Diffuse magnetic neutron scattering in the highly frustrated double perovskite ${\text{Ba}}_2{\text{YRuO}}_6$

Diffuse magnetic scattering in the highly frustrated double perovskite ${\text{Ba}}_2{\text{YRuO}}_6$ was investigated using polarized neutrons. Consistent with previous reports, the material shows two apparent transitions at 47 and 36 K to an eventual type I face-centered-cubic magnetic ground state. The (100) magnetic reflection shows different behavior from the five other observed reflections upon heating from 1.8 K, with the former broadening well beyond the resolution limit near 36 K. Closer examination of the latter group reveals a small, but clear, increase in peak widths between 36 and 47 K, indicating that this regime is dominated by short-range spin correlations. Diffuse magnetic scattering persists above 47 K near the position of (100) to at least 200 K, consistent with strong frustration. Reverse Monte Carlo (RMC) modeling of the diffuse scattering from 45 to 200 K finds that the spin-spin correlations between nearest and next-nearest neighbors are antiferromagnetic and ferromagnetic, respectively, at temperatures near the upper ordering temperature, but both become antiferromagnetic and of similar magnitude above 100 K. The significance of this unusual crossover is discussed in light of the super-superexchange interactions between nearest and next-nearest neighbors in this material and the demands of type I order. The dimensionality of the correlations is addressed by reconstructing the scattering in the $\left(hk0\right)$ plane using the RMC spin configurations. This indicates that one-dimensional spin correlations dominate at temperatures close to the first transition. In addition, a comparison between mean-field calculations and $\left(hk0\right)$ scattering implies that further neighbor couplings play a significant role in the selection of the ground state. The results and interpretation are compared with those recently published for monoclinic ${\text{Sr}}_2{\text{YRuO}}_6$, and similarities and differences are emphasized.

Figure 1

(a) The crystal structure of the $B$-site ordered double perovskite, $A_{2}B{B}^{\prime }{\text{O}}_6$. The gray spheres, purple octahedra, and dark blue octahedra represent $A$ ions, $B{\text{O}}_6$ octahedra, and $B^{\prime }{\text{O}}_6$ octahedra, respectively. (b) The geometrically frustrated face-centered-cubic lattice of edge-sharing tetrahedra formed by both the $B$ and $B^{\prime }$ sites. Solid and dashed black lines indicate nearest-neighbor and next-nearest-neighbor Ru-Ru distances for ${\text{Ba}}_2{\text{YRuO}}_6$.

Figure 2

The type I fcc magnetic structure found for ${\text{Ba}}_2{\text{YRuO}}_6$ and several other ${\text{Ru}}^{5+}$ based double perovskites. The chosen moment direction is arbitrary as this cannot be determined from powder data on a material with cubic symmetry.

Figure 3

Magnetic scattering after separation from other scattering contributions for ${\text{Ba}}_2{\text{YRuO}}_6$ at 35.8 K, showing the broadened (100) and relatively sharp (110), (210), (211), (300), and (310) magnetic reflections. The asterisks indicate the positions of the four strongest nuclear Bragg peaks (see the inset), which generate small anomalies in the magnetic cross section. The apparent peak at $\sim 1.3{\AA }^{-1}$ is probably spurious, as it has no systematic temperature dependence. Inset: The separation of the cross section into its magnetic (blue), spin-incoherent (red), and nuclear and isotope incoherent (II) (green) components by $XYZ$ polarization analysis.

Figure 4

(a) The temperature and $Q$ dependence of the magnetic scattering on passing through $T_{N1}$ and $T_{N2}$, indicated by white lines. (b) The integrated total magnetic cross section at various temperatures for ${\text{Ba}}_2{\text{YRuO}}_6$. A sharp drop is observed at $T_{N1}$, resulting from the opening of the gap.

Figure 5

The temperature dependence of the intensities (a) and Gaussian widths (b) of the (110) and (210) magnetic reflections for ${\text{Ba}}_2{\text{YRuO}}_6$. The vertical lines represent $T_{N2}$ and $T_{N1}$. Note the order-parameter-like behavior for the intensities below $T_{N2}$ and the more gradual decrease between $T_{N2}$ and $T_{N1}$. While both reflections broaden significantly above $T_{N2}$, the Gaussian (resolution) component remains dominant, making a Gaussian a good approximation of the line shape.

Figure 6

$S(Q,E)$ measured at 75 K from [15]. The detector trajectories integrated over in our polarized scattering experiments are indicated by white lines. The color scale is normalized to the magnetic intensity at $Q_{100}$ and $E=0$.

Figure 7

(a) Results of an RMC analysis of diffuse magnetic scattering data for ${\text{Ba}}_2{\text{YRuO}}_6$ at $T=45$, 60, 100, and 150 K. Experimental points are open blue circles, with the fit and difference indicated by red and black lines, respectively. (b) Normalized spin-spin correlations $\langle S_i·S_j\rangle /S(S+1)$ in direct space for several temperatures. (c) $T$ dependence of spin-spin correlations for the first two shells. Next-nearest-neighbor correlations cross over from antiferromagnetic to ferromagnetic at $\sim 100$ K.

Figure 8

Comparison between reconstructed single-crystal scattering for ${\text{Ba}}_2{\text{YRuO}}_6$ (left half) and the mean-field model (right half) described in the text. Exchange parameters for the latter were (a) $J_1=-1,J_2=-J_1/2,J_3=0,J_4=0$; and (b) $J_1=-1,J_2=3J_1/8,J_3=J_1/4,J_4=0$.

Figure 9

Comparison between the $\left(hk0\right)$ plane scattering reconstructed from the RMC fits to 45 K data (left) and the numerically evaluated scattering in the same plane for (right, upper) domains with ${\xi }_z=25$ Å and ${\xi }_{xy}=4.2$ Å, and (right, lower) domains with ${\xi }_z=8$ Å and ${\xi }_{xy}=16$ Å.

Figure 10

Normalized spin-spin correlations $\langle S_i·S_j\rangle /S(S+1)$ vs $T$ calculated from spin configurations obtained using an alternate code. The sign and magnitude of the nn correlations are well reproduced, while the nnn correlations tend on average slightly more toward antiferromagnetism.