Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet

TL;DR

This paper explores the complex ground states and excitations in a pyrochlore Heisenberg antiferromagnet with biquadratic interactions, revealing a rich landscape of spin configurations, modes, and fluctuation-driven phase transitions.

Contribution

It introduces the concept of color ice states, analyzes weathervane modes in three dimensions, and demonstrates fluctuation-driven state selection in the model.

Findings

Identification of extensive color ice ground states.

Characterization of membrane-like weathervane modes.

Quantum fluctuations induce a sequence of phase transitions.

Abstract

We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground state manifold of the model contains an extensively large family of non-coplanar spin states known as "color ice states". Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membrane-like" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and elucidate their physical properties. Furthermore, we study the order by disorder phenomenon in this model, focusing on the role of harmonic fluctuations. Our computationally-limited phase space search suggests that quantum fluctuations select three different states as the magnitude of the biquadratic interaction increases relative to the bilinear interaction, implying a sequence of phase transitions solely driven by fluctuations.