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Ba$_3$Mn$_2$O$_8$ is a geometrically frustrated spin dimer compound. Weinvestigate the effect of site disorder on the zero field phase diagram of thismaterial by considering the solid solutionBa$_{3}$(Mn$_{1-x}$V$_{x}$)$_{2}$O$_{8}$, where nonmagnetic V$^{5+}$ ionspartially substitute magnetic Mn$^{5+}$ ions. This substitution results inunpaired $S=1$ moments for half-substituted dimers, which are ungapped andtherefore susceptible to types of magnetic order not present in the parentcompound. AC susceptibility measurements of compositions between $x=0.046$ and$x=0.84$ show a sharp frequency- and composition-dependent kink at temperaturesbelow 210mK, suggesting that unpaired spins form a spin glass. The case for aglassy state is made clearer by the absence of any sharp features in thespecific heat. However, Ba$_{3}$(Mn$_{1-x}$V$_{x}$)$_{2}$O$_{8}$ is not aparadigmatic spin glass. Whereas both the freezing temperature and the Weisstemperature (determined from susceptibility above 1K) vary strongly as afunction of composition, the heat capacity per unpaired spin is found to beinsensitive (above the glass transition) to the density of unpaired spins forthe broad regime $0.18\leq x \leq 0.84$. This surprising result is consistentwith a scenario in which nearest-neighbor unpaired spins form local, possiblyfluctuating, spin-singlets prior to the eventual spin freezing. The spin glassstate is only found for temperatures below the energy scale of single-ionanisotropy, suggestive this plays a significant role in determining theeventual ground state. Possible ground states in the "dilute" limit ($x < 0.04$and $x > 0.9$) are also discussed.

Spin Freezing in The Frustrated Disordered Quantum Magnet Ba$_{3}$(Mn$_{1-x}$V$_{x}$)$_{2}$O$_{8}$