Spin diffusion in low-dimensional copper-amino-acid complexes

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Abstract
The magnetic dimensionality of paramagnets is responsible for the long time behaviour of their spin dynamics, where the decay of the correlation functions is governed by spin diffusion. To study this problem the authors have performed EPR measurements in single crystals of the copper complexes of L and DL racemic mixtures of the amino acids methionine and 2-aminobutyric acid. In all these systems the copper atoms are arranged in layers with Cu-Cu interlayer distances which are two or three times longer than those within the layers. In the DL compounds the copper atoms are located at inversion centres. There each copper atom is connected to four magnetically non-equivalent coppers via four identical pathways. In the L compounds this symmetry is broken and there are two distinct pairs of pathways connecting the four magnetically non-equivalent coppers. Consequently, each type of lattice (L or DL) has a different exchange network. That is, the DL compounds exhibit two-dimensional characteristics, while in the L compounds there is a preferred direction for the exchange coupling. This behaviour is manifested in the broader EPR linewidths of the L-type crystals as compared with those of the DL-types. To describe the changes in the spin correlation functions they introduce a model which allows for the quantum evolution of the spin system until many-body effects break down the quantum coherence. This time is of the order of h(cross)/ omega e, where omega e is the exchange frequency. In the long-time regime, their model allows one to pass with continuity from correlation functions which are solutions of the diffusion equation in one dimension to those corresponding to two or three dimensions. The model explains successfully their experimental data and it may be applied to systems where the magnitude of the exchange coupling varies along different directions.