Discovering classical spin liquids by topological search of high symmetry nets

The search for new frustrated states is a key challenge of condensed-matter physics. Traditionally, theory and experiment have focused on a relatively small number of high-symmetry nets. However, there are many three-dimensional nets, some of which can host frustrated states despite being less well studied. In this talk, I present a computational survey of high-symmetry nets -- those that are both vertex- and edge-transitive -- with nearest-neighbor antiferromagnetic interactions between classical Heisenberg or Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet that does not order, I present results on two other frustrated nets (lcx and thp) that possess finite temperature Heisenberg spin-liquid states with suppressed magnetic ordering and noncollinear ground states. With Ising spins, I present three new classical spin liquids that do not exhibit conventional magnetic ordering down to T/J = 0.01. For each system, I discuss signatures of these frustrated states using Monte Carlo calculations of diffuse scattering and thermomagnetic properties. I conclude by highlighting materials that contain unusual high-symmetry nets, and which could potentially host novel frustrated states.