Coexisting magnetic structures and spin reorientation in ${\mathrm{Er}}_{0.5}{\mathrm{Dy}}_{0.5}{\mathrm{FeO}}_3$: 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 ${\mathrm{\Gamma }}_4(G_x$, $A_y$, $F_z$) 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 $\sim 75$ K and 10 K, respectively. The neutron diffraction studies confirm an “incomplete” ${\mathrm{\Gamma }}_4\to {\mathrm{\Gamma }}_2(F_x$, $C_y$, $G_z$) spin-reorientation initiated $\le 75$ 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 ${\mathrm{\Gamma }}_2+{\mathrm{\Gamma }}_4$ ($G_z,G_x$) arrangement. A clear signature of the magnetic structure with ${\mathrm{\Gamma }}_1(G_y$) 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 ${\mathrm{Er}}^{3+}-{\mathrm{Fe}}^{3+}$ and ${\mathrm{Er}}^{3+}-{\mathrm{Dy}}^{3+}$ 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.

Figure 1

Observed and refined x-ray diffraction pattern of EDFO at room temperature. We also show the unit cell of EDFO, wherein the Er and Dy atoms occupy same crystallographic site. The Er/Dy, Fe, and O atoms are represented by silver/blue, green, and red spheres, respectively, in the unit cell.

Figure 2

[(a)–(c)] Temperature variation of lattice parameters, (d) unit cell volume of EDFO, and (e) anomalous rise in volume below 10 K.

Figure 3

ZFC-FC magnetization of EDFO at (a) 0.01 T and (b) 0.1 T. The inset shows enlarged portion of the graph below 70 K.

Figure 4

$M-H$ isotherms of EDFO at various temperatures.

Figure 5

Neutron powder diffraction pattern and refinements of EDFO at 200, 45, and 20 K (left panel) showing the systematic evolution of intensity of (011) and (101) magnetic peaks. In the right panel, patterns and refinement for 4, 2, and 1.5 K are shown. Additional magnetic peaks arising due to ordering of ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ moments are marked.

Figure 6

(a) Temperature variation of intensity of various magnetic peaks between 300 and 1.5 K. (b) Temperature variation of intensity of various magnetic peaks below 15 K. The development of peaks due to $R^{3+}$ ordering and anomalous rise in the intensity of (101) magnetic peak below 4 K is highlighted.

Figure 7

(011) and (101) magnetic Bragg peaks showing results of fitting by ${\mathrm{\Gamma }}_4+{\mathrm{\Gamma }}_2$ (upper panel) and ${\mathrm{\Gamma }}_4+{\mathrm{\Gamma }}_2+{\mathrm{\Gamma }}_1$ (lower panel) magnetic structures of the ${\mathrm{Fe}}^{3+}$ spins.

Figure 8

(a) Temperature variation of magnetic moment of ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ spins from 1.5 to 300 K for the various magnetic structures. (b) The variation of magnetic moments in the temperature range from 10 to 1.5 K. The arrow shows the discontinuity/sudden rise of $m_z^R$.

Figure 9

Magnetic structure of EDFO at (a) 50 K: $G_x$, $G_z$ arrangement of ${\mathrm{Fe}}^{3+}$ spins, (b) 4 K: ($G_x$, $G_z$, $c_y^R$), and (c) 1.5 K: ($G_x$, $G_z$, $c_y^R$, $c_z^R$). Red spheres represent Fe atoms, violet spheres represent Er/Dy atoms.

Figure 10

The low-temperature specific heat of EDFO for 0, 2, and 5 T. The dashed and solid lines show the fitting of specific heat to Schottky and lattice terms.

Figure 11

Partial density of states(DOS) of EDFO for the (a) alternate (111) (b) layered (001) calculated within $\mathrm{GGA}+\mathrm{U}+\mathrm{SO}$ approximation with noncollinear spin arrangements of Er and Dy as shown in the inset.