Dimerized quantum magnets provide a unique possibility to investigate the Bose-Einstein condensation of magnetic excitations in crystalline systems at low temperature. Here, we model the low-temperature magnetic properties of the recently synthesized spin $S=1$ dimer system ${\mathrm{K}}_2\mathrm{Ni}{\left({\mathrm{MoO}}_4\right)}_2$ and propose it as a candidate material for triplon and quintuplon condensation. Based on a first-principles analysis of its electronic structure, we derive an effective spin dimer model that we first solve within a mean-field approximation to refine its parameters in comparison to experiment. Finally, the model is solved by employing a numerically exact quantum Monte Carlo technique which leads to magnetic properties in good agreement with experimental magnetization and thermodynamic results. We discuss the emergent spin model of ${\mathrm{K}}_2\mathrm{Ni}{\left({\mathrm{MoO}}_4\right)}_2$ in view of the condensation of magnetic excitations in a broad parameter regime. Finally, we comment on a geometrical peculiarity of the proposed model and discuss how it could host a supersolid phase upon structural distortions.

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• Magnetism
• Quantum phase transitions
• Magnetic systems
• Density functional theory
• Mean field theory
• Quantum Monte Carlo