EPR Overview

In crystalline materials, electron paramagnetic resonance (EPR) can be used to study paramagnetic defects. EPR spectra of spin ½ centers have two contributions: the hyperfine tensor ${\bf A}$ and the g-tensor ${\bf g}$, which are defined through the following effective Hamiltonian \begin{equation} H_{eff}=\frac{\alpha}{2}{\bf S}\cdot{\bf g}\cdot{\bf B} + \sum_I {\bf S}\cdot{\bf A}_{I}\cdot{\bf I}_I \end{equation} where $\alpha$ is the fine structure constant and the summation $I$ runs over nuclei. The hyperfine tensor arises from the interaction of the nuclei with the ground-state spin density. This term has been calculated within the planewave-pseudopotential approach; indeed it was for this property that the PAW scheme was first introduced.\cite{walle93} The g-tensor arises from the interaction of the electronic spin with the external magnetic field. This term plays an somewhat similar role to the shielding in NMR; induced electronic currents in the sample modify the g-tensor from its vacuum value. The GIPAW approach has been used to compute g-tensors in several crystalline materials including defects in $\alpha$-quartz and zirconia.