Magnetism without Magnetic Ions: Percolation, Exchange, and Formation Energies of Magnetism-Promoting Intrinsic Defects in CaO

We investigate theoretically the prospects of ferromagnetism being induced by cation vacancies in nonmagnetic oxides. A single Ca vacancy $V_{\mathrm{Ca}}^0$ has a magnetic moment due to its open-shell structure but the ferromagnetic interaction between two vacancies extends only to four neighbors or less. To achieve magnetic percolation on a fcc lattice with such an interaction range one needs a minimum of 4.9% vacancies, or a concentration $1.8\times {10}^{21}{\mathrm{cm}}^{-3}$. Total-energy calculations for CaO show, however, that due to the high vacancy formation energy even under the most favorable growth conditions one can not obtain more than 0.003% or ${10}^{18}{\mathrm{cm}}^{-3}$ vacancies at equilibrium, showing that a nonequilibrium vacancy-enhancement factor of ${10}^3$ is needed to achieve magnetism in such systems.