J A M Paddison, M J Cliffe, Discovering classical spin liquids by topological search of high symmetry nets, ACS Central Science (2024). Featured in First Reactions: C R Wiebe, Fantastic frustrated materials – and where to find them, ACS Central Science (2024).

Spin liquids are a paradigmatic example of a nontrivial state of matter, and the search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration─where the geometry of the net that the spins occupy precludes the generation of a simple ordered state─is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this collaborative work with Matt Cliffe (University of Nottingham), we investigated the high symmetry nets─those which are both vertex- and edge-transitive─for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identified two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identified three new classical spin liquids that do not order down to T/J = 0.01. We highlighted materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states.