Origin of multiferroicity in hexagonal Y$_{1-x}$Dy$_{x}$MnO$_{3}$

Multiferroic materials, that offer the possibility of manipulating an ordered electric state by applying magnetic field, have attracted considerable attention in the recent past. Here we report a detailed analysis of structural, magnetic and dielectric properties of polycrystalline samples of Y$_{1-x}$Dy$_{x}$MnO$_{3}$ (0 $\le $ x $\le $ 0.2). These materials belong to space group $P6_{3}$\textit{cm }with hexagonal crystal structure and were synthesized by solid state reaction method. We have carried out extensive zero field and in-field neutron diffraction, and dielectric measurements. Our study provides evidence for change in the lattice parameters, buckling of Y (Dy) layers, Mn-O-Mn bond angles and tilting of MnO$_{5}$ pollyhedra as a function of temperature and magnetic field. We also study the magnetoelectric coupling in YMnO$_{3}$ as well as doped samples by in-field dielectric measurements. A distinct anomaly near N\'{e}el temperature is observed in these measurements that vary with the application of magnetic field. In essence, we develop a model to understand the magnetoelectric coupling of these antiferromagnetic multiferroics with their field dependent magnetic structure.