Abstract
Ba${}_{3}$Mn${}_{2}$O${}_{8}$ is a hexagonally coordinated Mn${}^{5+}$ $S=1$ spin dimer system with small uniaxial single-ion anisotropy. ${}^{135,137}$Ba NMR spectroscopy is used to measure the longitudinal (${M}_{\ensuremath{\ell}}$) magnetization in the vicinity of the critical field at ${H}_{c1}$ for the onset of magnetic order for $\mathbf{H}\ensuremath{\parallel}\mathbf{c}$ and $\mathbf{H}\ensuremath{\perp}\mathbf{c}$. ${M}_{\ensuremath{\ell}\ensuremath{\parallel}}(T,{H}_{c1})$, ${M}_{\ensuremath{\ell}\ensuremath{\perp}}(T,{H}_{c1})$ are reproduced by solving a low-energy model for a dilute gas of interacting bosons.
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