Abstract
In earlier work, we previously established a formalism that allows to express the exchange energy J vs. fundamental molecular integrals without crystal field, for a fragment A–X–B, where A and B are 3d1 ions and X is a closed-shell diamagnetic ligand. In this article, we recall this formalism and give a physical interpretation: we may rigorously predict the ferromagnetic (J < 0) or antiferromagnetic (J > 0) character of the isotropic (Heisenberg) spin-spin exchange coupling. We generalize our results to ndm ions (3 ≤ n ≤ 5, 1 ≤ m ≤ 10). By introducing a crystal field we show that, starting from an isotropic (Heisenberg) exchange coupling when there is no crystal field, the appearance of a crystal field induces an anisotropy of exchange coupling, thus leading to a z-z (Ising-like) coupling or a x-y one. Finally, we discuss the effects of a weak crystal field magnitude (3d ions) compared to a stronger (4d ions) and even stronger one (5d ions). In the last step, we are then able to write the corresponding Hamiltonian exchange as a spin-spin one.
Highlights
It was necessary to wait until the end of the 1950s to achieve a good understanding of superexchange interactions, when Anderson first proposed the theory of coupling between identical ions, characterized by a 3dm electronic configuration without orbital degeneracy (m = 1) [1,2], later generalized to m > 1
We have proposed a first generalization of the various mechanisms involved in superexchange for identical 3d1 ions: the exchange energy constant J has been expressed vs
J is expressed vs. fundamental molecular integrals in the absence of a crystal field, uniquely, for the sake of simplicity; we show that the introduction of a crystal field may be achieved very allowing us to discuss further the notion of anisotropic couplings; For the first time, we may rigorously predict the ferromagnetic (J < 0) or antiferromagnetic (J > 0) character of spin-spin couplings whereas, so far, we have dealt with empirical rules, i.e., the Goodenough–Kanamori rules published between the middle of the 1950s and the beginning of the 1960s [11,12,13,14]
Summary
When considering lattices composed of transition ions, there is a more or less important effect coming from the electrostatic potential due to the ionic environment: this effect is well known as that of the “crystal field”. These findings allow us to directly lead to the determination of adequate orbitals describing the ion’s magnetic properties. Hund’s rules allow the determination of the orbital and spin momenta characterizing the ion’s ground state These rules try to explain how Coulomb repulsion and. When considering the formal coupling of two spins, each one belonging to a magnetic center, one can speak about direct exchange If these ions are isolated, we deal with an isotropic (Heisenberg) coupling. In a first step, we exclusively consider the “toy model” of two magnetic centers, A and B, i.e., two transition ions, 3d1 , characterized by a single spin, 12 , and coupled through a diamagnetic ligand X without a crystal field. We consider a situation in which there is no crystal field and one for which a crystal field is introduced
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
