David Colignon

GetDDM: An open framework for testing optimized Schwarz methods for time-harmonic wave problems☆

We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples for Helmholtz and Maxwell’s equations, is freely available online for further testing.

An open source domain decomposition solver for time-harmonic electromagnetic wave problems

We present a flexible finite element solver for testing optimized Schwarz domain decomposition techniques for the time-harmonic Maxwell equations. After a review of non-overlapping Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples, is available online for further testing.

Optical and magnetic properties of Fe2+ and Cr2+ in II–VI semiconductors: the Jahn-Teller effect

The 5 D terms of Fe 2+ and Cr 2+ in the tetrahedral potential at cation sites in II-VI compounds split into orbital doublet and triplet states. While in Cr 2+ the orbital triplet has lower energy than the doublet, the opposite is the case in Fe 2+ . Both ions have singlet ground states after the spin-orbit interaction is taken into account and, hence, both are Van Vleck paramagnets. The optical absorption spectra of Fe and Cr based materials differ and are explained on the basis of a dynamic Jahn-Teller effect in the former and a static one in the latter. These considerations permit us to explain the optical as well as the magnetic properties observed in these materials.

The effect of electron-phonon interaction in iron-doped III-V cubic semiconductors

A theoretical study of optical absorption and emission measurements of Fe2+ as a substitutional impurity in InP and GaP is presented. A new interpretation of the low-temperature absorption spectrum is proposed based on a weak Jahn-Teller interaction between the electronic excited states and a local gap mode of 5 symmetry. The model also includes the crystal potential, hybridization with the orbitals of the ligands of the host crystal, spin-orbit interaction and a weak dynamic Jahn-Teller coupling of the orbital ground state of Fe2+ with transverse acoustic phonons of 3 symmetry. The theoretical model describes with good accuracy the measured positions and relative intensities of the spectral lines. In addition, the mass dependence of the local gap mode of 5 symmetry reproduces the general features of the fine structures associated with the isotopic shifts of the zero-phonon line and the contribution to the isotopic shifts arising from the difference in zero-point energy between the initial and final states of the transition is evaluated.

Isotope splitting of the zero-phonon line of Fe2+ in cubic III–V semiconductors

Abstract A theoretical study of the isotopic-mass dependence of the internal transitions of Fe2+ at a cation site in a cubic zinc-blende semiconductor is presented. The model used is based on crystal-field theory and includes the spin-orbit interaction and a weak dynamic Jahn-Teller coupling between the 5Φ5 excited manifold of Fe2+ and a local vibrational mode (LVM) of Φ5 symmetry. The mass dependence of the LVM frequency is described, in the harmonic approximation, within two different limits: the rigid-cage model and a molecular model. In the rigidcage model, the Fe2+ ion undergoes a displacement but the rest of the lattice is fixed. In this case, a simple M −1 2 dependence of the frequency is obtained and the Jahn-Teller energy, EJT, is independent of the mass. In the molecular model, the four nearest neighbors of the magnetic ion are allowed to move and the LVM then behaves as the Φ5 mode of a MX4 tetrahedral molecule leading to a more complicated dependence of the frequency on the isotopic mass and to a mass-dependence of EJT. The theoretical results obtained with these two models are compared with the observed isotopic shifts of the zero-phonon lines in InP:Fe and GaP:Fe corresponding to an optical transition between the vibronic Φ1 ground state and the lowest Φ5 state originating from the 5Φ5 excited orbital multiplet. A prediction of the isotopic shifts of the zero-phonon line in GaAs:Fe is also presented.