Altermagnetism and anomalous transport in the Ag 2 + fluorides KAgF 3 and K 2 AgF 4

Compounds containing 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 Ruels. Our first-principles calculations reveal that the ground state of KAgF$_3$ exhibits collinear A-type antiferromagnetic (A-AFM) ordering accompanied by C-type orbital ordering. In contrast, K$_2$AgF$_4$ adopts a collinear intralayer antiferromagnetic configuration coupled with ferromagnetic orbital ordering. The A-AFM KAgF$_3$ presents distinct altermagnetic responses, including: (i) prominent anomalous transport effects, such as anomalous Hall conductivity (AHC), anomalous Nernst conductivity (ANC), and thermal anomalous Hall conductivity (TAHC); and (ii) strong magneto-optical responses, manifested through pronounced Kerr and Faraday effects. On the other hand, K$_2$AgF$_4$ behaves as a conventional collinear antiferromagnet preserving $\mathcal{PT}$ symmetry, hence precluding the emergence of an anomalous Hall response.