Super exchange
Super exchange results in an indirect, antiferromagnetic spin coupling ( exchange interaction ) of magnetic moments in a substance.
The coupling takes place via a mediating, diamagnetic particle (e.g. ligand ). Here, the spin inducing an occupied metal orbitals (usually a d-orbital) a spin polarization in a fully occupied, adjacent atomic orbital (usually a p-orbital) of the ligand. According to the Pauli prohibition, the spins in this neighboring orbital must have an anti-parallel arrangement, which leads to an anti-parallel coupling of the spins in another neighboring metal atom and thus to an anti-ferromagnetic (partial) order .
The superexchange is only effective with an (approximately) linear arrangement (~ "180 ° superexchange"), because if the deviation from linearity is too great, it is no longer one, but several, but magnetically independent mediating orbitals.
The name was coined in 1934 by Hendrik Anthony Kramers and deepened in 1950 by the winner of the Nobel Prize in Physics Philip Warren Anderson . These authors have not only described the mechanism, but also indicated typical applications.
Examples
Examples are oxides that crystallize in the NaCl type (antiferromagnetic, see fig.) Or spinels ( ferrimagnetic ).
Quantum mechanical perturbation calculation yields the energy operator for the antiferromagnetic interaction of the spins on neighboring positions 1 or 2 of manganese atoms in the crystal lattice of manganese (II) oxide :
in which
- is the hopping energy between Mn and oxygen atoms,
- U the Hubbard energy characteristic of manganese and
- the scalar product of the spin vectors in the Heisenberg model .
The super-exchange is responsible for the fact that with manganese chalcogens (MnO, MnS, MnSe) an increase in the Néel temperature can be observed with increasing atomic number . This is due to the fact that the p orbitals of the heavier chalcogens increase in size, thus ensuring a better overlap with the metal orbitals; this increases the hopping energy.