EPR G-tensor
Electron Spin Resonance (EPR - also known as Electron Paramagnetic Resonance) is a powerful experimental probe of the structure of defects in solids. EPR spectra of spin ½ centers are made up of two contributions:
- the hyperfine parameters
- the g-tensor
The g-tensor arises from the interaction of the electronic spin with external magnetic field. This term plays a somewhat similar role to the shielding in NMR; induced electronic currents in the sample modify the g tensor from its vacuum value.
EPR spectrum can be modeled using the following effective Hamiltonian, bilinear in the total electron spin S, and the applied uniform magnetic field or nuclear spins, B and II, respectively:
where:
atomic units are used
α is the fine structure constant
the summation I runs over the nuclei
The tensors AI are the hyperfine parameters, and the tensor g is the EPR g-tensor.
The Gauge Including Projector Augmented Waves (GIPAW) approach has been used to compute g tensors in several crystalline materials including defects in α-quartz and zirconia.
The hyperfine tensor can be obtained from the ground state charge density. In CASTEP it is computed using the PAW approach of Van de Walle and Blöchl (1993). The calculation of the g-tensor is more involved, requiring the linear response currents. These are computed using the GIPAW approach of Pickard and Mauri (2001). The total g-tensor is obtained as:
Where the contributions to the total change in the g-tensor are the electron Zeeman kinetic energy, spin-orbit, and the spin-other-orbit correction. The calculation of these terms follows the approach of Pickard and Mauri (2002) extended for the use of ultrasoft potentials by Yates et al. (2007). The GIPAW approach has been used to compute g-tensors in several crystalline materials including defects in quartz and zirconia by Pietrucci et al. (2006).