II. EXPERIMENTAL

Polycrystalline samples of Y_1−xDy_xMnO₃ (x = 0.1, 0.2, 0.3, 0.4, 0. 5, 0.6, 0.7, 0.8, 0.9, and 1.0) were synthesized by the solid-state reaction. The structure of each sample was characterized by X-ray diffraction (XRD), which was performed on a Rigaku Dmax-rB diffractometer at room temperature with a step scanning model. The scan range of 2θ was from 15 to 90^o with a step size of 0.02^o. The structural parameters were obtained from a standard Rietveld program of GSAS. Magnetization characteristics were measured using a superconducting quantum interference device magnetometer (SQUID) with a magnetic field of 200 Oe at room temperature.

III. RESULTS AND DISCUSSION

Figure 1 shows the XRD patterns of all samples with different dopant concentrations measured at room temperature. The XRD patterns of the samples with x ≤ 0.5 can be well characterized by a hexagonal YMnO₃ structure with a space group of P6₃cm, which indicates that all samples are of a single hexagonal phase. For 0.6 ≤ x ≤ 0.8, mixed phases of orthorhombic and hexagonal phases are observed, and for x ≥ 0.9, orthorhombic symmetry stabilizes. The present study is focused on the dopant hexagonal Y_1−xDy_xMnO₃ (x ≤ 0.5). The XRD patterns for samples (x ≤ 0.5) with a hexagonal symmetry were all refined using the standard Rietveld program. And the agreement factors of the refinement were all within 13%. Figure 2 shows the refined XRD patterns of all the samples. The dopant dependence of unit-cell parameters of a, c, the ratio of c/a, and the unit-cell volume were obtained from Rietveld refinements as shown in Figure 3. With the Dy dopant concentration x increasing, the in-plane unit-cell parameter a, the out of plane unit-cell parameter c, and the unit-cell volume increase, which is ascribed to the larger ionic radius of Dy³⁺. It is notable that the unit-cell parameter ratio c/a is reduced by Dy substitution, which may be ascribed to the orbital shape of f electrons for Dy³⁺ ion. The change of unit-cell parameters may be related to the distortion of MnO₅ trigonal bipyramids and the buckling of R layers, which may change the ferroelectric polarization and magnetic ordering of Y_1−xDy_xMnO₃.

Figure 1.

X-ray diffraction patterns of Y_1−xDy_xMnO₃ with different Dy³⁺ dopant concentrations measured at room temperature.

Figure 2.

The observed (cross), calculated (line), and difference profiles at room temperature after Rietveld refinement using the P6₃cm space group for samples with doping content x = 0.0, 0.3, and 0.5. Bars represent the Bragg positions.

Figure 3.

Variations of the in-plane (a) and out-of-plane unit-cell parameters, the ratio of c/a (c) and unit-cell volume (d) vs. Dy³⁺ dopant concentration in YMnO₃.

Figure 4.

Bond lengths of Y1–O3 and Y2–O4 as a function of the dopant concentration in Y_1−xDy_xMnO₃.

Table I lists the Mn–O bond lengths obtained from the refinement. The planar Mn–O bond lengths (Mn–O3 and Mn–O4) are significantly larger than the apical Mn–O1 and Mn–O2 bond lengths, which are consistent with the results in the literature (Nugroho et al., Reference Nugroho, Bellido, Adem, Nénert, Simon, Tjia, Mostovoy and Palstra2007). There is no obvious change of the bond lengths Mn–O_p and Mn–O_T with Dy dopant concentration as seen from the refined data listed in the Table. The MnO₅ bipyramids remain centrosymmetric, and Mn³⁺ remains at the center of MnO₅. These results show that the Mn atoms framework is not obviously disturbed by the Dy substitution at the Y-site. Therefore, it may be deduced that the magnetic interplay between Mn ions is not affected by substituting Y with Dy. However, structural distortion is not unavoidable because Dy³⁺ has slightly larger ionic radii, which will induce magnetization and ferroelectric polarization and change the magnetoelectric coupling (Park et al., Reference Park, Lee, Kang, Jang, Lee, Streltsov, Mazurenko, Valentyuk, Medvedeva, Kamiyama and Park2010).

Table I.

Mn–O bond lengths in Y_1−xDy_xMnO₃ obtained from X-ray diffraction refinement.

The important characterization of the ferroelectric distortion of YMnO₃ is that one of the Y–O_P bond lengths is reduced, while the other is enlarged. To further study the effect of Dy doping on the ferroelectric distortion, the bond lengths of Y1–O3 and Y2–O4 were obtained from the refinement results of XRD. The bond length of Y2–O4 is elongated from 2.38 to 2.81 Å, while that of Y1–O3 is shortened from 2.43 to 2.08 Å, with increasing the Dy dopant concentration as shown in Figure 4. As we all know, the ferroelectricity comes from the off-center displacement of Y-atom between the in-plane oxygen along the c-axis. The structural distortion and enhanced R–Mn coupling may strengthen the ferroelectric distortion with increasing the Dy doping content and strengthen the magnetoelectric coupling, which was reported in related systems (Magesh et al., Reference Magesh, Murugavel, Mangalam, Singh, Simon and Prellier2012).

