Coexisting Paramagnetic Spins and Long-Range Magnetic Order in Ba$_4$(Ru$_{0.92}$Ir$_{0.08}$)$_3$O$_{10}$

Abstract

We investigate the effect of dilute Ir substitution on the magnetism of the trimer-based ruthenate Ba$_4$Ru$_3$O$_{10}$ using neutron diffraction, magnetic susceptibility measurements, atomistic simulations, and first-principles calculations. Neutron diffraction shows that Ir doping preserves the zigzag antiferromagnetic structure and the ordered-moment magnitude of the parent compound, in which the moments reside exclusively on the two outer Ru(2) sites of each $\rm Ru_3O_{12}$ trimer, while the central Ru(1) site remains nonmagnetic. The Néel temperature is reduced from $\approx\!105$ K to 84.0(1) K upon 8% Ir substitution, while magnetic susceptibility reveals a pronounced low-temperature Curie-like upturn, indicating the coexistence of paramagnetic spins with long-range antiferromagnetic order. Density-functional calculations shows that Ir preferentially occupies the central Ru(1) site, where its extended $5d$ orbitals disrupt the Ru-Ru molecular-orbital network and intra/inter-trimer exchange pathways. Atomistic simulations incorporating this paramagnetic dilution reproduce the suppressed ordering temperature and the coexistence of ordered and paramagnetic components.

Figures (4)

• Figure 1: Magnetic structure of parent and Ir-doped Ba$_4$Ru$_3$O$_{10}$, showing the three-dimensional network of face-sharing RuO$_6$ octahedra; oxygen and barium atoms omitted for clarity. The face-sharing geometry forms Ru$_3$O$_{12}$ trimers composed of a central Ru(1) ion and two outer Ru(2) ions. The arrows illustrate the dominant magnetic exchange pathways: the intra-trimer coupling $J_{\rm trimer}$ (red), the inter-trimer chain coupling $J_{\rm chain}$ (blue), and the in-plane inter-trimer coupling $J_{\rm plane}$ (black).
• Figure 2: Temperature-dependent magnetic susceptibility $\chi(T)$ of (a) Ba$_4$Ru$_3$O$_{10}$ and (b) Ba$_4$(Ru$_{0.92}$Ir$_{0.08}$)$_3$O$_{10}$, measured with magnetic fields applied along the three crystallographic axes. The dotted curves are results of Monte Carlo spin-dynamics simulations described in Appendix \ref{['Appendix:Sunny']}. In the parent compound, $\chi_a(T)$ shows a pronounced anomaly at $T_{\mathrm N}\!\approx\!105$ K and suppression at lower temperatures, consistent with an easy axis along $a$. Upon Ir substitution, the anomaly shifts to $T_{\mathrm N}\!\approx\!84$ K and a Curie-like upturn develops at low temperature for all field directions, indicating the emergence of weakly coupled paramagnetic spins. In the simulations, Ir substitution is modeled by diluting the exchange network through the removal of exchange bonds associated with a fraction of paramagnetic Ru sites.
• Figure 3: Neutron diffraction map of Ir-doped Ba$_4$Ru$_3$O$_{10}$ in the $(H,K,0)$ plane at (a) $T=5$ K and (b) $T=120$ K, showing enhanced magnetic Bragg peak intensity (circled) at low temperature. (c) Line cuts along the $K$ direction, obtained by integrating over $H\in[0.9,1.1]$ and $L\in[-0.1,0.1]$, comparing data at $T=5$ K and $120$ K and highlighting the enhanced magnetic intensity at the $(1,1,0)$ and $(1,2,0)$ reflections at low temperature. (d) Thermal evolution of the integrated magnetic intensity of the $(1,1,0)$ peak measured on VERITAS (HB-1A), fitted to extract Néel temperature $T_{\mathrm N}=84.0(1)$ K. Monte Carlo (MC) spin-dynamics simulations reproduce the ordering temperatures of both the parent compound ($T_{\mathrm N}\!\approx\!105$ K) and the Ir-doped sample. In the simulations, Ir substitution is modeled by diluting the exchange network through the introduction of weakly interacting paramagnetic Ru sites.
• Figure 4: Spin-density maps for (a) the parent and (b) the Ir-substituted Ba$_4$Ru$_3$O$_{10}$ compound. Blue and red elliptical outlines mark the parent and Ir-substituted Ru$_3$O$_{12}$ trimers, respectively. In the parent system, the spin density is concentrated on the two outer Ru(2) sites of each trimer, while the central Ru(1) site exhibits negligible spin polarization, highlighting the site-selective nature of magnetism. The substituted Ru(1) site shows negligible spin polarization, indicating that Ir remains magnetically silent.