  In a topological insulator (TI)/magnetic insulator (MI) hetero-structure,
large spin-orbit coupling of the TI and inversion symmetry breaking at the
interface could foster non-planar spin textures such as skyrmions at the
interface. This is observed as topological Hall effect in a conventional Hall
set-up. While this effect has been observed at the interface of TI/MI, where MI
beholds perpendicular magnetic anisotropy, non-trivial spin-textures that
develop in interfacial MI with in-plane magnetic anisotropy is under-reported.
In this work, we study Bi$_2$Te$_3$/EuS hetero-structure using planar Hall
effect (PHE). We observe planar topological Hall and spontaneous planar Hall
features that are characteristic of non-trivial in-plane spin textures at the
interface. We find that the latter is minimum when the current and magnetic
field directions are aligned parallel, and maximum when they are aligned
perpendicularly within the sample plane, which maybe attributed to the
underlying planar anisotropy of the spin-texture. These results demonstrate the
importance of PHE for sensitive detection and characterization of non-trivial
magnetic phase that has evaded exploration in the TI/MI interface.
