Three dimensional magnetic correlations in LuFe$_{2}$O$_{4}$

LuFe$_{2}$O$_{4}$ has recently attracted much attention due to a novel electronically driven ferroelectric transition and concomitant indications of coupling between magnetic degrees of freedom and a large spontaneous polarization. To examine the behavior of LuFe$_{2}$O$_{4}$ in further detail, we have performed extensive polarized and unpolarized neutron diffraction experiments on high quality single crystal specimens. These measurements reveal two phase transitions involving magnetic degrees of freedom below 300 K. At 240 K we find the onset of three dimensional ferrimagnetic order. The refined ferrimagnetic spin structure is a symmetry allowed magnetic structure of the parent R-3m space group with a propagation vector of (1/3 1/3 0). Below 175 K many of the magnetic Bragg peaks become significantly broadened and a broad diffuse component to the magnetic scattering becomes evident. In addition, a new set of satellites is observed indexed as (1/3$\pm \delta $ 1/3$\pm \delta $ 3L/2) where $\delta \sim $0.027. Polarized neutron diffraction measurements indicate that these satellites have a substantial magnetic component.