Low temperature magnetic imaging of strained multiferroic EuTiO$_3$ thin films*

It has been predicted that the competition between paraelectric antiferromagnetic state and ferroelectric ferromagnetic state in perovskite EuTiO$_3$ can be tuned by epitaxial strain.\footnote{C.J. Fennie and K.M. Rabe, Phys. Rev. Lett. 97, 267602 (2006).} Tensile-strained EuTiO$_3$ thin films grown on DyScO$_3$ (110) substrate by molecular-beam epitaxy are confirmed to be ferromagnetic at low temperature by magnetometry and magneto-capacitance. Here we present magnetic imaging of EuTiO$_3$/DyScO$_3$ thin film using low temperature magnetic force microscopy (LT-MFM). Temperature dependence of MFM contrast confirms the ferromagnetic ground state. The magnetic field dependence of MFM images will be discussed in conjunction with magnetometry and magneto-capacitance measurements.