In this thesis work, the crystal structure, magnetic and spin-phonon studies of the quasi-two-dimensional single-layered Ruddlesdenâ€“Popper phase have been studied, in which 3d hetero cations are considered at B-site such as SrLnM0.5Mn0.5O4 (Ln= La, Pr, and Nd, M= Co or Ni). Giant exchange bias (EB) of about ~ 1 to 5.5 kOe are observed in CoMn-based layered compounds, which is the highest ever reported in any layered transition metal oxides. Additionally, the observation of strong spin-phonon coupling in all these layered compounds provides a new set of multifunctional materials. A detailed study of crystal structure, magnetic, and spin-phonon coupling has been carried out in Nd2CoMnO6 double perovskite compound. Our analysis infers that the presence of competing magnetic interactions are sufficient to induce EB and thereby a wide range of materials exhibiting large EB phenomenon can be achieved.