Quantum magnetism on the Cairo pentagonal lattice

TL;DR

This paper investigates the quantum phases of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, revealing complex magnetic and non-magnetic states influenced by quantum fluctuations and lattice geometry.

Contribution

It provides the first detailed analysis of quantum effects on the Cairo pentagonal lattice, identifying novel magnetic and spin-nematic phases with potential experimental relevance.

Findings

Discovery of a collinear and four-sublattice orthogonal phase due to order-by-disorder.

Identification of a non-magnetic spin-nematic phase with d-wave symmetry.

Elucidation of the classical and quantum phase diagram as a function of exchange ratio.

Abstract

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S=5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S=1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 >> J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.