Theory of Ca$_{10}$Cr$_7$O$_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics

TL;DR

This paper investigates the spin-liquid behavior of Ca$_{10}$Cr$_7$O$_{28}$ using a Heisenberg model on a bilayer breathing-kagome lattice, combining simulations and experiments to reveal different fluctuation timescales and excitation features.

Contribution

It introduces a minimal microscopic Heisenberg model for Ca$_{10}$Cr$_7$O$_{28}$ and analyzes its thermodynamic and dynamic properties through simulations, linking them to experimental observations.

Findings

Ground state is a slowly-fluctuating spiral spin liquid.

Fast fluctuations resemble a U(1) spin liquid.

Distinct longitudinal and transverse spin excitations in magnetic field.

Abstract

Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.