Successive spin reorientations and rare earth ordering in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Nd</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>Dy</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:mi>Fe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>: Experimental and <i>ab initio</i> investigations

Abstract

In the present paper, the magnetic structure and spin reorientation of mixed rare-earth orthoferrite ${\mathrm{Nd}}_{0.5}{\mathrm{Dy}}_{0.5}\mathrm{Fe}{\mathrm{O}}_{3}$ have been investigated. At room temperature, our neutron-diffraction measurements reveal that the magnetic structure of ${\mathrm{Fe}}^{3+}$ spins in ${\mathrm{Nd}}_{0.5}{\mathrm{Dy}}_{0.5}\mathrm{Fe}{\mathrm{O}}_{3}$ belongs to ${\mathrm{\ensuremath{\Gamma}}}_{4}$ irreducible representation (${G}_{x}, {F}_{z}$) as observed in both parent compounds ($\mathrm{Nd}\mathrm{Fe}{\mathrm{O}}_{3}$ and $\mathrm{Dy}\mathrm{Fe}{\mathrm{O}}_{3}$). The neutron-diffraction study also confirms the presence of a spin-reorientation transition where the magnetic structure of ${\mathrm{Fe}}^{3+}$ spins changes from ${\mathrm{\ensuremath{\Gamma}}}_{4}$ to ${\mathrm{\ensuremath{\Gamma}}}_{2}({F}_{x}, {G}_{z}$) representation between 75 and 20 K while maintaining a G-type antiferromagnetic configuration. Such a gradual spin reorientation is unusual since the large single ion anisotropy of ${\mathrm{Dy}}^{3+}$ ions is expected to cause an abrupt ${\mathrm{\ensuremath{\Gamma}}}_{4}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{1}({G}_{y}$) rotation of the ${\mathrm{Fe}}^{3+}$ spins. At 10 K, the ${\mathrm{Fe}}^{3+}$ magnetic structure is represented by ${\mathrm{\ensuremath{\Gamma}}}_{2}$ (${F}_{x}, {G}_{z}$). Unexpectedly, the ${\mathrm{\ensuremath{\Gamma}}}_{4}$ structure of ${\mathrm{Fe}}^{3+}$ spins re-emerges below 10 K, which also coincides with the development of rare-earth (${\mathrm{Nd}}^{3+}/{\mathrm{Dy}}^{3+}$) magnetic ordering having ${c}_{y}^{R}$ configuration. Such re-emergence of a magnetic structure has been a rare phenomenon in orthoferrites. The absence of a second-order phase transition in rare-earth ordering, interpreted from heat capacity data, suggests the prominent role of ${\mathrm{Nd}}^{3+}\ensuremath{-}{\mathrm{Fe}}^{3+}$ and ${\mathrm{Nd}}^{3+}\ensuremath{-}{\mathrm{Dy}}^{3+}$ exchange interactions. These interactions suppress the independent rare-earth magnetic ordering observed in both parent compounds due to ${\mathrm{Nd}}^{3+}/{\mathrm{Dy}}^{3+}\ensuremath{-}{\mathrm{Nd}}^{3+}/{\mathrm{Dy}}^{3+}$ exchange interactions. Our density-functional-theory calculations including Coulomb correlation and spin-orbit interaction effects ($\mathrm{DFT}+U+\mathrm{SO}$) reveal that the C-type arrangement of rare-earth ions (${\mathrm{Nd}}^{3+}/{\mathrm{Dy}}^{3+}$), with ${\mathrm{\ensuremath{\Gamma}}}_{2}$ (${F}_{x}, {G}_{z}$) configuration for ${\mathrm{Fe}}^{3+}$ moments, is energetically very close to a phase with the same rare-earth magnetic ordering but ${\mathrm{\ensuremath{\Gamma}}}_{4}$ (${G}_{x}, {F}_{z}$) configuration of ${\mathrm{Fe}}^{3+}$ spins. Further, the ${\mathrm{Nd}}^{3+}\ensuremath{-}{\mathrm{Fe}}^{3+}$ and ${\mathrm{Nd}}^{3+}\ensuremath{-}{\mathrm{Dy}}^{3+}$ exchange interactions are observed to play significant roles in the complex ${\mathrm{Fe}}^{3+}$ spin reorientation with the re-emergence of ${\mathrm{\ensuremath{\Gamma}}}_{4}$ at low temperature. Consistent with the experimental observations, our calculations established the mixed phase (${\mathrm{\ensuremath{\Gamma}}}_{2}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}$) to be the magnetic ground state of ${\mathrm{Fe}}^{3+}$ moments.

Topics & Concepts