2002/07/01 by Wojciech Florek, Sylwia Bucikiewicz · 16 citations
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Algorithm #Antiferromagnetism #Chemistry #Combinatorics #Condensed matter physics #Crystallography #Lanthanide and Transition Metal Complexes #Magnetism in coordination complexes #Mathematical physics #Mathematics #Multiplet #Physics #Quantum mechanics #Ring (chemistry) #Spectral line #Spin (aerodynamics) #Spin states #Spins #State (computer science) #Thermodynamics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.66.024411
published in Physical review. B, Condensed matter 66(2) (American Physical Society) · 13 pages, 7 figs, 5 tabs, revtex 4
openalex publication_date 2002/07/01 · arxiv created 2002/12/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The spin correlations \ensuremathωrz, r=1,2,3, and the probability pN of finding a system in the N'eel state for the antiferromagnetic ring Fe6III (the so-called ``small ferric wheel'') are calculated. States with magnetization M=0 and total spin 0<~S<~15, labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D6, are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S multiplet. Taking into account the Clebsch-Gordan coefficients for coupling total spins of sublattices (SA=SB=(15)/(2)) the global N'eel probability pN* can be determined. Dependences of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined pN(S), etc., for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results are calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 000 basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S=0). The largest eigenproblem has to be solved for S=4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm the efficiency and usefulness of such an approach, so it is briefly discussed here.