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We theoretically investigate modulation of a tunable δ-potential to the lateral displacement of electrons across a magnetically modulated semiconductor nanostructure. Experimentally, this nanostructure can be produced by depositing a nanosized ferromagnetic stripe with in-plane magnetization on top of a semiconductor heterostructure, while the δ-potential can be realized by means of the atomic layer doping technique. Theoretical analysis reveals that this δ-doping can break the intrinsic symmetry in nanostructure and a considerable spin polarization in the lateral displacement will appear. Numerical calculations demonstrate that both magnitude and sign of spin polarization can be manipulated by changing the height and/or position of the δ-doping, giving rise to a structurally tunable spin spatial splitter. [ABSTRACT FROM AUTHOR]