First-principles scattering matrices for spin transport

TLDR

The paper presents an efficient first‑principles formalism for computing transmission and reflection matrices in layered materials. The method employs spin‑density functional theory with tight‑binding muffin‑tin orbitals, matching wave functions at lead–scattering region boundaries, and is demonstrated on Co/Cu multilayers and interfaces using large lateral supercells to model disorder. The approach scales linearly with the number of principal layers and as H²N (≈10⁶) for metallic systems, enabling efficient treatment of large supercells, and allows explicit channel decomposition of interface scattering for clean and disordered interfaces.

Abstract

Details are presented of an efficient formalism for calculating transmission and reflection matrices from first principles in layered materials. Within the framework of spin density functional theory and using tight-binding muffin-tin orbitals, scattering matrices are determined by matching the wave functions at the boundaries between leads which support well-defined scattering states, and the scattering region. The calculation scales linearly with the number of principal layers $N$ in the scattering region and as the cube of the number of atoms $H$ in the lateral supercell. For metallic systems for which the required Brillouin zone sampling decreases as $H$ increases, the final scaling goes as ${H}^{2}N$. In practice, the efficient basis set allows scattering regions for which ${H}^{2}N\ensuremath{\sim}{10}^{6}$ to be handled. The method is illustrated for $\mathrm{Co}∕\mathrm{Cu}$ multilayers and single interfaces using large lateral supercells (up to $20\ifmmode\times\else\texttimes\fi{}20$) to model interface disorder. Because the scattering states are explicitly found, ``channel decomposition'' of the interface scattering for clean and disordered interfaces can be performed.