Electric Field Effect on the Magnetic Order in Multiferroic LuMnO$_{\mathrm{3}}$*

Multiferroic materials have been intensively studied in recent years. The main focus lays on the coupling of the ferroelectric and magnetic orders. Among the varieties of the multiferroics is the rare-earth manganites LuMnO$_{\mathrm{3}}$, with a hexagonal P6$_{\mathrm{3}}$cm crystal structure. This structure consists a triangular layer of Mn$^{\mathrm{3+}}$ with S$=$2, surrounded by O$^{\mathrm{2-}}$ ions in a bipyramid local structure, and the rare-earth element goes in between the layers, making the intralayer spin-spin interaction stronger than the interlayer spin-spin interaction. Although geometrically frustrated, the spin on Mn ions can order antiferromagnetically at T$_{\mathrm{N}}$ \textasciitilde 90 K. The ferroelectric transition, on the other hand, happens at much higher temperature (T$_{\mathrm{E}}$ \textgreater 900 K) with the ion displacement in the c direction. Despite the fact that these two transition temperatures are well separated, our neutron scattering experiments on single crystal LuMnO$_{\mathrm{3}}$ carried at SPINS at NCNR demonstrate an electric field effect on magnetic peak intensity. This electric field effect on magnetic peaks can be explained by the coupling of ferroelectric domain walls and AFM walls, and a Monte Carlo simulation with the domain wall coupling is able to reproduce the observed effect.