The temperature-dependent dc magnetization curves of samples with the different doping concentration of Dy³⁺ ion under zero-field-cooling (ZFC) and field-cooling (FC) conditions are shown in Figure 5. The applied magnetic field is 200 Oe. As seen in Figure 5, the AFM transition is not visible in the magnetization curves, which is because of the huge paramagnetic susceptibility stemming from Dy³⁺ (Harikrishnan et al., Reference Harikrishnan, Rößler, Naveen Kumar, Bhat, Rößler, Wirth, Steglich and Elizabeth2009). At low temperature, because Dy³⁺ ions which adopt a Г₂ structure with a ferrimagnetic alignment of moments below 10 K (Nandi et al., Reference Nandi, Kreyssig, Yan, Vannette, Lang, Tan, Kim, Prozorov, Lograsso, McQueeney and Goldman2008), the increasing magnetic moment may be mainly resulting from spin order of Dy³⁺. For pure YMnO₃, because Y³⁺ is a non-magnetic ion, there is no interaction between Y³⁺ and Mn³⁺. When Y³⁺ is partly substituted by magnetic Dy³⁺ with a larger ionic radius, interaction between Dy³⁺ and Mn³⁺ is introduced, which will induce spin reorientation (SR) effect below T _SR (Vajk et al., Reference Vajk, Kenzelmann, Lynn, Kim and Cheong2005; Magesh et al., Reference Magesh, Murugavel, Mangalam, Singh, Simon and Prellier2012). Meanwhile, interaction between inter-planar Mn³⁺–O–O–Mn³⁺ may be changed (Lonkai et al., Reference Lonkai, Tomuta, Hoffmann, Rschneider, Hohlwein and Ihringer2003), which need to be further checked. Therefore, the spin order of Dy³⁺ ions and Dy³⁺–Mn³⁺ coupling result in the increasing magnetic moment at low temperature with increasing Dy³⁺dopant concentration. No obvious bifurcation of ZFC and FC magnetization is observed at different doping concentrations of Dy, though obvious bifurcation is observed in DyMnO₃ single crystal at a temperature below 10 K (Mansouri et al., Reference Mansouri, Jandl, Laverdìere, Fournier, Mukhin, Ivanov and Balbashov2013). Spin-glass effect is not observed in our samples from M_T curves, which is different from B-site doping YMnO₃. These results may further show MnO₅ trigonal bipyramids is not obviously affected by Dy substitution.

Figure 5.

Temperature dependence of FC and ZFC of magnetization at H = 200 Oe for Dy³⁺-dopping YMnO₃.

Temperature dependence of the inverse susceptibility is shown in Figure 6 for three doped samples of Y_1−xDy_xMnO₃ (x = 0.0, 0.2, 0.4, and 0.6). There is no clear anomaly at the expected AFM transition temperatures for all the samples. By fitting the temperature dependence of inverse susceptibility 1/χ curves using the Curie–Weiss law χ = C/(T − θ _CW) (Figure 6), the Curie–Weiss temperatures θ _CW of samples with different Dy dopants were obtained. The Curie–Weiss temperatures are found to change from θ _CW = −560 K for x = 0.0 to −56 K (x = 0.2), −35 K (x = 0.4). The negative value of θ _CW indicates the presence of AFM exchange interactions. However, θ _CW does not directly relate to the physics of the coupled magnetic sublattices as in other hexagonal RMnO₃ systems (Harikrishnan et al., Reference Harikrishnan, Rößler, Naveen Kumar, Bhat, Rößler, Wirth, Steglich and Elizabeth2009). Based on the theoretical value of Curie–Weiss temperature θ _CW = 2J ₀S(S + 1)/3, the exchange constant J ₀ is proportional to θ _CW (Park et al., Reference Park, Lee, Kang, Jang, Lee, Streltsov, Mazurenko, Valentyuk, Medvedeva, Kamiyama and Park2010). The decreased J ₀ is owing to combined interactions of Mn³⁺–O–Mn³⁺, Mn³⁺–O–O–Mn³⁺ and Dy³⁺–Mn³⁺ in the Dy³⁺ doping YMnO₃ system. It is difficult to separate these different interactions in polycrystalline samples.

Figure 6.

Temperature dependence of the inverse susceptibility for four samples of Y_1−xDy_xMnO₃ (x = 0.0, 0.2, 0.4, and 0.6).