We report the magnetic and microstructural properties of antiferromagnetic MnO nanoparticles with shells of ferrimagnetic ${\mathrm{Mn}}_3{\mathrm{O}}_4$, which is opposite the usual arrangement of antiferromagnetically coated ferromagnetic nanoparticles. In addition, the antiferromagnetic MnO cores order at much higher temperature $(T_N=118\mathrm{K})$ than the ferrimagnetic ${\mathrm{Mn}}_3{\mathrm{O}}_4$ shells $(T_C=43\mathrm{K})$—another reversal of the usual situation. The single crystal MnO cores, with rocksalt structure, are crystallographically aligned with the tetragonal spinel structure of the ${\mathrm{Mn}}_3{\mathrm{O}}_4$ shells. Particles field cooled in $50\mathrm{kOe}$ have large coercive force and exchange bias below $T_C$, e.g., 5800 and $2950\mathrm{Oe}$, respectively, at $5\mathrm{K}$. The spontaneous magnetization at $T_C\left({\mathrm{Mn}}_3{\mathrm{O}}_4\right)$ is $\sim 20\%$ of its value at $5\mathrm{K}$, and remains finite for more than $20\mathrm{K}$ above $T_C\left({\mathrm{Mn}}_3{\mathrm{O}}_4\right)$. Hysteresis with exchange bias is present in this anomalous region. The MnO cores with their uncompensated spins are responsible for the behavior above $T_C\left({\mathrm{Mn}}_3{\mathrm{O}}_4\right)$. The MnO cores have a blocking temperature of $95\mathrm{K}$, and the hysteresis and exchange bias above $T_C\left({\mathrm{Mn}}_3{\mathrm{O}}_4\right)$ results from the switching of the MnO spin lattices by their uncompensated spins. Analysis of the thermoremanent magnetization and field cooling and/or zero field cooling in $50\mathrm{kOe}$, and the dependence of exchange bias on the temperature at which the cooling field was applied support this model.

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