Experiments

Two-gram samples of the Gd, Dy, and Ho analogs of Sr₂LnSbO₆ and Ba₂LnSbO₆ were prepared from the high-purity starting materials SrCO₃, BaCO₃, Gd₂O₃, Dy₂O₃, Ho₂O₃, and Sb₂O₅. Stoichiometric mixtures of these powders were mixed in an agate mortar and heated in air in dense, high-purity Al₂O₃ crucibles. Samples were heated at 1,400°C for a total of 48 h with several intermediate grindings and were observed to be single phase by powder x-ray diffraction (Cu Kα radiation) before study by neutron diffraction or magnetic susceptibility measurements.

Magnetic susceptibilities were measured between 2 and 320 K in an applied field of 200 Oe in a SQUID magnetometer (Quantum Design, San Diego). The crystal structures of the Dy- and Ho-based compounds were determined at ambient temperature by powder neutron diffraction, at the National Institute of Standards and Technology Center for Neutron Research, on the high-resolution powder neutron diffractometer with monochromatic neutrons of wavelength 1.540 2Å produced by a Cu(311) monochromator. (The Gd-based compounds were studied by susceptibility only, because of the strong neutron absorption of Gd.) Data were collected at ambient temperature between 3° and 168° diffraction angles with a step size of 0.05°. Collimators with horizontal divergences of 15′, 20′, and 7′ of arc were used before and after the monochromator, and after the sample, respectively. Structure refinement by the Rietveld method was carried out with the program GSAS (14). The neutron scattering amplitudes used in the refinement were 0.525, 0.702, 1.69, 0.808, 0.564, and 0.581 (×10^-12 cm) for Ba, Sr, Dy, Ho, Sb, and O, respectively (14). Statistical uncertainties quoted in all of the neutron results represent one standard deviation.

Results

The ambient temperature powder neutron diffraction patterns for the Ba₂HoSbO₆ and Sr₂HoSbO₆ double perovskites are presented in Fig. 2. The data from the Dy analogs are very highly analogous. Qualitative inspection of the patterns shows that the Sr variant has lower symmetry than the Ba variant. Both patterns can be indexed by crystallographic cells that are commonly found for double perovskites. The Ba variants can be best described by the high-symmetry cubic doubled perovskite cell, space group Fmm, with cell parameters (Å): a = 8.4119(1) and a = 8.4247(1) for Ho and Dy, respectively. The Sr variants can best be described by a monoclinic symmetry cell, space group P2₁/n. The cell parameters are: (Å) a = 5.8141(2), b = 5.8400(2), c = 8.2361(3), β = 90.162(2)° for Ho, and a = 5.8224(2), b = 5.8538(2), c = 8.2507(3), β = 90.186(2)° for Dy. The latter cells are very similar to those recently reported for the equivalent lanthanides in the Sr₂LnTaO₆ and Sr₂LnIrO₆ double perovskite families (15, 16). The Ba₂LnNbO₆ family is also apparently monoclinic (17).

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Fig. 2.

Ambient temperature powder neutron diffraction data for Ba₂HoSbO₆ (Upper) and Sr₂HoSbO₆ (Lower). Crosses are raw data, and solid line indicates fit. Vertical lines indicate calculated peak positions. Shown below is the difference between observed and calculated intensities.

The structural refinements indicate that the compounds display classic double-perovskite structures. As observed previously in other lanthanide-containing double perovskites (15–17), the present compounds show full ordering of the Ln³⁺ B-site ion and the nonmagnetic 5+ B-site ion, in this case Sb, in the available B sites, with the perfect ordering likely driven by differences in both charge and size. This is very important from the magnetic point of view, as disorder among the magnetic atoms significantly disrupts the geometrical frustration (1, 18). There are only minor differences in the structures for the two lanthanides in the current compounds, attributable to the slight difference in size between Ho and Dy. The structural parameters, bond lengths, and refinement particulars are summarized in Tables 1 and 2. The crystal structures are presented in Fig. 3. Fig. 3 shows that the reduced symmetry of the Sr variants is caused by the relatively smaller size of the Sr on the A site, resulting in the frequently observed partial collapse of the ideal perovskite cavity through rotations of the BO₆ octahedra about their shared corners, allowing for the appropriate Sr—O bond lengths.

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Fig. 3.

