Enhanced magnetization of ultrathin NiFe$_2$O$_4$ films on SrTiO$_3$(001) related to cation disorder and anomalous strain

NiFe$_2$O$_4$ thin films with varying thickness were grown on SrTiO$_3$(001) by reactive molecular beam epitaxy. Soft and hard x-ray photoelectron spectroscopy measurements reveal a homogeneous cation distribution throughout the whole film with stoichiometric Ni:Fe ratios of 1:2 independent of the film thickness. Low energy electron diffraction and high resolution (grazing incidence) x-ray diffraction in addition to x-ray reflectivity experiments were conducted to obtain information of the film surface and bulk structure, respectively. For ultrathin films up to 7.3 nm, lateral tensile and vertical compressive strain is observed, contradicting an adaption at the interface of NiFe$_2$O$_4$ film and substrate lattice. The applied strain is accompanied by an increased lateral defect density, which is decaying for relaxed thicker films and attributed to the growth of lateral grains. Determination of cationic site occupancies in the inverse spinel structure by analysis of site sensitive diffraction peaks reveals low tetrahedral occupancies for thin, strained NiFe$_2$O$_4$ films, resulting in partial presence of deficient rock salt like structures. These structures are assumed to be responsible for the enhanced magnetization of up to $\sim$250\% of the NiFe$_2$O$_4$ bulk magnetization as observed by superconducting quantum interference device magnetometry for ultrathin films below 7.3 nm thickness.