A study of magnetic ordering in multiferroic hexagonal Ho<inf>1-</inf><inf>x</inf>Dy<inf>x</inf>MnO<inf>3</inf>

This paper investigates the magnetic properties of Ho1-xDyxMnO3 by considering the inter-planar Mn3+-O-O-Mn3+ interaction. The theoretical analysis shows that the asymmetric in-plane exchange interaction couples the in-plane and inter-planar Mn3+ spin structures via asymmetry parameter δ. This leads to the existence of both the in-plane and inter-planar ordering, which in turn restricted the allowed magnetic space groups to Γ1 and Γ4. The experimental studies confirmed the concomitant nature of the in-plane and the inter-planar ordering at TN, TSR, and T2. It also showed that the magnetic phase diagram is dominated by the allowed magnetic structures Γ1 and Γ4. Furthermore, an effort is made to resolve the inconsistency regarding the TSR (32 or 40 K). The studies revealed that the antiferromagnetic inter-planar interaction is switched to the ferromagnetic interaction (40 K) upon cooling, which in turn drives the spin reorientation at 32 K. The Mn3+ spin structure is seen to be coupled to rare earth sub-lattice through the modulation of the inter-planar interaction.