Persistence of the flat band in a kagome magnet with dipolar interactions

The weathervane modes of the classical Heisenberg antiferromagnet on the kagome lattice constitute possibly the earliest and certainly the most celebrated example of a flat band of zero-energy excitations. Such modes arise from the underconstraint that has since become a defining criterion of strong geometrical frustration. We focus on the fate of this flat band in the presence of additional dipolar interactions. These change the nearest-neighbour model fundamentally as they remove the Heisenberg spin-rotational symmetry while also introducing a long- range component to the interaction. Curiously, the modes continue to remain approximately dispersionless, while being lifted to finite energy. This phenomenon provides interesting connections between concepts such as constraint counting and self-screening underpinning the field of frustrated magnetism. Moreover, this property is found to be remarkably stable to a wide range of additional interactions.