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The geometric frustration in a class of the mixed spin-1/2 and spin-SIsing-Heisenberg diamond chains is investigated by combining three exactanalytical techniques: Kambe projection method, decoration-iterationtransformation and transfer-matrix method. The ground state, the magnetizationprocess and the specific heat as a function of the external magnetic field areparticularly examined for different strengths of the geometric frustration. Itis shown that the increase of the Heisenberg spin value S raises the number ofintermediate magnetization plateaux, which emerge in magnetization curvesprovided that the ground state is highly degenerate on behalf of a sufficientlystrong geometric frustration. On the other hand, all intermediate magnetizationplateaux merge into a linear magnetization versus magnetic field dependence inthe limit of classical Heisenberg spin S -> infinity. The enhancedmagnetocaloric effect with cooling rate exceeding the one of paramagnetic saltsis also detected when the disordered frustrated phase constitutes the groundstate and the external magnetic field is small enough.

Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain