  Magnetoelectric multiferroics are key materials for next-generation
spintronic devices due to their entangled magnetic and ferroelectric
properties. Spiral multiferroics possess ferroelectric polarization and are
particularly promising for electric control of magnetism and magnetic control
of ferroelectricity. In this work, we uncover long-period incommensurate states
characterized by unique multiferroic kinks in corundum nickelate
Ni$_{2}$InSbO$_6$, a member of a promising family of polar magnets. Utilizing a
2-orbital $S=1$ model, we derive formulas for Heisenberg and anisotropic
magnetic exchanges and magnetically-induced polarization, enabling their
calculations from first principles. We use these parameters in Monte Carlo and
Landau theory-based calculations to reproduce experimentally observed magnetic
structures and polarization dependence on the magnetic field. We predict
magnetic phase transitions between flat spiral, conical spiral, canted
antiferromagnetic and ferromagnetic states under increasing magnetic fields.
Kinks in the spiral phases repel each other through a Yukawa-like potential
arising from exchange of massive magnons. We also find that suitably directed
electric fields can be used to stabilize the ferromagnetic and spiral states.
The findings open a new pathway to predictive first-principles modelling of
multiferroics and will inspire experiments and technological applications based
on multiferroic kinks.
