Noncollinear cluster magnetism in the framework of the Hubbard model

TL;DR

This paper investigates noncollinear magnetic states in clusters using the Hubbard model and unrestricted Hartree-Fock approximation, revealing diverse magnetic configurations and analyzing electron correlation effects.

Contribution

It introduces a comprehensive noncollinear magnetic analysis of clusters within the Hubbard model without symmetry constraints, highlighting complex magnetic orders and environment effects.

Findings

Diverse self-consistent magnetic solutions found

Inhomogeneous charge and spin distributions observed

Correlation effects quantified by comparing UHF and exact results

Abstract

Noncollinear magnetic states in clusters are studied by using the single-band Hubbard Hamiltonian. The unrestricted Hartree-Fock (UHF) approximation is considered without imposing any symmetry constraints neither to the size or orientation of the local magnetic moments $<\vec S_l>$ nor to the local charge densities $<n_l>$. A variety of qualitatively different selfconsistent solutions is obtained as a function of cluster size, structure, number of valence electrons $\nu$ 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 antiferromagnetic and ferromagnetic-like 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.