Crystallization is a very old and well-known phenomenon that typically involves elementary units such as atoms or molecules. We are, however, slowly discovering that nonelementary mesoscale topological structures involving many electrons or spins from a large number of atoms or molecules can “crystallize” into their own lattices as if they were particles. The Abrikosov vortex lattice induced by a magnetic field in type-II superconductors is one of the best-known examples. “Crystals” of skyrmions (hedgehog-like magnetic structures) recently discovered in a family of magnetic compounds constitute another example. Their fundamental interest and their promise of functionalities relevant to future memory technologies are fueling an explosion of research in these “emergent mesoscale structures.” In this paper, we predict a new class of magnetic vortex crystals for frustrated quantum magnets.

“Frustration” in this context means that exchange interactions between the electronic spins (magnetic moments) compete with each other and can lead to a rich variety of potential magnetic orderings. We have investigated a frustrated quantum magnet on the verge of becoming magnetically ordered, i.e., near its quantum critical point. Because of frustration, several magnetic orderings, which range from simple spiral phases to more exotic structures such as vortex crystals, would compete on an equal footing (or are “degenerate”) if the quantum nature of the spins were irrelevant. But, in the frustrated quantum magnet we study, the quantum spin fluctuations are important and select the actual state of equilibrium from the degenerate set. By evaluating the exact effective spin-spin interaction near the quantum critical point, we demonstrate that vortex crystals are stabilized under quite general conditions. We have also shown that these vortex crystals produce rich magnetoelectric responses, which are potentially relevant for moving these crystals by applying electric-field gradients.