3 "Ab-initio" modeling of bulk Co and its interfaces

The "ab-initio" calculations presented in this thesis are based on the fully relativistic Screened Korringa-Kohn-Rostoker (SKKR) Green's function method [86]. Within this method the spin-polarization and the relativistic effects are treated on equal theoretical footing by solving the Kohn-Sham-Dirac equation. We used the local spin-density approximation (LSDA) for the exchange-correlation term and the effective potential and field were treated within the atomic sphere approximation (ASA), with an angular momentun cutoff of $l=2$.

In ASA the effective potential is of a muffin-tin type, surrounding each atom there is a sphere of radius $S_{MT}$ outside of which the potential has a value equal to a constant, and within the sphere the potential is assumed to be spherically symmetric leaving only a radial dependence of the potential. Within ASA , the effective potential $V_{eff}$, at one atomic site can be written as:

$$V_{eff}\approx V_{MT}=\Bigl\{\begin{array}{cccc} v(r) & r & \leq & S_{MT} \ V_{MTZ} & r & > & S_{MT}, \end{array}$$ (93)

here $V_{MT}$ is the Muffin-Tin potential, where $V_{MTZ}$ is the muffin-tin zero potential, which is defined as the value of the muffin-tin potential at a distance $S_{MT}$ ( $V_{MTZ}=v(r=S_{MT})$) and $v(r)$ is the spherical potential inside the muffin-tin sphere.

Henceforth we will apply a spin-polarized relativistic version of the screened Korringa-Kohn-Rostoker Green's function method to calculate the magnetic properties: spin and orbital moments, exchange constants, and magnetocrystalline anisotropy energy. Once reached this point, we would like to point out some issues, which will be important throughout this chapter:

• The system simulated in "ab-initio" calculations presents a 2D periodicity.
• The Budapest-Vienna Code, can provide layered resolve spin and orbital magnetic moments, exchange parameters and magneto-crystalline energy.
• The Budapest-Vienna Code has not implemented the option to evaluate the structural relaxation of the lattice in a self-consistent way. There are other codes like SIESTA which has implemented these possibilities.

The theoretical and computational details of the SKKR method used in our calculations can be found in the Weinberger book [155].

First we will discuss the results of a self-consistent calculation of the work function, the spin and orbital moments in the $Co/Ag$ layered system, after that we will analyze the results for the exchange interaction and the magneto-crystalline anisotropy (MCA) energy, obtained using the "magnetic force theorem". Finally we will study the magnetic behavior of a particular system $Co(111)\setminus Ag_{1}$ with the temperature.