Magnetic inhomogeneity in a multiferroic EuTiO 3 thin film

We report on variable temperature magnetic force microscopy studies of a strain-enabled multiferroic EuTiO${}_{3}$ film epitaxially grown on a (110)-oriented DyScO${}_{3}$ substrate. Our temperature- and magnetic-field-dependent studies clearly reveal an inhomogeneous magnetic state with the coexistence of ferromagnetic and nonferromagnetic states at low magnetic fields, which provides a microscopic origin of the anomalous missing moment in previous studies [Lee et al., Nature (London) 466, 954 (2010)]. The spins of the nonferromagnetic phase can be aligned by modest magnetic fields (>1.5 T). The observed magnetic inhomogeneity probably originates from the coexistence of nearly degenerate magnetic ground states.