  We have developed a vectorial type of measurement for the spin Seebeck effect
(SSE) in epitaxial NiFe$_2$O$_4$ thin films which have been grown by pulsed
laser deposition on MgGa$_2$O$_4$ (MGO) with (001) and (011) orientation as
well as CoGa$_2$O$_4$ (011) (CGO), thus varying the lattice mismatch and
crystal orientation. We confirm that a large lattice mismatch leads to strain
anisotropy in addition to the magnetocrystalline anisotropy in the thin films
using vibrating sample magnetometry and ferromagnetic resonance measurements.
Moreover, we show that the existence of a magnetic strain anisotropy in
NiFe$_2$O$_4$ thin films significantly impacts the shape and magnitude of the
magnetic-field-dependent SSE voltage loops. We further demonstrate that
bidirectional field-dependent SSE voltage curves can be utilized to reveal the
complete magnetization reversal process, which establishes a vectorial
magnetometry technique based on a spin caloric effect.
