Magnetic frustration and disorder are key ingredients to prevent the onset of magnetic order. In the disordered hexagonal double perovskite ${\mathrm{BaTi}}_{1/2}{\mathrm{Mn}}_{1/2}{\mathrm{O}}_3$, ${\mathrm{Mn}}^{4+}$ cations, with $S=3/2$ spins, can either form highly correlated states of magnetic trimers or dimers or remain as weakly interacting orphan spins. At low temperature ($T$), the dimer response is negligible, and magnetism is dominated by the trimers and orphans. To explore the role of magnetic frustration, disorder and possibly of quantum fluctuations, the low-$T$ magnetic properties of the remaining magnetic degrees of freedom of ${\mathrm{BaTi}}_{1/2}{\mathrm{Mn}}_{1/2}{\mathrm{O}}_3$ are investigated. Heat-capacity data and magnetic susceptibility display no evidence for a phase transition to a magnetically ordered phase but indicate the formation of a correlated spin state. The low-temperature spin dynamics of this state is then explored by $\mu \mathrm{SR}$ experiments. The zero-field ${\mu }^{+}$ relaxation rate data show no static magnetism down to $T=19$ mK and longitudinal field experiments support as well that dynamic magnetism persists at $\mathrm{low}T$. Our results are interpreted in terms of a spin-glass state which stems from a disordered lattice of orphans spins and trimers. A spin liquid state in ${\mathrm{BaTi}}_{1/2}{\mathrm{Mn}}_{1/2}{\mathrm{O}}_3$, however, is not excluded and is also discussed.

• Received 7 March 2018
• Revised 31 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.054412