Classical dipoles on the kagome lattice

TL;DR

This study explores the effects of dipolar interactions on spins on the kagome lattice, revealing various ordered states and phase transition behaviors through multiple analytical and numerical methods.

Contribution

It provides a comprehensive analysis of dipolar spin ordering on the kagome lattice, including the impact of dipolar interactions on ground states and excitations, which was not previously detailed.

Findings

Long-range three-sublattice order for weak and moderate dipolar interactions

Ferrimagnetic three-sublattice order when dipolar interactions dominate

Minimal dispersion of the flat band of zero-energy excitations with added dipolar interactions

Abstract

Motivated by recent developments in magnetic materials, frustrated nanoarrays and cold atomic systems, we investigate the behaviour 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 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; while 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 behaviour consistent with Ising criticality for the 120-degree state, while the ferrimagnetic state appears to be associated with drifting exponents. The celebrated flat band of zero-energy excitations of the kagome nearest-neighbour Heisenberg model is lifted to finite energies but acquires only minimal dispersion as dipolar interactions are added.