Successive spin reorientations and rare earth ordering in Nd0.5Dy0.5Fe O3 : Experimental and ab initio investigations

In the present paper, the magnetic structure and spin reorientation of mixed rare-earth orthoferrite Nd_0.5Dy_0.5Fe O₃ have been investigated. At room temperature, our neutron-diffraction measurements reveal that the magnetic structure of Fe^{3 +} spins in Nd_0.5Dy_0.5Fe O₃ belongs to Γ₄ irreducible representation (G_x, F_z) as observed in both parent compounds (Nd Fe O₃ and Dy Fe O₃ ). The neutron-diffraction study also confirms the presence of a spin-reorientation transition where the magnetic structure of Fe^{3 +} spins changes from Γ₄ to Γ₂( 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 Dy^{3 +} ions is expected to cause an abrupt Γ₄→Γ₁( G_y ) rotation of the Fe^{3 +} spins. At 10 K, the Fe^{3 +} magnetic structure is represented by Γ₂ (F_x, G_z). Unexpectedly, the Γ₄ structure of Fe^{3 +} spins re-emerges below 10 K, which also coincides with the development of rare-earth (Nd^{3 +}/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 Nd^{3 +}- Fe^{3 +} and Nd^{3 +}- Dy^{3 +} exchange interactions. These interactions suppress the independent rare-earth magnetic ordering observed in both parent compounds due to Nd^{3 +}/Dy^{3 +}- Nd^{3 +}/Dy^{3 +} exchange interactions. Our density-functional-theory calculations including Coulomb correlation and spin-orbit interaction effects (DFT +U +SO ) reveal that the C-type arrangement of rare-earth ions (Nd^{3 +}/Dy^{3 +}), with Γ₂ (F_x, G_z) configuration for Fe^{3 +} moments, is energetically very close to a phase with the same rare-earth magnetic ordering but Γ₄ (G_x, F_z) configuration of Fe^{3 +} spins. Further, the Nd^{3 +}- Fe^{3 +} and Nd^{3 +}- Dy^{3 +} exchange interactions are observed to play significant roles in the complex Fe^{3 +} spin reorientation with the re-emergence of Γ₄ at low temperature. Consistent with the experimental observations, our calculations established the mixed phase (Γ₂ and Γ₄) to be the magnetic ground state of Fe^{3 +} moments.