# Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)$_2$Br$_2$: An experimental and theoretical study

## TL;DR

This study combines experimental ESR measurements and theoretical modeling to analyze the magnetic anisotropy and spin dynamics of the quasi-one-dimensional compound Cu(py)$_2$Br$_2$, revealing detailed spin interactions and effects of doping.

## Contribution

It provides a comprehensive experimental and theoretical analysis of ESR properties, magnetic anisotropy axes, and doping effects in Cu(py)$_2$Br$_2$, advancing understanding of anisotropic spin-chain systems.

## Key findings

- Weakly coupled spin chains are described by Heisenberg-Ising models with perpendicular anisotropy axes.
- The exchange coupling is determined as $J/k_B = 52.0$ K, with an anisotropy parameter $ ext{delta} \, \approx -0.02$.
- Doping with Cl ions affects the spin dynamics by decoupling anisotropic interactions from isotropic exchange.

## Abstract

We compare theoretical results for electron spin resonance (ESR) properties of the Heisenberg-Ising Hamiltonian with ESR experiments on the quasi-one-dimensional magnet Cu(py)$_2$Br$_2$ (CPB). Our measurements were performed over a wide frequency and temperature range giving insight into spin dynamics, spin structure, and magnetic anisotropy of this compound. By analyzing the angular dependence of ESR parameters (resonance shift and linewidth) at room temperature we show that the two weakly coupled inequivalent spin chain types inside the compound are well described by Heisenberg-Ising chains with their magnetic anisotropy axes perpendicular to the chain direction and almost perpendicular to each other. We further determine the full $g$-tensor from these data. In addition, the angular dependence of the linewidth at high temperatures gives us access to the exponent of the algebraic decay of a dynamical correlation function of the isotropic Heisenberg chain. From the temperature dependence of static susceptibilities we extract the strength of the exchange coupling ($J/k_B = 52.0\,\text{K}$) and the anisotropy parameter ($\delta\approx -0.02$) of the model Hamiltonian. An independent compatible value of $\delta$ is obtained by comparing the exact prediction for the resonance shift at low temperatures with high-frequency ESR data recorded at $4\,\text{K}$. The spin structure in the ordered state implied by the two (almost) perpendicular anisotropy axes is in accordance with the propagation vector determined from neutron scattering experiments. In addition to undoped samples we study the impact of partial substitution of Br by Cl ions on spin dynamics. From the dependence of the ESR linewidth on doping level we infer an effective decoupling of the anisotropic component $J\delta$ from the isotropic exchange $J$ in these systems.