  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.
