Energy functional dependence of exchange coupling and magnetic properties of $\mathrm{Fe}∕\mathrm{Nb}$ multilayers

We present an ab initio calculation of the exchange coupling for $\mathrm{Fe}∕\mathrm{Nb}$ multilayers using the self-consistent full-potential linearized augmented plane-wave method. The exchange correlation potential has been treated in the local spin density approximation (LSDA) as well as generalized gradient approximation (GGA). We find that for the LSDA as well as the GGA the exchange coupling oscillates with a period of $6.0\mathrm{\AA }$ of Nb spacer thickness which is close to the experimental value in the pre-asymptotic region. This is also close to the earlier calculated period (i.e., $4.5\mathrm{\AA }$) by augmented spherical wave method. The LSDA shows antiferromagnetic coupling for 2 and $5\mathrm{Nb}$ monolayers but the GGA shows the ferromagnetic coupling for all Nb spacer layers. The period of oscillation is found to be in good agreement with the period calculated using the Ruderman-Kittel-Kasuya-Yosida and quantum well models. The magnetic moment of Fe is found to be higher in the GGA than the LSDA. Fe magnetic moment also shows strong oscillations as a function of the spacer layer thickness, in agreement with the experimental results. We find that the GGA results show better agreement with the experiment than the LSDA results.

Figure 1

Supercell used for $\mathrm{Fe}{\mathrm{Nb}}_4$ multilayer.

Figure 2

Interlayer exchange coupling, $J\left(\mathrm{meV}\right)$ for $\mathrm{Fe}{\mathrm{Nb}}_n$ multilayers as a function of $\mathbf{k}$ points in the IBZ for different number of Nb layers for (a) LSDA and (b) GGA. The calculated results are shown by filled squares, circles and stars.

Figure 3

Interlayer exchange coupling, $J\left(\mathrm{meV}\right)$ for $\mathrm{Fe}{\mathrm{Nb}}_n$ multilayers as a function of Nb spacer layer thickness (Å) for the LSDA and GGA.

Figure 4

Induced magnetic moment on Nb spacer layer in ferromagnetic $\mathrm{Fe}{\mathrm{Nb}}_7$ multilayer. The Fe atoms are placed at positions 0 and 8. The filled squares show the calculated results.

Figure 5

Magnetic moments on Fe atoms in $\mathrm{Fe}{\mathrm{Nb}}_n$ multilayers as a function of Nb spacer layers. The dots correspond to the GGA and filled squares to the LSDA results. The experimental results of Mattson et al. (see Ref. 13) are shown in the inset.

Figure 6

The top panel shows the partial density of states of spin-up and spin-down $d$ bands for ferromagnetic bulk Fe using the GGA. The bottom panel shows the partial density of states of spin-up and spin-down $d$ bands for Fe in ferromagnetic $\mathrm{Fe}∕{\mathrm{Nb}}_4$ system using the LSDA and GGA.

Figure 7

The top panel shows the partial density of states of spin-up and spin-down $d$ bands for Nb in ferromagnetic $\mathrm{Fe}∕{\mathrm{Nb}}_4$ system. Nb1 denotes the $d$-DOS at the interface while Nb2 denotes the $d$-DOS at the middle layer. The bottom panel shows the $d$-DOS for bulk Nb using the GGA.

Figure 8

Density of states of $s$ and $p$ states of Nb at Fermi level as a function of Nb spacer layer thickness.