Abstract
We calculate the interlayer exchange coupling in (111) $\mathrm{Co}/\mathrm{Cu}/\mathrm{Co}$ trilayers with tight-binding band structures in two independent ways: a full-band calculation and an approximate calculation in terms of reflection amplitudes. An analytic Green's function method is used for the full-band calculation. The calculation involves solving the Green's function analytically for each fixed in-plane wave vector $({\mathbf{k}}_{\ensuremath{\Vert}})$ and an accurate integration over ${\mathbf{k}}_{\ensuremath{\Vert}}$ with nonuniform sampling. In the approximate method, we calculate the spin-dependent reflection amplitudes, which are complex numbers due to the effects of evanescent waves, and their phase factors depend on both the energy and wave vector. In the approximate method, the integration over ${\mathbf{k}}_{\ensuremath{\Vert}}$ near the extremal points is carried out analytically with the stationary phase approximation and contributions for ${\mathbf{k}}_{\ensuremath{\Vert}}$ far away from the extremal points are ignored. The method describes well the overall behavior of the interlayer exchange coupling for thick spacers. However, for thin spacers we found that the stationary phase approximation gives poor results and the full-band calculation is needed for accurate estimate of the coupling strength.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
