Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets

Spin liquids are a paradigmatic example of a nontrivial state of matter. 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 paper, we investigate 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 identify 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 identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

Quantum Effects on Unconventional Pinch Point Singularities

Fracton phases are a particularly exotic type of quantum spin liquids where the elementary quasiparticles are intrinsically immobile. These phases may be described by unconventional gauge theories known as tensor or multipolar gauge theories, characteristic for so-called type-I or type-II fracton phases, respectively. Both variants have been associated with distinctive singular patterns in the spin structure factor, such as multifold pinch points for type-I and quadratic pinch points for type-II fracton phases. Here, we assess the impact of quantum fluctuations on these patterns by numerically investigating the spin S=1/2 quantum version of a classical spin model on the octahedral lattice featuring exact realizations of multifold and quadratic pinch points, as well as an unusual pinch line singularity. Based on large scale pseudofermion and pseudo-Majorana functional renormalization group calculations, we take the intactness of these spectroscopic signatures as a measure for the stability of the corresponding fracton phases. We find that in all three cases, quantum fluctuations significantly modify the shape of pinch points or lines by smearing them out and shifting signal away from the singularities in contrast to effects of pure thermal fluctuations. This indicates possible fragility of these phases and allows us to identify characteristic fingerprints of their remnants.