Abstract
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…L–M-type exchanges in which the two metal ions do not share a common ligand. The latter can be further modified by d0 cations A such as V5+ and W6+ to bridge the L…L contact generating M–L…A…L–M-type exchanges. We describe several qualitative rules for predicting whether the M–L…L–M and M–L…A…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: α-CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu3(CO3)2(OH)2.
Highlights
An extended solid consisting of transition metal magnetic ions has closely packed energy states (Figure 1a,b) so that, at a given non-zero temperature, the ground state as well as a vast number of the excited states can be thermally occupied
Goodenough for his long and illustrious scientific career culminating with the Nobel Prize in 2019, we review what electronic factors govern the nature of the M–L–M, M–L . . . L–M and M–L . . . A . . . L–M
Α-CuV2 O6, LiCuVO4, and (CuCl)LaNb2 O7 were chosen to show that correct spin lattices can be readily predicted by the qualitative rules of Section 4.3, they have to be confirmed by performing the energy-mapping analyses
Summary
An extended solid consisting of transition metal magnetic ions has closely packed energy states (Figure 1a,b) so that, at a given non-zero temperature, the ground state as well as a vast number of the excited states can be thermally occupied. Each transition metal ion M is typically surrounded with main-group ligand atoms L to form an MLn polyhedron (n = 3–6), and each unpaired electron of MLn resides in a singly-occupied d-state (referred to as a magnetic orbital) of MLn , in which the d-orbital of M is combined out-of-phase with the p-orbitals of L. In this molecular orbital picture, the unpaired spin density is already delocalized from the d-orbital of M (the “magnetic orbital head”) to the p-orbitals of L (the “magnetic orbital tails”) [1,2,3].
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