  Noncollinear and noncoplanar magnetic textures including skyrmions and
vortices act as emergent electromagnetic fields and give rise to novel
electronic and transport properties. We here report a unified understanding of
noncoplanar magnetic orderings emergent from the spin-charge coupling in
itinerant magnets. The mechanism has its roots in effective multiple spin
interactions beyond the conventional Ruderman-Kittel-Kasuya-Yosida (RKKY)
mechanism, which are ubiquitously generated in itinerant electron systems with
local magnetic moments. Carefully examining the higher-order perturbations in
terms of the spin-charge coupling, we construct a minimal effective spin model
composed of the bilinear and biquadratic interactions with particular wave
numbers dictated by the Fermi surface. We find that our effective model
captures the underlying physics of the instability toward noncoplanar
multiple-$Q$ states discovered recently in itinerant magnets: a single-$Q$
helical state expected from the RKKY theory is replaced by a double-$Q$ vortex
crystal with chirality density waves even for an infinitely small spin-charge
coupling on generic lattices [R. Ozawa $\mathit{et \ al.}$, J. Phys. Soc. Jpn.
$\mathbf{85}$, 103703 (2016)], and a triple-$Q$ skyrmion crystal with a high
topological number of two appears with increasing the spin-charge coupling on a
triangular lattice [R. Ozawa, S. Hayami, and Y. Motome, to appear in Phys. Rev.
Lett. (arXiv: 1703.03227)]. We find that, by introducing an external magnetic
field, our effective model exhibits a plethora of multiple-$Q$ states. Our
findings will serve as a guide for exploring further exotic magnetic orderings
in itinerant magnets.
