Two-Dimensional Magnetic Correlations and Partial Long-Range Order in Geometrically Frustrated ${\mathrm{Sr}}_2{\mathrm{YRuO}}_6$

Neutron diffraction on the double perovskite ${\mathrm{Sr}}_2{\mathrm{YRuO}}_6$ with a quasi-fcc lattice of Ru moments reveals planar magnetic correlations that condense into a partial long-range ordered state with coupled alternate antiferromagnetic (AFM) ${\mathrm{YRuO}}_4$ square layers coexisting with the short-range correlations below $T_{N1}=32\mathrm{K}$. A second transition to a fully ordered AFM state below $T_{N2}=24\mathrm{K}$ is observed. The reduced dimensionality of the spin correlations is arguably due to a cancellation of the magnetic coupling between consecutive AFM square layers in fcc antiferromagnets, which is the simplest three-dimensional frustrated magnet model system.

Figure 1

High-resolution neutron powder diffraction pattern of ${\mathrm{Sr}}_2{\mathrm{YRuO}}_6$ at 3 K. The cross symbols and solid lines represent observed and calculated patterns, respectively. The difference curve is shown at the bottom. Vertical bars indicate the expected Bragg peak positions according to the nuclear (upper) and magnetic (lower) structure models described in the text and refined parameters given in Ref. 22. The fitting residuals are ${\chi }^2=1.895$, the weighted profile residual $R_{\mathrm{wp}}=4.35\%$, and the profile residual $R_p=3.45\%$. The insets illustrate the observed type-I antiferromagnetic (AFM) structure of ${\mathrm{Sr}}_2{\mathrm{YRuO}}_6$, where only the magnetic Ru ions are displayed and different shades (colors) represent opposite magnetic moments. Two representative edge-shared Ru tetahedra, which are the basic units leading to geometric frustration in this system, are illustrated in the left, also showing the monoclinic axes with lengths $a$, $b$, and $c$ and quasicubic unit cell ($a^{\prime }\sim b^{\prime }\sim c^{\prime }$). Satisfied (frustrated) nearest-neighbor AFM interactions are represented as gray (black) bonds. In the right inset, the same magnetic structure is visualized in terms of consecutive AFM square layers in the $ABAB$ sequence (shaded). The net magnetic coupling between consecutive $AB$ layers is null, while alternate $AA$ layers are coupled by weak next-nearest-neighbor exchange interactions such as those between atoms 1 and 2 (see text).

Figure 2

(a) High-intensity diffraction pattern of ${\mathrm{Sr}}_2{\mathrm{YRuO}}_6$ at selected temperatures. The indexing of magnetic and nuclear Bragg reflections according to the quasicubic unit cell of Fig. 1 is indicated, as well as a weak peak due to a minor unidentified impurity phase (IP). (b) Magnetic diffuse scattering at 35 K (symbols) after subtraction of the nonmagnetic background [24]. The thin solid and dotted lines are simulations using a two-dimensional scattering model with lateral widths $L_1=130$ and $L_2=23\AA$, respectively, and the thick solid line is the sum of these contributions. The dashed line is a fit of the low-$Q$ side of the scattering to a Lorentzian line shape, yielding an average in-plane correlation length $\overline{L}=60(3)\AA$.

Figure 3

(a), (b) Integrated intensity of the $(110{)}^{\prime }$ magnetic reflection on both log and linear temperature scales, highlighting the long-range order parameter. The data in (b) clearly indicate there are two components to the scattering with distinct transition temperatures, and the solid line is a guide to the eye. (c), (d) Integrated scattering for $0.82<Q<0.96{\AA }^{-1}$, capturing signal from short-range magnetic correlations; (e) integrated scattering for $0.35<Q<0.47{\AA }^{-1}$, showing the development of weakly correlated spins in the paramagnetic state at high temperatures; (f) average in-plane antiferromagnetic correlation length $\overline{L}$ obtained from half-Lorentzian fits to the diffuse scattering component for $Q<0.77{\AA }^{-1}$ [see text and Fig. 2b].