Quasiparticle Dynamics in the 4d-4f Ising-like Double Perovskite Ba2DyRuO6 Probed by Neutron Scattering and Machine-Learning Framework

TL;DR

Ba2DyRuO6 is explored as a prototypical 4$d$–4$f$ double perovskite where exchange between Ru5+ and Dy3+ drives a single magnetic transition near $T_N\approx47$ K and an Ising-like, collinear antiferromagnetic ground state. The authors integrate TOF neutron diffraction, INS, Raman, crystal-field theory, SpinW spin-wave modeling, and machine-learning–based phonon calculations to quantify exchange couplings, anisotropy, and lattice dynamics, revealing $J_{Dy-Ru} > J_{Ru-Ru} > J_{Dy-Dy}$ and an off-diagonal anisotropy $D_{xz}=D_{zx}=0.10$ meV that constrain spins to the $ac$-plane. Dy$^{3+}$ CEF levels are captured by a point-charge model with fitted Stevens parameters, reproducing CEF transitions at 46.5 and 71.8 meV and exposing significant admixture in the ground-state wavefunctions, indicating deviation from an ideal Ising limit. ML-based phonon simulations reproduce the measured phonon spectrum and suggest potential CEF–phonon coupling, underscoring the strong entanglement of spin, lattice, and orbital degrees of freedom in this system. Overall, the work demonstrates how 4$d$–4$f$ hybridization and subtle single-ion anisotropy govern quasiparticle dynamics in Ba2DyRuO6 and suggests avenues to tune exchange via A-site substitution in related double perovskites.

Abstract

Double perovskites containing 4d--4f interactions provide a platform to study complex magnetic phenomena in correlated systems. Here, we investigate the magnetic ground state and quasiparticle excitations of the fascinating double perovskite system, Ba$_2$DyRuO$_6$, through Time of flight (TOF) neutron diffraction (TOF), inelastic neutron scattering (INS), and theoretical modelling. The compound Ba$_2$DyRuO$_6$ is reported to exhibit a single magnetic transition, in sharp contrast to most of the other rare-earth (R) members in this family, A$_2$RRuO$_6$ (A = Ca/Sr/Ba), which typically show magnetic ordering of the Ru ions, followed by R-ion ordering. Our neutron diffraction results confirm that long-range antiferromagnetic order emerges at $T_\mathrm{N} \approx 47$~K, primarily driven by 4d--4f Ru$^{5+}$--Dy$^{3+}$ exchange interactions, where both Dy and Ru moments start to order simultaneously. The ordered ground state is a collinear antiferromagnet with Ising character, carrying ordered moments of $μ_{\mathrm{Ru}} = 1.6(1)~μ_\mathrm{B}$ and $μ_{\mathrm{Dy}} = 5.1(1)~μ_\mathrm{B}$ at 1.5~K. Low-temperature INS reveals well-defined magnon excitations below 10~meV. SpinW modelling of the INS spectra evidences complex exchange interactions and the presence of magnetic anisotropy, which governs the Ising ground state and accounts for the observed magnon spectrum. Combined INS and Raman spectroscopy reveal crystal-electric-field (CEF) excitations of Dy$^{3+}$ at 46.5 and 71.8~meV in the paramagnetic region. The observed CEF levels are reproduced by point-charge calculations consistent with the $O_h$ symmetry of Dy$^{3+}$. A complementary machine-learning approach is used to analyse the phonon spectrum and compare with INS data. Together, these results clarify the origin of phonon and magnon excitations and their role in the ground-state magnetism of Ba$_2$DyRuO$_6$.

Figures (14)

• Figure 1: (a) Rietveld refinement of the X-ray diffraction (XRD) pattern of Ba$_2$DyRuO$_6$ measured at room temperature, with intensity (I) plotted as a function of 2$\theta$ (°). Open black circles represent the observed data, the solid red line corresponds to the calculated pattern, vertical pink ticks indicate Bragg reflection positions, and the blue line at the bottom shows the difference between observed and calculated intensities. (b) Crystal structure of Ba$_2$DyRuO$_6$ crystallizing in the cubic Fm-$3$m space group. Red spheres represent oxygen sites and green spheres represent barium sites.
• Figure 2: Comparison of neutron powder diffraction (NPD) patterns collected at 1.5 K, 15 K, 30 K, 45 K, and 55 K, with intensity $I$ plotted as a function of momentum transfer $Q$ (Å$^{-1}$), highlighting the magnetic reflections from the WISH bank with average $2\theta = 58.33^{\circ}$. The inset shows an enlarged view of the two prominent magnetic peaks at $Q = 1.06$ and $1.84$ Å$^{-1}$.
• Figure 3: (a)Rietveld refinement of neutron diffraction data from the WISH Bank with average $2\theta = 58.33^{\circ}$ collected at $1.5$ K, and (b) at $300$ K in the range $0.65 \leq Q \leq 2~\mathrm{\AA^{-1}}$. Open black circles show the observed pattern, and the solid red line is the calculated profile. Vertical purple and green ticks indicate the nuclear (top) and magnetic (bottom) Bragg positions, respectively, while the blue curve represents the difference between the observed and calculated intensities. (c) Rietveld refinement of neutron diffraction data from the WISH Bank with average $2\theta = 152.82^{\circ}$ collected at 1.5 K, and (d) at 300 K in $2 \le Q \le 12~\mathrm{\AA^{-1}}$.
• Figure 4: Magnetic ground state of Ba$_2$DyRuO$_6$ at 1.5 K, drawn in the cubic unit cell of the parent structure showing a collinear magnetic structure within the $ac$ plane with propagation vector $\mathbf{k} = (0, 1, 0)$. Yellow spheres represent Dy atoms, and green spheres represent Ru atoms. The dominant exchange path is indicated by red dotted lines.
• Figure 5: Thermal variation of (a) Dy$^{3+}$ and Ru$^{5+}$ moments based on refinement, (b) normalised moments of Dy$^{3+}$ and Ru$^{5+}$, and (c) temperature dependence of the integrated intensity $I(T)$ below the ordering temperature. A uniform uncertainty of $\pm 0.1\,\mu_{\mathrm{B}}$ is considered for the refined magnetic moments. The data are fitted with $I(T) = I_0(1 - T/T_N)^{2\beta}$ using $\beta = 0.325(2)$ (Ising model).