Interplay between trimer structure and magnetic ground state in Ba₅Ru₃O₁₂ probed by neutron and μSR techniques

We report a detailed inelastic neutron scattering (INS) and muon spin relaxation (μSR) investigations of a trimer ruthenate Ba₅Ru₃O₁₂ 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 ∼5.6 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 Ba₅Ru₃O₁₂ 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 μSR 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 μSR 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 Ru₃O₁₂-isolated trimer through theoretical calculations which agree with the experimentally observed spin excitation.