Noncollinear cluster magnetism in the framework of the Hubbard model

Noncollinear magnetic states in clusters having $N<~43$ atoms are studied by using the single-band Hubbard Hamiltonian within the fully unrestricted Hartree-Fock (UHF) approximation. The spin and charge degrees of freedom 〈Sₗ〉 and 〈nₗ〉 at every cluster atom are treated as independent variables. A variety of qualitatively different self-consistent solutions is obtained as a function of cluster size, structure, number of valence electrons ν, and Coulomb interaction strength $U/t.$ This includes inhomogeneous density distributions, paramagnetic solutions, magnetic solutions with collinear moments, and noncollinear spin arrangements that show complex antiferromagneticlike or ferromagneticlike orders. The environment dependence of the magnetic properties is analyzed giving emphasis to the effects of antiferromagnetic frustrations in compact structures close to half-band filling. Electron correlation effects are quantified by comparing UHF and exact results for the local magnetic moments, total spin, spin-correlation functions, and structural stability of $13$-atom clusters. Goals and limitations of the present noncollinear approach are discussed.