  Normally $4d$ or $5d$ transition metals are in a low-spin state. Here using
first-principles calculations, we report on a rare case of a high-spin $S$=1
magnetic state for the Ag$^{3+}$ ion in the double perovskite
Cs$_{2}$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 loss
exceed the e$_{g}$ crystal-field energy gain, thus making the low-spin
tetragonal structure less favorable than the high-spin cubic structure. We
conclude that the compact perovskite structure of Cs$_{2}$KAgF$_{6}$ is an
important factor in stabilizing the unusual high-spin ground state of
Ag$^{3+}$.
