Neutron scattering from magnetic polymers

Some of the static and dynamic properties of a simple magnetic polymer are calculated. The localized magnetic moments on each monomer interact via a nearest-neighbor Heisenberg exchange. While $\overrightarrow{\mathrm{k}}$-independent quantities, like the free energy and the spin-wave density of states are independent of polymer conformation, $\overrightarrow{\mathrm{k}}$-dependent quantities like the wave-vector-dependent susceptibility $\chi \left(\overrightarrow{\mathrm{k}}\right)$ and the neutron scattering law $S(\overrightarrow{\mathrm{k}},\omega )$ can yield useful information about the polymer conformation statistics. Explicit expressions are derived for these quantities for a freely jointed polymer chain. It is shown that the inverse correlation length in a ferromagnetic polymer, which can be determined from $\chi \left(\overrightarrow{\mathrm{k}}\right)$, goes as $T^{\frac{1}{2}}$. The neutron scattering law $S(\overrightarrow{\mathrm{k}},\omega )$ measures essentially the spin-wave density of states at low temperatures although there is some weak $\overrightarrow{\mathrm{k}}$ dependence.