Classical dipoles on the kagome lattice

Abstract

Motivated by recent developments in magnetic materials, frustrated nanoarrays, and cold atomic systems, we investigate the behavior of dipolar spins on the frustrated two-dimensional kagome lattice. By combining the Luttinger-Tisza approach, numerical energy minimization, spin-wave analysis, and parallel tempering Monte Carlo, we study long-range ordering and finite-temperature phase transitions for a Hamiltonian containing both dipolar and nearest-neighbor interactions. For antiferromagnetic exchange and both weak and moderate dipolar interactions, the system enters a three-sublattice long-range ordered state with each triangle having vanishing dipole and quadrupole moments; whereas for dominating dipolar interactions we uncover ferrimagnetic three-sublattice order. These are also the ground states for $XY$ spins. We discuss excitations of, as well as phase transitions into, these states. We find behavior consistent with Ising criticality for the ${120}^{\ensuremath{\circ}}$ state, whereas the ferrimagnetic state appears to be associated with drifting exponents. The celebrated flat band of zero-energy excitations of the kagome nearest-neighbor Heisenberg model is lifted to finite energies but acquires only minimal dispersion as dipolar interactions are added.