We study from ab initio density functional theory calculations the structural and magnetic properties of the crystal ${\mathrm{KCoF}}_3$. We found that the experimentally reported cubic to tetragonal phase transition is due to an electronic first-order Jahn-Teller effect from the $R$ zone boundary point. We also obtain that the magnetic ground state is the G-type antiferromagnetic order, in agreement with the $R$-point Jahn-Teller distortion and that the magnetic moment of the Co atoms contains a strong orbital contribution ($m_L=0.95 {\mu }_B$ in the cubic phase and 0.55 ${\mu }_B$ in the tetragonal phase). Furthermore, we compute the dynamical magnetic effective charges and show that it is zero by symmetry for the Co and they can reach a value as large as 200 ${10}^{-2}{\mu }_{\text{B}}/\text{Å}$ for the apical F anion. This large magnetic effective charge comes from the spin-orbit coupling (50% of the response is from the orbital moment) contrary to the rare-earth manganites and ferrites with similar order of magnitude but originating from the exchange striction mechanism. The fact that the dynamical magnetic effective charges are nonzero also proves that the tetragonal phase of ${\mathrm{KCoF}}_3$ is antimagnetoelectric with a large magnetic sublattice magnetoelectric response of 210 ps/m per spin channel. We also discuss the generality of these magnetic effective charges.

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• Antiferromagnetism
• Jahn-Teller effect
• Magnetoelectric effect
• Magnons
• Phonons
• Spin-orbit coupling