| By combining density functional theory and linear response theory, the normal mode frequencies of lattice vibration---phonons---are calculated from first-principles. Corresponding to the original Kohn-Sham equation with an external perturbation, the perturbed Kohn-Sham equation is solved self-consistently to give the variations in the density and the effective potential to linear order of the external perturbation. From these results, the dynamical matrices are calculated, and the phonon frequencies are obtained through direct diagonalization of the dynamical matrix.; This so-called density functional perturbation theory (DFPT) is implemented by using the highly precise full-potential linearized augmented plane wave (FLAPW) method within the local density approximation (LDA). To show the effectiveness and accuracy of the method, we calculated the phonon frequencies of simple metals, Al, Li and Pb, and transition metals, Cu and Ni, both at the LDA lattice constant and at the experimental one, and obtained good agreement with available experiments in both cases. It is found that the frequencies calculated with the LDA lattice constants are always higher than the ones at the experimental lattice constant because the LDA lattice constants are smaller than the experimental ones.; As an innovative and complex application, the effect of magnetism on the phonon frequency was determined by calculating the phonon dispersion of Ni as a function of its magnetic moment. To this end, we combined the DFPT and the fixed spin moment (FSM) calculation methods, and calculated the phonon frequencies at mu = 0.0, 0.3 and 1.0 muB, and also the optimal magnetic moment, muopt = 0.63 muB. The important findings are (i) the dispersions show an appreciable change as the magnetic moment varies for Ni, (ii) the frequency difference, nu(mu) - nu(mu opt), shows a consistent behavior: the frequencies near the zone center with smaller and larger magnetic moment than muopt are smaller and larger than nu(muopt), respectively, whereas the situation reverses as the zone boundary is approached. Calculations of the electronic polarizability which describes the screening of an external perturbation by the electrons show that the magnetic dependence of the phonon frequency comes from the spin-dependent screening of the electrons. |
