Chapter 6
Magnetism and Conduction
Abstract After the description of the electron hopping in systems where not all
the magnetic centers have the same number of unpaired electrons, a short account
is given of the double exchange mechanism in mixed-valence systems. Although
this phenomenon can certainly be found in transition metal complexes, it is more
common to happen in doped systems in the solid state. Therefore, the second part
of this chapter introduces the basics of the quantum chemical approach to magnetic
interactions in extended systems. The embedded cluster approach will be contrasted
against band structure calculations. Thereafter, some concepts will be introduced that
are widely used in the condensed matter physics community. We do not give a full
description of all the magnetic phenomena in solid state compounds but rather help
the reader with a quantum chemical background to find its way in the rich literature
on this topic.
6.1 Electron Hopping
In all the magnetic systems described so far the number of magnetic orbitals was equal
to the number of unpaired electrons. These systems are generally known as half-filled
systems and the price (in terms of energy) to move an electron from one site to another
is proportional to the on-site repulsion parameter U. Since this parameter is in general
huge in comparison to the magnetic interactions, the electrons are considered to be
immobile or in other words, trapped on the magnetic sites. The situation changes
drastically when the number of electrons in the magnetic orbitals is no longer equal
to the number of magnetic orbitals, that is when the system is doped with electrons
(more electrons than magnetic orbitals) or doped with holes (less electrons than
magnetic orbitals). In these systems, the electron is no longer necessarily trapped and
can move from site to site under certain circumstances that will be described below.
A commonly used classification of magnetic compounds by the degree of electron
mobility was given by Robin and Day [1], who divided the so-called mixed valence
compounds into three groups. Class I contains all the compounds where the magnetic
centers have different oxidation states but the electrons are nevertheless trapped. Class
III is quite the opposite; the magnetic centers have formally a distinct oxidation state
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5_6
177
Magnetism and Conduction
Abstract After the description of the electron hopping in systems where not all
the magnetic centers have the same number of unpaired electrons, a short account
is given of the double exchange mechanism in mixed-valence systems. Although
this phenomenon can certainly be found in transition metal complexes, it is more
common to happen in doped systems in the solid state. Therefore, the second part
of this chapter introduces the basics of the quantum chemical approach to magnetic
interactions in extended systems. The embedded cluster approach will be contrasted
against band structure calculations. Thereafter, some concepts will be introduced that
are widely used in the condensed matter physics community. We do not give a full
description of all the magnetic phenomena in solid state compounds but rather help
the reader with a quantum chemical background to find its way in the rich literature
on this topic.
6.1 Electron Hopping
In all the magnetic systems described so far the number of magnetic orbitals was equal
to the number of unpaired electrons. These systems are generally known as half-filled
systems and the price (in terms of energy) to move an electron from one site to another
is proportional to the on-site repulsion parameter U. Since this parameter is in general
huge in comparison to the magnetic interactions, the electrons are considered to be
immobile or in other words, trapped on the magnetic sites. The situation changes
drastically when the number of electrons in the magnetic orbitals is no longer equal
to the number of magnetic orbitals, that is when the system is doped with electrons
(more electrons than magnetic orbitals) or doped with holes (less electrons than
magnetic orbitals). In these systems, the electron is no longer necessarily trapped and
can move from site to site under certain circumstances that will be described below.
A commonly used classification of magnetic compounds by the degree of electron
mobility was given by Robin and Day [1], who divided the so-called mixed valence
compounds into three groups. Class I contains all the compounds where the magnetic
centers have different oxidation states but the electrons are nevertheless trapped. Class
III is quite the opposite; the magnetic centers have formally a distinct oxidation state
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5_6
177