Magnetic Phase Diagram and Skyrmions of the Hubbard Model on the β-Mn Type Lattice

Magnetic phase diagram for the Hubbard model on the β-Mn type lattice has been calculated as a function of the Coulomb interaction energy parameter U and the electron number per atom n by using the generalized Hartree–Fock approximation combined with the recursion method for electronic-structure calculations. The ferromagnetic state, the ferrimagnetic state, and the helimagnetic state as well as the 3Q multiple spin density waves (3QMSDW) states have been obtained on the U–n plane. Their detailed structures are examined with use of the Fourier analysis. It is shown that the calculated phase diagram and the Dzyaloshinskii–Moriya interaction elucidate the magnetic interactions for the itinerant-electron skyrmions in transition metal alloys and compounds on the β-Mn type lattice.