Magnetodielectric Effects and Transport Study in LuFe$_{2}$O$_{4}$ Single Crystal

Magnetic, dielectric, and magnetodielectric properties of geometrically frustrated mixed valance LuFe$_{2}$O$_{4}$ single crystal are discussed to clarify the charge order based ferroelectricity and its coupling with magnetism. From the magnetization and dielectric constant measurement, a new anomalous temperature point T$_{N\mbox{'}}(\sim $160 K) in both magnetization and dielectric constant versus temperature curve below the ferrimagnetic transition temperature T$_{N}(\sim $225 K) has been observed. The sign of magnetodielectric effect (MDE) also changes from positive T $>$ T$_{N\mbox{'}}$ into negative T $<$ T$_{N\mbox{'}}$. No field hysteresis in positive MDE temperature region was found. However a large hysteretic behavior in negative MDE below T$_{N\mbox{'}}$ with the same magnetic coercive field measured in M (H) curve was observed. This indicates a strong coupling between magnetism and ferroelectricity in the charge and spin frustrated ferrimagnetic LuFe$_{2}$O$_{4}$ system.