Successive spin reorientation and rare earth ordering in Nd${}_{0.5}$Dy${}_{0.5}$FeO${}_3$: Experimental and $Ab$-$initio$ investigations

Abstract

In present study, the magnetic structure and spin reorientation of mixed doped orthoferrite Nd${}_{0.5}$Dy${}_{0.5}$FeO${}_3$ have been investigated. Similar to both parent compounds (NdFeO${}_3$ and DyFeO${}_3$), the magnetic structure of Fe${}^{3+}$ belongs to ${\Gamma }_4$ irreducible representation (G${}_x$, F${}_z$) at room temperature. The experimental measurements confirmed the spin reorientation where magnetic structure of Fe${}^{3+}$ changes from ${\Gamma }_4$ to ${\Gamma }_2$(F${}_x$, G${}_z$) between 75 and 20 \,K while maintaining G-type configuration. Such a gradual spin reorientation is unusual since the large single ion anisotropy of Dy${}^{3+}$ ions causes an abrupt ${\Gamma }_4$$\to$ ${\Gamma }_1$(G${}_y$) spin reorientation in DyFeO${}_3$. Between 20 and 10 \,K, the Fe${}^{3+}$ magnetic structure is represented by ${\Gamma }_2$ (F${}_x$, G${}_z$). Unexpectedly, magnetic structure of Fe${}^{3+}$ with ${\Gamma }_4$ representation re-emerges below 10\,K which also coincides with the development of rare-earth (Nd${}^{3+}$/Dy${}^{3+}$) magnetic ordering having C${}_y$ configuration with magnetic moment of 1.8 ${\mu }_B$. The absence of any signature of second order phase transition in the specific heat confirms the role of $R$(Nd${}^{3+}$/Dy${}^{3+}$)-Fe${}^{3+}$ exchange interaction in the observed "rare-earth ordering" unlike DyFeO${}_3$ where Dy${}^{3+}$ ordering takes place independently to the magnetic ordering of Fe${}^{3+}$ magnetic structure. Our (DFT+U+SO) calculations show that the C-type arrangement of rare-earth ions (Nd${}^{3+}$/Dy${}^{3+}$) with ${\Gamma }_2$ configuration for Fe${}^{3+}$ moments is the ground state whereas ${\Gamma }_4$ phase is energetically very close. Nd-Fe and Nd-Dy exchange interactions, estimated from DFT, are observed to have significant roles in the rare earth ordering and Fe spin reorientation corroborating our experimental results.

11 pages, 11 figures