# Magnetic excitations from the two-dimensional interpenetrating Cu framework in Ba$_2$Cu$_3$O$_4$Cl$_2$

## TL;DR

This study investigates the magnetic excitations in Ba$_2$Cu$_3$O$_4$Cl$_2$, revealing distinct behaviors of two interpenetrating Cu sublattices through neutron scattering and theoretical modeling.

## Contribution

It provides a detailed neutron scattering analysis of the two Cu sublattices and develops an effective spin Hamiltonian from a Hubbard model, highlighting differences in their magnetic excitations.

## Key findings

- Cu$_A$ sublattice exhibits high-energy excitations up to 300 meV.
- Cu$_B$ sublattice shows weaker, lower-energy dispersion up to 20 meV.
- Magnetic field effects on Cu$_B$ are inconsistent with simple spin-wave theory.

## Abstract

We report detailed neutron scattering studies on Ba$_2$Cu$_3$O$_4$Cl$_2$. The compound consists of two interpenetrating sublattices of Cu, labeled as Cu$_{\rm A}$ and Cu$_{\rm B}$, each of which forms a square-lattice Heisenberg antiferromagnet. The two sublattices order at different temperatures and effective exchange couplings within the sublattices differ by an order of magnitude. This yields an inelastic neutron spectrum of the Cu$_{\rm A}$ sublattice extending up to 300 meV and a much weaker dispersion of Cu$_{\rm B}$ going up to around 20 meV. Using a single-band Hubbard model we derive an effective spin Hamiltonian. From this, we find that linear spin-wave theory gives a good description to the magnetic spectrum. In addition, a magnetic field of 10 T is found to produce effects on the Cu$_{\rm B}$ dispersion that cannot be explained by conventional spin-wave theory.