Understanding the Local Structure, Magnetism, and Optical Properties in Layered Compounds with d⁹Ions: 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 MF6 4– units. Instead, first-principles calculations carried out in the I4/mmm parent phase of these two compounds show that MF6 4– units are axially compressed because the electrostatic potential from the rest of the lattice ions forces the hole to lie in the 3z 2–r 2 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 MF6 4– 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 d n 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.

Understanding Pressure Effects on Structural, Optical, and Magnetic Properties of CsMnF4 and Other 3dn Compounds

“…It is worth noting that, in CsMnF 4 , two adjacent MnF 6 3– units share a common ligand, a fact that is behind the instability developed in K 2 CuF 4 or Cs 2 AgF 4 , but not in K 2 ZnF 4 :Cu 2+ ,,, or even in KAlCuF 6 − where the CuF 6 4– units are well-separated. In addition, the parent phase of CsMnF 4 involves compressed MnF 6 3– units giving rise to softer bonds in the layer plane, a fact that also helps to develop the orthorhombic instability such as has previously been discussed. ,, …”

“…In K 2 CuF 4 and Cs 2 AgF 4 , the shift from AFM to FM ordering when R y – R x increases has proved to arise from deep changes in chemical bonding in the MF 6 4– units (M = Cu, Ag). Indeed, an increase of the orthorhombicity enhances the charge, q ( R X ), transferred to the closest ligands, placed at R X from the cation, at the expense of two ligands at R Y whose charge, q ( R Y ), is drastically reduced, being null at equilibrium . As the AFM contribution to the exchange constant depends on q ( R X ) × q ( R Y ), this fact favors the shift to a FM phase …”

“…Seeking to understand the origin of the local structure in CsMnF 4 , it is useful to analyze the evolution of the crystal structure when Mn 3+ is replaced by a cation like Fe 3+ with a similar ionic radius, giving rise to the so-called high-symmetry parent phase. ,,, Under strict octahedral symmetry, Fe 3+ in high-spin configuration ( S = 5/2) exhibits a nearly spherical electronic density which is however never found for a 3d 4 ion like Mn 3+ or a 3d 9 ion like Cu 2+ in the same situation. After the Mn 3+ → Fe 3+ substitution, we carried out a geometry optimization of the CsFeF 4 structure maintaining fixed the experimental P 4/ n space group of CsMnF 4 .…”

“…Finally, the present work also pays attention to the ferromagnetism displayed by CsMnF 4 at zero pressure, as well as the evolution of the magnetic order under an applied pressure. At this point, the recent results derived for insulating layered compounds like K 2 CuF 4 or Cs 2 AgF 4 shed light on that issue. ,, …”

Chemical Bonding, 10Dq Parameter and Superexchange in the Model Compound KNiF3

“…[33] To answer this key question requires to study in detail the chemical bonding in the dimer following the way used in the analysis of K 2 CuF 4 , K 2 NiF 4 and Cs 2 AgF 4 . [61] Work along this line is now in progress.…”