Uniaxial Magnetism versus Jahn-Teller Instability

3 Uniaxial Magnetism versus Jahn-Teller Instability 

To examine the magnetic moment associated with the doublet 4 and 4, we consider if the doublet is split in energy under magnetic field H (see equation 24.2) [78]. The Zeeman interaction under magnetic field is given by 

If we take the z-axis along the linear C-Fe-C direction, the Zeeman interaction for the field along the z-direction, Hy, is written as 

This Hamiltonian gives rise to nonzero matrix element between two states with identical value. The Zeeman interaction for the field perpendicularto the z-direction, H , is written as 

Consequently, the magnetic moment is zero along all directions perpendicular to the z-axis and hence the linear C-Fe-C system with high-spin Fe ion is uniaxial. Theg-factors for the parallel and perpendicular directions are then given by 

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