Multiple-Q instability by (d-2)-dimensional connections of Fermi surfaces

We propose a general mechanism of multiple-Q ordering with noncollinear and noncoplanar spin textures in itinerant magnets. By analyzing the fourth-order perturbation with respect to the spin-charge coupling, we find that the instability toward multiple-Q ordering is caused by (d - 2)-dimensional connections of the Fermi surfaces in the extended Brillouin zone by the multiple-Q wave vectors: zero(one)-dimensional point (line) connections in the two(three)-dimensional systems. The instabilities are obtained as the fixed points in the two-parameter flow diagram, irrespective of lattice structures. The hidden Fermi surface instability provides a universal origin of noncollinear and noncoplanar instabilities common to frustrated and unfrustrated lattice systems.