The effect of dynamic distortions on the magnetic behavior of transition metal clusters
Creators: name: Jones, Donald H.
Publisher: name: University of British Columbia
Year: 2010

description: The effect of dynamic distortions on the magnetic behavior of clusters which contain magnetic ions with isotropically coupled spins is studied using the simplifying assumption that the coupling constants are linear in small distortions from the mean cluster configuration. It is found that dynamic distortions may have a particularly pronounced effect on clusters with symmetry equivalent magnetic ions for which the spectrum of magnetic energy states contains degeneracy in addition to that associated with different orientations of the total spin. Dynamic distortions in these clusters can be regarded as a special type of vibrational/magnetic or magnetostrictive coupling. A dynamic distortion model for the magnetic behavior of clusters which contain equilateral triangles and regular tetrahedra of isotropically coupled ions of S=l/2 to S=5/2 is derived. Numerical complications associated with matrix methods are avoided by the use of group theory and 'factorable' Hamiltonians which can be usefully simplified by the introduction of intermediate quantum numbers. Distortions are considered in a basis defined by the normal modes of the metal core of the cluster. The dynamic distortion model for equilateral trimetallic and tetrahedral clusters is tested against magnetic susceptibility data for the clusters Cu₄OX₆L₄ ( X=halide L=Lewis base) and M₃O(RCOO)₆+ (M = Fe(lII) or Cr(lll), RCOO = carboxylate). The dynamic distortion model is shown to provide the most satisfactory interpretation to date for the data for Cu₄OX₆L₄ which exhibit a rather unusual maximum in the moment as a function of temperature. For the trimetallic systems the agreement between the experimental data and the model is excellent but there are difficulties in evaluating the relative importance of static and dynamic distortions. Infinite Heisenberg linear chains are then examined using numerical extrapolations from finite chains and also the 'Odd/Even' Hamiltonian, which is defined in terms of intermediate spins on the odd and even numbered atoms of the chain. The results of the numerical extrapolation are shown to be consistent with an expression for the ground state energy of the antiferromagnetic chain, E₀ = -2S(S+21n2-1). A phase transition characterised by a discontinuity in the specific heat appears when the Odd/Even Hamiltonian is solved for large numbers of spins; this makes the Hamiltonian more appropriate for 3-D than 1-D systems. The Spin-Peierls transition, in which an infinite chain becomes alternating at a well defined transition temperature, can be regarded as a freezing out of dynamic distortions. It is shown numerically that, for S=1/2, end effects associated with lattice imperfections are associated with a significant tendency towards dimerisation in chains of as many as several tens of atoms. Dynamic distortions of high symmetry clusters can be considered as arising from their Jahn-Teller activity and for S=l/2 the matrices for the vibrational/magnetic coupling are identical to those for paramagnetic Jahn-Teller systems. Interpretation of the dynamic distortion model in Jahn-Teller terms highlights the importance of non-magnetic intercluster interactions which provide the symmetry-lowering distortion terms in the dynamic distortion Hamiltonian.