Single-ion anisotropy in a four-spin system: mixing of S-states

• Published in: Central European journal of chemistry Vol. 7; no. 2; pp. 211 - 214
• Main Authors: Florek, Wojciech, Jaśniewicz-Pacer, Katarzyna, Kaliszan, Leonard A., Kamieniarz, Grzegorz
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Versita 01.06.2009; Versita
• Subjects: Anisotropy; Biochemistry; Biological and Medical Physics; Biophysics; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Geochemistry; Heisenberg Hamiltonian; Level mixing; Magnetic molecules; Heisenberg Hamiltonian; Magnetic molecules; Anisotropy; Level mixing
• ISSN: 1895-1066; 2391-5420; 1644-3624; 2391-5420
• DOI: 10.2478/s11532-008-0103-7

A four-spin system with s=1 and the single-ion anisotropy, D∑ j [s jz ] 2 , is considered. When D≠0 the Hamiltonian of the system does not commute with S 2 and, therefore, S cannot be used as an additional label of energy levels. In this work we concentrate on the problem of mixing states with different total spins S . The Hamiltonian matrix is transformed to the symmetry-adapted basis (with subspaces labeled by the irreducible representations of the symmetry group) and next, after solving the eigenproblem for S 2 , to the basis with vectors labeled by S . Each eigenproblem is solved exactly (at least numerically) and the eigenstates are expressed as ∑ S a S ¦S〉. The coefficients a S are analyzed, especially for their D -dependence. Even in such a small system different schemes of level mixing can be observed.