In this thesis we studied hole-magnon dynamics to understand the contribution of theirrninteraction on the enhancement of ferromagnetism in diluted magnetic semiconductorsrn(DMS). The t-J model is used as the interaction Hamiltonian with a method of per-rnturbation mathematical approach in which canonical transformation is used to obtainrnconvergent values starting with canting the quantum anti-ferromagnetism from its Neelrnstate by some angle _ with respect to the z-axis. Employing a spinless fermion represen-rntation for hole operators, Holstein-Primako_ and Bogoliubou transformations are usedrnto change the hole and spin dynamics to the many body problem. Our calculations in-rndicated that motion of a hole in the anti-ferromagnetic background is dependent on thernmagnetic correlation of the system and the tilted angle. The motion of a hole around thernanti-ferromagnetic order is shown to be characterized by high and low energy dispersionrnuctuation as the angle changes from 00 to 900. This uctuation in energy spectrum isrnattributed as arising from the pair repair spin alignment which could happen in anti-rnferromagnetic(AF) background because of the hole motion e_ect. This is to mean thatrnthe motion of the hole causes a disturbance on the spin cloud of the localized electrons.rnThis also infer that e_ect of hole motion gives a ferromagnetic (FM) order (maxima) andrnanti-ferromagnetic (AF) order (minima) uctuation. Making use of the obtained result,rnenergy dispersion (Ek), spectral function (density function) (Ak) and quasiparticle weightrn(Zk) for the t=J > 1 limit were numerically evaluated and plotted.