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We compare theoretical results for electron spin resonance (ESR) propertiesof the Heisenberg-Ising Hamiltonian with ESR experiments on thequasi-one-dimensional magnet Cu(py)$_2$Br$_2$ (CPB). Our measurements wereperformed over a wide frequency and temperature range giving insight into spindynamics, spin structure, and magnetic anisotropy of this compound. Byanalyzing the angular dependence of ESR parameters (resonance shift andlinewidth) at room temperature we show that the two weakly coupled inequivalentspin chain types inside the compound are well described by Heisenberg-Isingchains with their magnetic anisotropy axes perpendicular to the chain directionand almost perpendicular to each other. We further determine the full$g$-tensor from these data. In addition, the angular dependence of thelinewidth at high temperatures gives us access to the exponent of the algebraicdecay of a dynamical correlation function of the isotropic Heisenberg chain.From the temperature dependence of static susceptibilities we extract thestrength of the exchange coupling ($J/k_B = 52.0\,\text{K}$) and the anisotropyparameter ($\delta\approx -0.02$) of the model Hamiltonian. An independentcompatible value of $\delta$ is obtained by comparing the exact prediction forthe resonance shift at low temperatures with high-frequency ESR data recordedat $4\,\text{K}$. The spin structure in the ordered state implied by the two(almost) perpendicular anisotropy axes is in accordance with the propagationvector determined from neutron scattering experiments. In addition to undopedsamples we study the impact of partial substitution of Br by Cl ions on spindynamics. From the dependence of the ESR linewidth on doping level we infer aneffective decoupling of the anisotropic component $J\delta$ from the isotropicexchange $J$ in these systems.

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