Neutron scattering from magnetic polymers

Abstract

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 $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-independent quantities, like the free energy and the spin-wave density of states are independent of polymer conformation, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-dependent quantities like the wave-vector-dependent susceptibility $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ and the neutron scattering law $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ 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 $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$, goes as ${T}^{\frac{1}{2}}$. The neutron scattering law $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ measures essentially the spin-wave density of states at low temperatures although there is some weak $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ dependence.