Critical magnetic scattering in geometric frastrated multiferroic LuMnO$_3$

The coexistence of competing order parameters in the class of materials referred to as the multiferroics is of great interest. The hexagonal manganites \textit{A}MnO$_3$ (\textit{A} = Y, Lu, Ho and Yb) with the \textit{P6$_3$cm} space group exhibit a ferroelectric transition, at very high temperatures, typically $\sim$ 1000 K, while the antiferromagnetic transition, \textit{T$_N$}, occurs at $\sim$ 100K. Earlier studies on YMnO$_3$ and LuMnO$_3$ using neutron scattering on single crystals showed that diffuse scattering is present around the forbidden nuclear (100) Bragg peak which corresponds to \textit{Q}=1.20 \AA$^{-1}$.Its intensity rises very sharply and drops just around \textit{T$_N$}. We performed inelastic neutron scattering measurement on a powder sample of LuMnO$_3$ form 4 to 250 K using the DCS at NIST. Strong inelastic intensity, not due to magnon excitations, is observed at \textit{Q}=1.32 and 2.50 \AA$^{-1}$. With cooling, the intensity gradually rises and reaches a peak around 100 K. Below, it drops drastically once the system orders. This kind of scattering is due to critical scattering arising from magnetic fluctuations above \textit{T$_N$}. The S(Q, $\omega$) is asymmetric suggesting that the Mn spin correlations are mosmost likely 2-dimensional in nature.