The effects of dimerization and frustration in Heisenberg ferrimagnetic systems with alternating spins s1 and s2 on one- and two-dimensional lattices have been studied in this thesis. The ground state energy is found to decrease with dimerization, but with frustration it first increases to a maximum then starts to decrease just before the disorder point. The sublattice magnetization as well as correlation length are shown to decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic.
The usual way to parametrize dimerization is by writing the alternating spin-spin exchange couplings as J (1 ± s). In order to take care of changing distances in a two dimensional lattice, we have proposed a different parametrization, We argue that without this parametrization, it is not possible to describe all the possible configurations that result from the dimerization of a two-dimensional lattice. With the help of this, we find that a square lattice dimerizes into a plaquette lattice.
The effect of dimerization is observed most markedly in the excitation modes of the spin systems, both acoustic and optic and in both one- and two-dimensions. With the former choice, dimerization suppresses the excitation modes whereas with the latter choice, dimerization pushes them up. The effect of frustration, on the other hand, on the two modes is to suppress the excitation energies.
Within the linear spin wave theory, we identify two critical values of frustrat.ion: a threshold value ac that marks the onset of transition from a classical ferrimagnetic state to a spiral state, and a disorder point ad where the energies become imaginary.
Within the zero-temperature spin wave analysis, the combined effect of frustration and dimerization are shown to have an interesting feature in terms of these threshold values. In ferrimagnetic chains we find, that both the values decrease with dimerization. The decrease in ac indicates that dimerization of a frustrated chain facilitates the frustration-induced transition to a spiral state. On the other hand, in ferrimagnetic square lattices while decreases with dimerization, ac increases with s opposing the frustration-induced transition to a spiral magnetic state. This increase in ac shows that the transition to spiral state is inhibited in a square lattice beyond a certain extent of dimerization.
Thermal properties of frustrated and dimerized Heisenberg ferrimagnetic systems on one- and two-dimensional lattices have also been investigated within the linear spin-wave approximation. The thermal behavior of a ferrimagnetic system comes out as a sum of ferromagnetic and anti ferromagnetic behaviors. From the shift of the minimum of susceptibility times temperature, XT, and the Schottky-like peak of the heat capacity Cv at intermediate temperatures we find that frustration enhances the anti ferromagnetic character of ferrimagnetic systems. The effect of dimerization is different for the two forms of the spin-spin coupling. While the expanded form J(l ± g) boosts the antiferromagnetic character of the system by shifting the Cv peak and the XT minimum to lower temperatures, the distance-variable coupling j/1±g shifts them to higher temperatures enhancing the ferromagnetic character. We have verified the classification of ferrimagnetic systems with the help of frustration and dimerization in the system, which we have shown to be also valid for square lattices.