Coexisting magnetic structures and spin reorientation in Er0.5Dy0.5FeO3 : Bulk magnetization, neutron scattering, specific heat, and density functional theory studies

The complex magnetic structures, spin reorientation, and associated exchange interactions have been investigated in ${\mathrm{Er}}_{0.5}{\mathrm{Dy}}_{0.5}{\mathrm{FeO}}_{3}$ using bulk magnetization, neutron diffraction, specific heat measurements, and density functional theory calculations. The ${\mathrm{Fe}}^{3+}$ spins order as G-type antiferromagnet structure depicted by ${\mathrm{\ensuremath{\Gamma}}}_{4}({G}_{x}$, ${A}_{y}$, ${F}_{z}$) irreducible representation below 700 K, similar to its end compounds. The bulk magnetization data indicate occurrence of the spin-reorientation and rare-earth magnetic moments' polarization below $\ensuremath{\sim}75$ K and 10 K, respectively. The neutron diffraction studies confirm an ``incomplete'' ${\mathrm{\ensuremath{\Gamma}}}_{4}\ensuremath{\rightarrow} {\mathrm{\ensuremath{\Gamma}}}_{2}({F}_{x}$, ${C}_{y}$, ${G}_{z}$) spin-reorientation initiated $\ensuremath{\le}75$ K. Although the relative volume fraction of the two magnetic structures varies with decreasing temperature, both coexist even at 1.5 K. Below 10 K, the polarization of ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ moments in a ${c}_{y}^{R}$ arrangement develops, which gradually increases with decreasing temperature. At 2 K, magnetic structure associated with ${c}_{z}^{R}$ arrangement of ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ moments also appears. At 1.5 K, while the rare-earth magnetic moments show a ${c}_{y}^{R}+{c}_{z}^{R}$-type arrangement, the ${\mathrm{Fe}}^{3+}$ spins are represented by a combination of a ${\mathrm{\ensuremath{\Gamma}}}_{2}+{\mathrm{\ensuremath{\Gamma}}}_{4}$ (${G}_{z},{G}_{x}$) arrangement. A clear signature of the magnetic structure with ${\mathrm{\ensuremath{\Gamma}}}_{1}({G}_{y}$) representation, symmetrically compatible with the ${c}_{z}^{R}$-type arrangement of rare-earth moments, is not confirmed from the refinement of the neutron diffraction data. The observed Schottky anomaly at 2.5 K suggests that the ``rare-earth ordering'' is induced by polarization due to ${\mathrm{Fe}}^{3+}$ spins. The ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Fe}}^{3+}$ and ${\mathrm{Er}}^{3+}\ensuremath{-}{\mathrm{Dy}}^{3+}$ exchange interactions, obtained from first principle calculations, indicate that these interactions primarily cause the complicated spin reorientation and ${c}_{y}^{R}$ rare-earth ordering in the system, respectively, while the dipolar interactions between rare-earth moments result in the ${c}_{z}^{R}$ type rare-earth ordering at 2 K.