Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals

In this review on spin exchanges, written to provide guidelines useful for finding the spin lattice relevant for any given magnetic solid, we discuss how the values of spin exchanges in transition metal magnetic compounds are quantitatively determined from electronic structure calculations, which electronic factors control whether a spin exchange is antiferromagnetic or ferromagnetic, and how these factors are related to the geometrical parameters of the spin exchange path. In an extended solid containing transition metal magnetic ions, each metal ion M is surrounded with main-group ligands L to form an MLn polyhedron (typically, n = 3-6), and the unpaired spins of M are represented by the singly-occupied d-states (i.e., the magnetic orbitals) of MLn. Each magnetic orbital has the metal d-orbital combined out-of-phase with the ligand p-orbitals; therefore, the spin exchanges between adjacent metal ions M lead not only to the M-L-M-type exchanges, but also to the M-L horizontal ellipsis L-M-type exchanges in which the two metal ions do not share a common ligand. The latter can be further modified by d(0) cations A such as V5+ and W6+ to bridge the L horizontal ellipsis L contact generating M-L horizontal ellipsis A horizontal ellipsis L-M-type exchanges. We describe several qualitative rules for predicting whether the M-L horizontal ellipsis L-M and M-L horizontal ellipsis A horizontal ellipsis L-M-type exchanges are antiferromagnetic or ferromagnetic by analyzing how the ligand p-orbitals in their magnetic orbitals (the ligand p-orbital tails, for short) are arranged in the exchange paths. Finally, we illustrate how these rules work by analyzing the crystal structures and magnetic properties of four cuprates of current interest: alpha-CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu-3(CO3)(2)(OH)(2).

Automated summary

This review provides guidelines for finding the spin lattice relevant for any magnetic solid by discussing how spin exchanges in transition metal magnetic compounds are determined quantitatively, how electronic factors control the nature of spin exchanges, and how these factors relate to the geometrical parameters of the spin exchange path. Analyzing the arrangement of ligand p-orbitals in the exchange paths, qualitative rules are proposed for predicting whether the exchanges are antiferromagnetic or ferromagnetic.