Abstract
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total spin and point group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
