Compounds containing ${\mathrm{Ag}}^{2+}$ ion with $4d^9$ configuration will cause significant Jahn-Teller distortions and orbital ordering. Such orbital order is closely related to the magnetic coupling, according to Goodenough-Kanamori rules. Our first-principles calculations reveal that the ground state of ${\mathrm{KAgF}}_3$ exhibits collinear A-type antiferromagnetic (A-AFM) ordering accompanied by C-type orbital ordering. In contrast, ${\mathrm{K}}_2{\mathrm{AgF}}_4$ adopts a collinear intralayer antiferromagnetic configuration coupled with ferromagnetic orbital ordering. The A-AFM ${\mathrm{KAgF}}_3$ presents distinct altermagnetic responses, including: (i) prominent anomalous transport effects, such as anomalous Hall conductivity (AHC), anomalous Nernst conductivity, and thermal anomalous Hall conductivity (TAHC); and (ii) strong magneto-optical responses, manifested through pronounced Kerr and Faraday effects. On the other hand, ${\mathrm{K}}_2{\mathrm{AgF}}_4$ behaves as a conventional collinear antiferromagnet preserving $\mathcal{PT}$ symmetry, hence precluding the emergence of an anomalous Hall response.

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• Density of states
• Electronic structure
• Fermi surface
• Magnetism
• Magneto-optics
• Altermagnets
• Insulators
• Discrete symmetries in condensed matter
• First-principles calculations
• Symmetries in condensed matter