Verification of first-principles codes: comparison of total energies, phonon frequencies, electron-phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo

With the ever-increasing sophistication of codes, the verification of the implementation of advanced theoretical formalisms becomes critical. In particular, cross comparison between different codes provides a strong hint in favor of the correctness of the implementations, and a measure of the (hopefully small) possible numerical differences. We lead a rigorous and careful study of the quantities that enter in the calculation of the zero-point motion renormalization of the direct band gap of diamond due to electron-phonon coupling, starting from the total energy, and going through the computation of phonon frequencies and electron-phonon matrix elements. We rely on two independent implementations : Quantum Espresso + Yambo and ABINIT. We provide the order of magnitude of the numerical discrepancies between the codes, that are present for the different quantities: less than $10^{-5}$ Hartree per atom on the total energy (-5.722 Ha/at), less than 0.07 cm$^{-1}$ on the $Gamma,L,X$ phonon frequencies (555 to 1330 cm$^{-1}$), less than 0.5% on the square of the electron-phonon matrix elements and less than 4 meV on the zero-point motion renormalization of each eigenenergies (44 to 264 meV). Within our approximations, the DFT converged direct band gap renormalization in diamond due to the electron-phonon coupling is -0.409 eV (reduction of the band gap).

High coercivity induced by mechanical milling in cobalt ferrite powders

In this work we report a study of the magnetic behavior of ferrimagnetic oxide CoFe2O4 treated by mechanical milling with different grinding balls. The cobalt ferrite nanoparticles were prepared using a simple hydrothermal method and annealed at 500oC. The non-milled sample presented coercivity of about 1.9 kOe, saturation magnetization of 69.5 emu/g, and a remanence ratio of 0.42. After milling, two samples attained coercivity of 4.2 and 4.1 kOe, and saturation magnetization of 67.0 and 71.4 emu/g respectively. The remanence ratio MR/MS for these samples increase to 0.49 and 0.51, respectively. To investigate the influence of the microstructure on the magnetic behavior of these samples, we used X-ray powder diffraction (XPD), transmission electron microscopy (TEM), and vibrating sample magnetometry (VSM). The XPD analysis by the Williamson-Hall plot was used to estimate the average crystallite size and strain induced by mechanical milling in the samples.