Neel probability and spin correlations in some nonmagnetic and nondegenerate states of the hexanuclear antiferromagnetic ring Fe-6: Application of algebraic combinatorics to finite Heisenberg spin systems - art. no. 024411

摘要

The spin correlations omega(r)(z), r=1,2,3, and the probability p(N) of finding a system in the Neel state for the antiferromagnetic ring Fe-6(III) (the so-called "small ferric wheel") are calculated. States with magnetization M=0 and total spin 0less than or equal toSless than or equal to15, labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D-6, 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 (S-A=S-B=15/2) the global Neel probability p(N)(*) 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 p(N)(S), etc., for other antiferromagnetic rings (Fe-10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe-18. Since thermodynamic properties of Fe-6 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. [References: 52]