Eur. Phys. J. B 84, 29-35 (2011)
https://doi.org/10.1140/epjb/e2011-20348-x

Regular Article

A matrix method for the calculation of nonlocal exchange potential and spin-orbit coupling in the first-principles calculation method

Department of Physics, National Sun Yat-Sen University, 80424 Kaohsiung, Taiwan

^a e-mail: tsai@mail.phys.nsysu.edu.tw

Received: 6 May 2011
Received in final form: 17 August 2011
Published online: 3 November 2011

Abstract

Adequate treatment of exchange interaction and inclusion of spin-orbit coupling are important in obtaining reliable electronic structures of semiconductors and magnetic materials. Here, a matrix method has been derived to calculate nonlocal exchange potential and spin-orbit coupling within a muffin-tin-orbital based first-principles calculation method. Good agreement between calculated and experimental band gaps for various zinc-blende and wurtzite semiconductors demonstrated that direct calculation of nonlocal exchange potential is feasible. This method may be an improvement over the currently used LSDA  +  U or LSDA  +  GGA  +  U method, which uses an adjustable U parameter, for wide-band-gap semiconductors and magnetic materials. In this method, the use of an extended Hamiltonian matrix, which contains off-diagonal matrix elements between up- and down-spin states due to spin-orbit coupling, enables mutual adjustment of the occupation of up- and down-spin states through atomic orbitals. In contrast, in the conventional spin-polarized calculation method up- and down-spin sub-matrices are diagonalized separately. The calculated spin-orbit splitting for the triplet states at the Γ point for GaAs and ZnS are in good agreement with experimental data.