Studies of a polymeric chromium phosphinate. Electron-spin resonance and spin dynamics

Magnetic properties of the chromium-tris-phosphinate polymer ${\left\{\mathrm{Cr}{\left[{\mathrm{O}}_2\mathrm{P}\right(\mathrm{C}{\mathrm{H}}_3\left)\right({\mathrm{C}}_6{\mathrm{H}}_5\left)\right]}_2\right[{\mathrm{O}}_2\mathrm{P}{\left({\mathrm{C}}_8{\mathrm{H}}_{17}\right)}_2\left]\right\}}_N$, known as PCrP-C, were studied with the use of conventional electron-spin-resonance (ESR) techniques. The chromium spins are coupled by antiferromagnetic Heisenberg exchange, with the value of $\frac{J}{k_B}=-2.5\mathrm{}$ K for the nearest-neighbor exchange parameter determined from static magnetic susceptibility measurements. The ESR results show that the spins comprise a quasi-one-dimensional magnetic system with crystal-field anisotropy characterized by the site anisotropy parameter $\frac{\mathrm{}\left|D\right|\mathrm{}}{k_B}=0.21\mathrm{}\pm 0.02$ K. Magnetic interactions between linear polymer chain segments significantly influence the spin dynamics. A traditional memory function formalism is used to analyze the temperature-dependent ESR absorption line shape and linewidth. The theoretical predictions show general agreement with the experimental data, but certain discrepancies are obvious. In order to understand the underlying collective spin dynamics of exchange-coupled systems in a more intuitive, physical framework, three simple classical models were constructed: the two-spin model, the correlated cluster model, and the random-walk model. In addition to reproducing the results of the more formal, less transparent theory, these models also provide important insight into possible origins of the disagreement between the theory and experiments. Part of this disagreement, combined with the results of susceptibility measurements, strongly suggests that the chromium spin sites along PCrP-C chains are inequivalent with respect to the orientation of the principal axes of the crystal-field anisotropy. The remainder of the disagreement between the theory and data indicates that there are inherent inadequacies in the traditional theoretical approach.