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Within the zero-temperature linear spin-wave theory we have investigated theeffect of frustration and dimerization of a Heisenberg system with alternatingspins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combinedeffect most visibly appears in the elementary excitation spectra. In contrastto the ground state energy that decreases with dimerization and increases withfrustration, the excitation energies are shown to be suppressed in energy byboth dimerization and frustration. The threshold value of frustration thatsignals a transition from a classical ferrimagnetic state to a spiral state,decreases with dimerization, showing that dimerization further helps in thephase transition. The correlation length and sublattice magnetization decreasewith both dimerization and frustration indicating the destruction of thelong-range classical ferrimagnetic. The linear spin wave theory shows that inthe case of a square lattice, dimerization initially opposes thefrustration-led transition to a spiral magnetic state, but then highermagnitudes of lattice deformation facilitate the transition. It also shows thatthe transition to spiral state is inhibited in a square lattice beyond acertain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

The combined effect of frustration and dimerization in ferrimagnetic chains and square lattices