Evidence of magneto-electric coupling on YMnO$_3$ thin films capacitors*

We report synthesis of phase pure multiferroic YMnO$_3$ thin films. Films were prepared by using rf magnetron sputtering technique using ultra high purity Argon gas at 0.07mbar at substrate temperature around 850$^{\circ}$C over Pt/TiO$_2$/SiO$_2$/Si substrates. Films were characterized by x-ray diffraction (XRD), Scanning electron microscopy (SEM), temperature-dependent magnetization curves by using a Vibrating sample magnetometer (VSM), Atomic force microscopy (AFM) and temperature-dependent polarization measurements of Au/YMnO$_3$/Pt capacitor heterostructures. Temperature dependence capacitance measurements show an anomaly close to the N\'{e}el temperature (70K) which is corroborated by electrical polarization hysteresis loops. We found a effect on the ferroelectric properties (saturation polarization and coercitive electric field) only explained by the antiferromagnetic phase of YMnO$_3$. We model the ferroelectric hysteresis loops by using a series of resistance-capacitor elements.