Abstract :
The group-theoretical analysis of the origin of high degeneracy of the spin states of the [Fe3(II)fe(III)] cluster (the iron core of the [Fe4S4]+ center) in trigonal Heisenberg coupling model is developed. It is shown that highly degenerate |S,S∗〉 Heisenberg states represent the sets of 2S+1Γi terms of trigonal symmetry group of the cluster. Thus the four-fold (five-fold) degenerate S = 12 state with intermediate spin S∗ = 3 (S∗ = 2) of the Fe3(II) subsystem represents three 2A+1Γi multiplets: |S = 12, S∗ = 3〉 ≐2A1 + 2A2 + 2E (|S = 12, S∗ = 2〉 ≐2A1 + 2E + 2E′). Biquadratic exchange HBE= σα,βjα,β(sαsβ2 leads to a qualitative effect — the splittings of the |S,S∗〉 Heinsenberg states on the 2S+1Γi terms of the symmetry group of the cluster. The splittings and shifts of spin levels are very essential: the biquadratic exchange splittings in the S = 12, S∗ = 2 [S∗ = 3] set are Δ(2A1, 2E) ≈ 108j, Δ(2E, 2E′) ≈ 98j [Δ(2A2, 2E) = 60j, Δ(2A1, 2E) = 30j]. These strong biquadratic exchange splittings may be of the order of the Heisenberg intervals (≈J) between spin levels, even in the case of very weak biquadratic coupling j/J = 0.01, j ⪡ J. Double exchange in mixed-valence pari Fe(II)Fe(III) of the cluster destroys teh biquadratic exchange ordering on trigonal 2S+1Γi terms, destroys the intermediate spin S* characteristics of the states of the Heisenberg trigonal model, and forms the states which are characterized by the pair intermediate spins S12, S34. In the Heisenberg system with a strong double exchange, the biquadratic exchange results in essential shifts of exchage-resonance levels. Biquadratic exchange reduces the magnetic moment of the cluster in a wide range of temperatures.
