Altermagnetism and Anomalous Transport in Ag$^{2+}$ Fluorides: KAgF$_3$ and K$_2$AgF$_4$

TL;DR

This work addresses how altermagnetism can arise in AgF-based compounds with Ag in a $4d^{9}$ configuration and Jahn–Teller–driven orbital order. Using first-principles GGA+$U$ calculations on KAgF3 and K2AgF4, along with a Heisenberg mapping to extract $J_{ab}$ and $J_c$ and Kubo-formula based transport calculations, the authors connect orbital patterns to magnetic ground states and anomalous transport. They find KAgF3 as an altermagnet with A-AFM and C-type orbital order that breaks $ ext{PT}$ symmetry, yielding nonzero Berry curvature and sizeable anomalous Hall (AHE), Nernst (ANC), and thermal Hall (TAHC) effects, as well as pronounced Kerr and Faraday responses. In contrast, K2AgF4 preserves $ ext{PT}$ symmetry and shows vanishing AHE, with a highly anisotropic but conventional optical response, underscoring the role of symmetry and Jahn–Teller distortions in governing altermagnetic phenomena and optics in Ag-based fluorides.

Abstract

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.

Figures (9)

• Figure 1: (a) The crystal structure of KAgF$_3$, we defined the x, y, z axes as the [1$\bar{1}$0], [110], and [001] directions of the unit cell respectively. (b) The FM, A-AF, C-AF, and G-AF magnetic configurations. (c) The crystal structure of K$_2$AgF$_4$. (d) The FM, AFM1, AFM2 magnetic configurations.
• Figure 2: (a) The total density states of KAgF$_3$ and the projected density states of Ag-e$_{g}$ orbital (b) , Ag-t$_{2g}$ orbital (c) and F-2p (d).
• Figure 3: (a) The total energies (relative to the NM state) and (b) magnetic moments of different spin configurations in KAgF$_{3}$. (c) The calculated exchange interactions for KAgF3 at temperatures of 2 K and 250 K.
• Figure 4: The PDOS of Ag$_{1}$(a), Ag$_{2}$(b), Ag$_{3}$(c) and the optical conductivity (d) of KAgF$_{3}$ calculated with GGA+U (U$_{\text{eff}}$ = 4.0 eV) method. $a_{xx}$ denotes the optical conductivity within the $ab$-plane, while $a_{zz}$ represents the optical conductivity along the $c$-axis. The line and arrow indicate the charge transition.
• Figure 5: (a) The charge density of both spin-up and spin-down states in the range of -1.4 eV to 0.0 eV (E$_{f}$) for A-AFM. (b) The charge density of the unoccupied state in the range of 0.0 eV to 2.0 eV, with spin-up in yellow and spin-down in green. (c) The contours of the charge density on the (100) plane.