The Classical Heisenberg Model on the Centred Pyrochlore Lattice

TL;DR

This paper investigates the classical Heisenberg model on the novel centred pyrochlore lattice, revealing complex magnetic phases, spin liquid behavior, and emergent gauge fields through analytical and simulation methods.

Contribution

It provides the first detailed theoretical analysis of the $J_1-J_2$ Heisenberg model on the centred pyrochlore lattice, uncovering its rich phase diagram and emergent phenomena.

Findings

Identification of ferrimagnetic, partial order, and spin liquid phases.

Observation of broadened pinch points indicating a Coulomb phase.

Demonstration that additional couplings stabilize a Coulomb phase.

Abstract

The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ (arXiv:2203.08780) where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.