Abstract: Using first-principles density functional theory calculations, we analyze the origin of the different crystal structures and optical and magnetic properties of two basic families of layered fluoride materials with the formula A2MF4 (M = Ag, Cu, Ni, and Mn; A = K, Cs, and Rb). On one hand, Cs2AgF4 and K2CuF4 compounds (both with d9 metal cations) crystallize in an orthorhombic structure with the Cmca space group and MA-F-MB bridge angle of 180°, and they exhibit a weak ferromagnetism (FM) in the layer plane. On the other hand, K2NiF4 or K2MnF4 compounds (with d8 and d5 metal cations, respectively) have a tetragonal I4/mmm space group with a 180° bridge angle and exhibit antiferromagnetism (AFM) in the layer plane. First, we show that, contrary to what is claimed in the literature, the Cmca structure of Cs2AgF4 and K2CuF4 is not related to a cooperative Jahn-Teller effect among elongated MF64- units. Instead, first-principles calculations carried out in the I4/mmm parent phase of these two compounds show that MF64- units are axially compressed because the electrostatic potential from the rest of the lattice ions forces the hole to lie in the 3z2-r2 molecular orbital (z being perpendicular to the layer plane). This fact increases the metal-ligand distance in the layer plane and makes that the covalency in the bridging ligand have a residual character (clearly smaller than in K2NiF4 or KNiF3) stabilizing for only a few meV (7.9 meV for Cs2AgF4), an AFM order. However, this I4/mmm parent phase of Cs2AgF4 is unstable, thus evolving toward the experimental Cmca structure with an energy gain of 140 meV, FM ordering, and orthorhombic MF64- units. As a salient feature, it is shown that the FM order in Cs2AgF4 and K2CuF4 is due to the asymmetry of the in-plane MA-F-MB bridge, giving rise to a negligible covalency for the long bond. Moreover, in K2NiF4 or K2MnF4, the lack of excited states within the dn manifold (n = 8 and 5) of M, which can be coupled to the ground state for a local b1g distortion mode, hampers the orthorhombic instability, thus favoring the AFM ordering. The present ideas also account for the experimental optical and EPR data of Cs2AgF4 and K2CuF4. An additional discussion on the silver compound Rb2AgF4 is also reported.

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