The crystal structures of Ba₂LnSbO₆ (Left) and Sr₂LnSbO₆ (Right). Atom types are as marked. Unit cell and B-site octahedra are outlined.

Fig. 4 shows the characteristics of the magnetic sublattices for the Dy and Ho double perovskites and compares them to that of the pyrochlore. Only the magnetic lanthanides are shown in Fig. 4a, which clarifies the arrangement of the edge-shared tetrahedra of magnetic ions found in the double perovskites. The fcc character of this arrangement is apparent. Fig. 4 b and c extracts individual magnetic ion tetrahedra from Ba₂DySbO₆ and Sr₂DySbO₆. In both compounds, only one type of magnetic tetrahedron is present. In the Ba compound, the tetrahedron is dimensionally regular, with a Dy–Dy separation of 5.96 Å. In the Sr compound, the Dy–Dy distances are somewhat shorter, ≈5.85 Å, and there is a range of separations of ≈0.03 Å, which is not substantial. Thus the magnetic tetrahedra are only slightly different in size and shape in the two kinds of compounds. Comparison to the size of the Dy tetrahedron in the Dy₂Ti₂O₇ pyrochlore is made in Fig. 4d. It is seen that the tetrahedra are quite different in size in the pyrochlore and double-perovskite structures, expected to significantly affect the relative strength of the magnetic coupling.

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Fig. 4.

The magnetic sublattice in the lanthanide double perovskites. Only magnetic lanthanide atoms are shown. (a) The arrangement of edge-shared magnetic atom tetrahedra in double perovskites. (b) The magnetic atom tetrahedron in Ba₂DySbO₆.(c) The magnetic atom tetrahedron in Sr₂DySbO₆. (d) The magnetic atom tetrahedron in Dy₂Ti₂O₇ for comparison. All distances are in Å.

The local coordination polyhedron of oxygen around the lanthanides in the double-perovskite and pyrochlore structures is quite different. A comparison of the shapes and sizes of the local lanthanide coordination polyhedra for the Dy double perovskites and the Dy pyrochlore is presented in Fig. 5. In the pyrochlore, the local Ln site symmetry is m, and there are six near-neighbor oxygens, two of which are substantially closer to the Dy than the other four (Fig. 5c). In the perovskites, the local lanthanide symmetry is mm in the cubic Ba variants, with six oxygen near-neighbors in an ideal octahedral geometry (Fig. 5b) and in the case of the monoclinic Sr variants, again with six oxygen neighbors, in a slightly distorted octahedral geometry. Fig. 5 shows that for the pyrochlores, very short Dy—O bond distances are found directly to an oxygen at the center of the magnetic tetrahedron, and to an equivalent oxygen in the directly opposite direction (<111> directions). These correspond exactly to the directions that the Ising-like Dy spins take in that compound, showing the structural origin of the strong crystal field (19) that determines the preferred orientations of the spins. For the double perovskites, on the other hand, the situation is quite different. For the Ba variant, six exactly equivalent lanthanide-oxygen bonds are pointed along cubic <100> directions, and not into the magnetic tetrahedra. The same is generally true in the Sr variants, except that the six lanthanide-oxygen bonds are not exactly equivalent by symmetry, with the directions still generally along what are in that case the pseudocubic <100> directions. The regular character of the Ln—O octahedra in the double perovskites suggests that the crystal field will not be axial in these compounds, as it is in the pyrochlore case. Fig. 5 also shows that the orientations of the LnO₆ local coordination octahedra with respect to the magnetic tetrahedra are slightly different in the two types of double perovskites. These differences in local coordination vs. magnetic geometry may lead to differences in magnetic behavior at low temperatures.

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Fig. 5.

The Ln-O coordination polyhedra and their relationship to the Ln tetrahedra in Sr₂DySbO₆ (a), Ba₂LnSbO₆ (b), and Dy₂Ti2O₇ (c). Large colored circles indicate Dy, and small black circles indicate oxygen.

