Compositional tuning of magnetic properties to provide technologically useful results is in the forefront of research in complex oxides. Taking advantage of the highly sensitive nature of magnetism in 6H barium ruthenates (Ba3MRu2O9, M = transition metals or rare earth ions) to composition, we have carried out M-site dual doping by 50% each of Co and Mn. The high pressure and high temperature synthesized sample of 6H Ba3Co0.5Mn0.5Ru2O9 shows giant exchange bias (5.71 kOe at 5 K and 50 kOe cooling field) and huge coercivity (9.42 kOe at 5 K) at low temperature along with Griffiths phase like behavior in the 136 K < T < 260 K temperature range. The presence of ferromagnetic (FM) clusters in a non-collinear antiferromagnetic (AFM) background for temperature below 136 K is assumed. These FM clusters extend above 136 K to persist until 260 K, and the system finally reaches the paramagnetic (PM) state closer to room temperature. The exchange bias phenomena diminish above 20 K and this could be correlated with the peculiar nature of magnetic isotherms above and below this temperature. The transition at 136 K is regarded as AFM short-range ordering from ac and dc magnetization studies and heat capacity measurement. The presence of short-range interactions at temperatures until the PM region forms the basis of Griffiths phase like behavior in this sample.
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