First-Principles Theory of the EPRgTensor in Solids: Defects in Quartz

Abstract

A theory for the reliable prediction of the EPR g tensor for paramagnetic defects in solids is presented. It is based on density functional theory and on the gauge including projector augmented wave approach to the calculation of all-electron magnetic response. The method is validated by comparison with existing quantum chemical and experimental data for a selection of diatomic radicals. We then perform the first prediction of EPR g tensors in the solid state and find the results to be in excellent agreement with experiment for the E 0 1 and substitutional phosphorus defect centers in quartz. DOI: 10.1103/PhysRevLett.88.086403 PACS numbers: 71.15. -m, 61.72.Bb, 76.30. -v Electron paramagnetic resonance (EPR), also known as electron spin resonance, is the most powerful spectroscopic technique for the study of paramagnetic defects in solids. Indeed, defect centers are often named directly after their EPR spectra. Applications of EPR extend to any situation where there are unpaired electrons, including the understanding of reactions involving free radicals in both biological and chemical contexts or the study of the structure and spin state of transition metal complexes.EPR spectra of spin 1͞2 centers are made up of two contributions: (i) the hyperfine parameters, which can be computed from the ground state spin density, and have been used to connect theoretical studies of defects to available experimental data [1 -6], and (ii) the g tensor. Only recently have there been attempts to calculate the g tensor in molecules from first principles using density functional theory (DFT) [7,8]. However, these approaches are valid only for finite systems and, thus, are not useful for the calculation of the g tensor for paramagnetic defects in solids, except possibly within a cluster approximation. In the absence of a predictive scheme, experimentally determined g tensors are, of necessity, interpreted in terms of their symmetry alone, leaving any remaining information unexploited. A reliable, first-principles approach to the prediction of g tensors in solids, in combination with structural and energetic calculations, would access this information, and could be used for an unequivocal discrimination between competing microscopic models proposed for defect centers. In this Letter we describe an approach for the calculation of the g tensor in extended systems, using periodic boundary conditions and supercells.In a previous paper [9] we have shown how to compute the all-electron magnetic linear response, in finite and extended systems, using DFT and pseudopotentials. To achieve this we introduced the gauge including projector augmented wave (GIPAW) method, which is an extension of Blöchl's projector augmented wave (PAW) method [10]. In Ref.[9], we used GIPAW to compute the NMR chemical shifts in molecules and solids. Here we apply the GIPAW approach to the first-principles prediction of EPR g tensors for paramagnetic defects in solids. We validate our theory and implementation for diatomic radicals, for which both all-electron...

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…In the GIPAW implementation in the Quantum-Espresso package, a mean-field approximation to the many-body Hamiltonian is made and as a result, the spin-orbit and spin-other-orbit operators are represented as a sum of one-electron terms, according to Ref. 47. Hybrid functionals were not used as the calculation of the g-tensor via the linear response method is not currently supported with these.…”

“…For these calculations, the PBE exchange functional was chosen [54]. Scalar-relativistic norm-conserving pseudopotentials with nonlinear core correction were used, and the all-electron information was reconstructed using PAW and gauge-including projector augmented-wave (GIPAW) [46,47]. A plane wave cutoff energy of 900 eV was chosen, yielding an energy convergence to within 6 meV per atom.…”

“…In the current DFT approach, the g-tensor for a material containing multiple paramagnetic centres is calculated by linear response [46,47], which results in a single overall g-tensor for the cell. The contribution to the gtensor from a particular TM site can be calculated by replacing the other TM sites in the cell with diamagnetic atoms.…”

Magnetic linear response properties calculations with the Gaussian and augmented-plane-wave method

“…[54]). To our knowledge, the g tensor of this defect has been calculated only once [16], using the GIPAW g-tensor method. However, the (periodic) simulation cell that was used included only 71 atoms (24 silicon atoms and 47 oxygen atoms), while the real E 1 center in nature has quite a long (up to 4-5 SiO 2 shells) defect geometry propagation, causing the structure to be somewhat biased by the periodic replica.…”

“…To this purpose, it is necessary to extend the concepts of the GAPW representation of the electronic density to the current density induced by the external magnetic field. To our knowledge, the gauge-including projector augmented wave (GIPAW) method [16,17] is the only other AE method (using a frozen-core approach) currently able to calculate these quantities for condensed phase systems using periodic boundary conditions (PBC).…”