Understanding the local structure, magnetism, and optical properties in layered compounds with d⁹ ions: insight into silver fluorides and K₂CuF₄

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.