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

## TL;DR

This paper explores how flat bands of zero-energy excitations in kagome antiferromagnets persist and evolve when dipolar interactions are introduced, revealing their robustness and modified properties.

## Contribution

It demonstrates that flat bands in kagome magnets remain approximately dispersionless under dipolar interactions, despite symmetry breaking and long-range effects, providing new insights into frustrated magnetism.

## Key findings

- Flat bands remain approximately dispersionless with dipolar interactions.
- Dipolar interactions lift the flat band to finite energy and alter its ellipticity.
- The phenomena connect constraint counting and self-screening in frustrated systems.

## Abstract

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 investigate the fate of this flat band when dipolar interactions are added. 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. We explain how the modes continue to remain approximately dispersionless, while being lifted to finite energy as well as being squeezed: they change their ellipticity described by the ratio of the amplitudes of the canonically conjugate variables comprising them. This phenomenon provides interesting connections between concepts such as constraint counting and self-screening underpinning the field of frustrated magnetism. We discuss variants of these phenomena for different interactions, lattices and dimension.