  For 2D Hubbard model with spin-orbit Rashba coupling in external magnetic
field the structure of effective spin interactions is studied in the regime of
strong electron correlations and at half-filling. It is shown that in the third
order of perturbation theory, the scalar and vector chiral spin-spin
interactions of the same order arise. The emergence of the latter is due to
orbital effects of magnetic field. It is shown that for nonuniform fields,
scalar chiral interaction can lead to stabilization of axially symmetric
skyrmion states with arbitrary topological charges. Taking into account the
hierarchy of effective spin interactions, an analytical theory on the optimal
sizes of such states -- the higher-order magnetic skyrmions -- is developed for
axially symmetric magnetic fields of the form $h(r) \sim r^{\beta}$ with $\beta
\in \mathbb{R}$.
