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We report a structural/magnetic investigation by X-ray absorptionspectroscopy (XAS), neutron diffraction, dc-susceptibility ($\chi_{\mbox{dc}}$)and electron spin resonance (ESR) of the 12R-type perovskiteBaTi$_{1/2}$Mn$_{1/2}$O$_{3}$. Our structural analysis by neutron diffractionsupports the existence of structural trimers with chemically disorderedoccupancy of Mn$^{4+}$ and Ti$^{4+}$ ions, with the valence of the Mn ionsconfirmed by the XAS measurements. The magnetic properties are explored bycombining dc-susceptibility and $X$-band ($9.4$ GHz) electron spin resonance,both in the temperature interval of $2\leq T\leq1000$ K. A scenario ispresented under which the magnetism is explained by considering magnetic dimersand trimers, with exchange constants $J_{a}/k_{B}=200(2)$ K and$J_{b}/k_{B}=130(10)$ K, and orphan spins. Thus, BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$is proposed as a rare case of an intrinsically disordered $S=3/2$ spin gapsystem with a frustrated ground state.

Magnetic dimers and trimers in the disordered $S=3/2$ spin system BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$