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Normally $4d$ or $5d$ transition metals are in a low-spin state. Here usingfirst-principles calculations, we report on a rare case of a high-spin $S$=1magnetic state for the Ag$^{3+}$ ion in the double perovskiteCs$_{2}$KAgF$_{6}$. We also explored a possibility of a conventional low-spin$S$=0 ground state and find an associated tetragonal distortion to be 0.29{\AA}. However, the lattice elastic energy cost and the Hund exchange lossexceed the e$_{g}$ crystal-field energy gain, thus making the low-spintetragonal structure less favorable than the high-spin cubic structure. Weconclude that the compact perovskite structure of Cs$_{2}$KAgF$_{6}$ is animportant factor in stabilizing the unusual high-spin ground state ofAg$^{3+}$.

Rare case of magnetic Ag$^{3+}$ ion: double perovskite Cs$_{2}$KAgF$_{6}$