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Magnetic frustration and disorder are key ingredients to prevent the onset ofmagnetic order. In the disordered hexagonal double perovskiteBaTi$_{1/2}$Mn$_{1/2}$O$_{3}$, Mn$^{4+}$ cations, with $S=3/2$ spins, caneither form highly correlated states of magnetic trimers or dimers or remain asweakly interacting orphan spins. At low temperature ($T$), the dimer responseis negligible, and magnetism is dominated by the trimers and orphans. Toexplore the role of magnetic frustration, disorder and possibly of quantumfluctuations, the low-$T$ magnetic properties of the remaining magnetic degreesof freedom of BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$ are investigated. Heat-capacitydata and magnetic susceptibility display no evidence for a phase transition toa magnetically ordered phase but indicate the formation of a correlated spinstate. The low-temperature spin dynamics of this state is then explored by$\mu$SR experiments. The zero field $\mu^{+}$ relaxation rate data show nostatic magnetism down to $T=19$ mK and longitudinal field experiments supportas well that dynamic magnetism persists at low $T$. Our results are interpretedin terms of a spin glass state which stems from a disordered lattice of orphansspins and trimers. A spin liquid state in BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$,however, is not excluded and is also discussed.

Dynamic magnetism in the disordered hexagonal double perovskite BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$