# Magnetic excitations in the trimeric compounds A$_3$Cu$_3$(PO$_4$)$_4$ (A = Ca, Sr, Pb)

## TL;DR

This paper investigates magnetic excitations in A$_3$Cu$_3$(PO$_4$)$_4$ compounds using a spin Hamiltonian approach, showing improved agreement with experimental data and revealing a flat energy band in the spectra.

## Contribution

It introduces a generic spin Hamiltonian that better captures the magnetic excitations than the traditional Heisenberg model for these compounds.

## Key findings

- The new model aligns more closely with experimental spectra.
- A flat energy band is identified in the excitation spectra.
- The analysis improves understanding of magnetic interactions in trimeric compounds.

## Abstract

We study the magnetic excitations of the trimeric magnetic compounds A$_3$Cu$_3$(PO$_4$)$_4$ (A = Ca, Sr, Pb). The spectra are analyzed in terms of the Heisenberg model and a generic spin Hamiltonian that accounts for the changes in valence electrons distribution along the bonds among magnetic ions. The analytical results obtained in the framework of both Hamiltonians are compared to each other and to the available experimental measurements. The results based on our model show better agreement with the experimental data than those obtained with the aid of the Heisenberg model. For all trimers, our analysis reveals the existence of one thin energy band referring to the flatness of observed excitation peaks.