Decoherence plays an important role in the evolution of quantum systems. In this thesis, we theoretically investigate the decoherence dynamics of two-dimensional spin- 1/2 structures coupled to an electron bath, with a focus on the influence of exchange and dipolar coupling. Using a combination of analytical derivations and numerical simulations, we explore the impact of interatomic distance, lattice symmetry, and external magnetic fields on quantum coherence. The study extends previous one-dimensional investigations to two-dimensional square, triangular, and hexagonal Ti-spin structures on an MgO substrate, where spin interactions can be manipulated at the atomic scale using scanning tunneling microscopy (STM). We analyse the eigenenergies and eigenstates of these systems and employ the Lindblad master equation to model decoherence processes. Our results show a competition between the Heisenberg exchange and the dipole-dipole coupling, with special attention to the intermediate regime. Additionally, we characterise spin relaxation and flipping dynamics, highlighting their dependence on structural variations. These insights contribute to the broader understanding of spin coherence in engineered quantum systems and provide a foundation for future experimental and theoretical studies in quantum nanoscience.