Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)