Analytic Property of Vortex-Type Spin Structures in Itinerant Electron System with Inversion Symmetry

Analytic properties of the multiple spin density waves showing vortex structures, which have recently been found in the fcc Hubbard model using the generalized Hartree-Fock (GHF) approximation, have been investigated. It is shown that the 2Q multiple helical spin density waves (SDW) consist of two types of half-skyrmion vortices and two types of antivortices. In the 3Q multiple helical SDW, the half-skyrmion vortex structures with the "westerlies" are shown to be twisted along the axis perpendicular to the vortex plane. The 12Q multiple SDW (12QMSDW) are analyzed as a superposition of the 2-4QMSDW on the (001) plane and the remaining 4QMSDW. It is shown analytically that the 2-4QMSDW forms the planar vortices and antivortices with zero core polarization, so that the 12QMSDW forms the same types of vortices with additional SDW polarization in the [001] direction. These results are in good agreement with the visualization image data based on the GHF calculations.