The temperature-dependent magnetic susceptibility data for the six double perovskites studied are shown in Figs. 6, 7, 8. No magnetic transitions are observed down to a temperature of 2 K, and the Ba and Sr variants with the same lanthanide do not show substantially different behavior. The data are well described by the Curie–Weiss law at high temperatures, χ = C/(T - θ_W), where the Curie constant C is proportional to the square of the effective magnetic moment and the Weiss temperature θ_W is a measure of the strength and type of near-neighbor magnetic interaction. Deviations from this behavior occur only at low temperatures (Figs. 6, 7, 8 Insets). The parameters for the fits are presented in Table 3, as are comparisons to the expected moments (20) for the lanthanides. The θ_Ws are all negative for the double perovskites, indicating the presence of antiferromagnetic nearest neighbor spin–spin interactions. In addition, the θ_W values for the Dy and Ho analogs for the high temperature fits (≈-8 and -5 K, respectively) are comparable to those found in the pyrochlores, despite the substantially larger Ln–Ln spacing in the perovskites. (The lower temperature portions of the susceptibility curves have also been fit to the Curie–Weiss law, with the parameters shown in Table 3, to facilitate comparison to the pyrochlores where this temperature region is sometimes quoted in the characterizations.) Figs. 6, 7, 8 Insets show an interesting difference between the lowest temperature behaviors of the Dy- and Ho-based compounds. The Ho susceptibilities deviate toward lower values at the lowest temperatures measured, suggesting increasing antiferromagnetic correlations and perhaps incipient long-range order. The Dy susceptibilities, on the other hand, deviate toward higher values at lower temperatures, suggesting increasing ferromagnetic correlations or the presence of a small paramagnetic component to the susceptibility, as has been observed in other geometrically frustrated magnets (21, 22). The Gd-based materials, on the other hand, maintain their strict Curie–Weiss behavior to the lowest temperatures studied, with the Curie–Weiss θ values relatively quite small, on the order of 1 K.

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Fig. 6.

Temperature dependence of the inverse magnetic susceptibilities for Ba₂DySbO₆ and Sr₂DySbO₆. (Inset) Detail of the low-temperature region.

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Fig. 7.

Temperature dependence of the inverse magnetic susceptibilities for Ba₂HoSbO₆ and Sr₂HoSbO₆. (Inset) Detail of the low-temperature region.

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Fig. 8.

Temperature dependence of the inverse magnetic susceptibilities for Ba₂GdSbO₆ and Sr₂GdSbO₆. (Inset) Detail of the low-temperature region.

The expected magnetic ordering behavior for antiferromagnetically interacting Heisenberg spins on an fcc lattice has been modeled and simulated theoretically (23). For such a system, the magnetic ordering is expected at a temperature of 0.45 J, where J is the strength of the nearest neighbor coupling. For fcc lattices, the geometry dictates that the measured θ_W in the Curie–Weiss fit is 4 J. Thus theory predicts an antiferromagnetic long-range ordering temperature (T_N) of T_N/θ_W = 8 as a result of the frustrating geometry of the fcc lattice. [In the mean field picture in nonfrustrating lattices, ordering is expected for T_N/θ_W = 1–2 (1).] Interactions between spins on the fcc lattice beyond nearest neighbor coupling will increase T_N toward θ_W. For the fcc Dy, Ho, and Gd lattices in the current materials, where no magnetic ordering is observed down to 2 K, only the Dy case can be considered to be clearly showing the effects of geometric frustration, as T_N/θ_W must be >4. Sub-2 K measurements will be required to clarify the behavior of all of these compounds.

Conclusions

Double perovskites with lanthanides ordered on one subset of the octahedrally coordinated B sites have recently been of crystal chemical interest (13–16). In the present work we have described a few members of a family of such double perovskites, with Ln³⁺–Sb⁵⁺ ordering on the B sites. The antiferromagnetic near-neighbor coupling found for the Ho- and Dy-based double perovskites is different from the spin-ice pyrochlores based on those elements, where the nearest-neighbor coupling is ferromagnetic. Critical to the observation of the spin ice behavior in the Dy and Ho pyrochlores is the presence of significant magnetocrystalline anisotropy. The spins are Ising-like, with preferred directions toward or away from the centers of the magnetic tetrahedra, the <111> orientations. It is not known at this time how the lanthanide spins interact in the double perovskites, but both the crystal fields and their orientations with respect to the magnetic tetrahedra are different from those in the pyrochlores. If the preferred spin directions are along <100>, a 6-fold degeneracy results, which, combined with the edge-sharing geometry in the double perovskites, makes the Dy and Ho double perovskites distinctly different from the equivalent pyrochlores. Detailed study of the magnetic properties of these and additional fcc lanthanide double perovskites at temperatures <2 K will be of significant interest.