; Singh, R.R. P.; Iqbal, Y.; Reuther, J.; Gingras, M.J. P.: Competing gauge fields and entropically driven spin liquid to spin liquid transition in non-Kramers pyrochlores. Proceedings of the National Academy of Sciences of the United States of America : PNAS 121 (2024), p. e2403487121/1-10
10.1073/pnas.2403487121
Open Accesn Version
Abstract:
Competing interactions in magnetic systems frustrate the development of long-range order, possibly down to absolute zero temperature, giving rise to a spin liquid. Gauge fields, akin to those used to describe the fundamental forces in the universe, are the mathematical objects of choice to describe spin liquids. In a model relevant to real magnetic pyrochlore materials, we uncover a spin liquid described by combined vector-like and matrix-like gauge fields. Classically, similarly to the liquid-to-liquid transition observed in some molecular liquids, this state disappears at low temperatures and gives way to a spin liquid with extensive entropy and with only the vector-like field thermally fluctuating. Quantum mechanically, the ground state is a spin liquid described by both gauge fields. Gauge theories are powerful theoretical physics tools that allow complex phenomena to be reduced to simple principles and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behavior at zero temperature but crucially determine the system?s temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and tensor gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the tensor gauge field, rendering the system spin-ice-like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and tensor gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers magnetic pyrochlore materials.