We report a detailed inelastic neutron scattering (INS) and muon spin relaxation $\left(\mu \mathrm{SR}\right)$ investigations of a trimer ruthenate ${\mathrm{Ba}}_5{\mathrm{Ru}}_3{\mathrm{O}}_{12}$ system, which undergoes long-range antiferromagnetic ordering at $T_N=60$ K. The INS reveals two distinct spin-wave excitations below $T_N$ : one at $\sim 5.6\mathrm{meV}$ and the other at 10–15 meV. By accompanying the INS spectra based on a linear spin-wave theory using spinw software and machine learning force fields (MLFFs), we show that ${\mathrm{Ba}}_5{\mathrm{Ru}}_3{\mathrm{O}}_{12}$ exhibits spin frustration due to competing exchange interactions between neighboring and next-neighboring Ru moments, exchange anisotropy, and strong spin-orbit coupling, which yields a noncollinear spin structure, in contrast to other ruthenate trimers in this series. Interestingly, these magnetic excitations do not completely vanish even at high temperatures above $T_N$ , evidencing short-range magnetic correlations in this trimer system. This is further supported by $\mu \mathrm{SR}$ spectroscopy, which exhibits a gradual drop in the initial asymmetry around the magnetic phase transition and is further verified through maximum entropy analysis. The results of $\mu \mathrm{SR}$ spectroscopy indicates a dynamic nature of magnetic order, attributed to local magnetic anisotropy within the trimer as a result of local structural distortion and different hybridization, consistent with canted spin structure. We predict the ground state of ${\mathrm{Ru}}_3{\mathrm{O}}_{12}$-isolated trimer through theoretical calculations which agree with the experimentally observed spin excitation.

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• Exchange interaction
• Frustrated magnetism
• Magnetic anisotropy
• Magnetism
• Spin dynamics
• Spin-orbit coupling
• Spin-phonon coupling
• Strongly correlated systems
• Muon spin relaxation & rotation
• Neutron scattering