Influence of interdiffusion on the magnetic moments in $\mathrm{Co}∕\mathrm{Au}$ multilayers

The electronic and magnetic structures of a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer, as well as the corresponding Au $L_{2,3}$-edge x-ray magnetic dichroism (XMCD) spectra, are calculated for various degrees of interdiffusion at the $\mathrm{Co}∕\mathrm{Au}$ interface. The experimental Au $L_{2,3}$-edge XMCD signal [F. Wilhelm et al., Phys. Rev. B 69, 220404(R) (2004)] cannot be reproduced unless a considerable interdiffusion at the $\mathrm{Co}∕\mathrm{Au}$ interface is assumed. Interdiffusion enhances the induced magnetism of Au, and the magnitudes of spin and orbital magnetic moments of Au increase linearly with the number of Co neighbors. For Co, there is a competition between lattice dilatation, which enhances magnetism, and having Au as a neighbor, which suppresses magnetism of Co atoms. Low symmetry and inhomogeneity of the interface region cause the magnetic-dipole term $T_z$ and the number of holes in the $d$ band to have a significant influence on quantities related to the XMCD sum rules.

Figure 1

(Color online) Geometry of the ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer. Layers are represented by lines; numbers in between are interlayer spacings in Å. Only layers around the Au block are depicted. The labeling of layers is shown at the bottom. Concentration of Au atoms for various models of interdiffusion is written above the respective layers (interdiffusion at both $\mathrm{Co}∕\mathrm{Au}$ interfaces is always assumed).

Figure 2

(Color online) Theoretical and experimental Au $L_{2,3}$-edge XANES (upper panel) and XMCD (lower panel) of a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer. The experiment is taken from Wilhelm et al. (Ref. 3). Theoretical XANES and XMCD signals are presented for a perfect interface and for two models of interdiffusion. Additionally, XMCD calculated for an Au impurity in a Co host is also shown. Note that the XANES curves for interdiffusion within two layers and within four layers practically coincide.

Figure 3

(Color online) Magnetic moments for Au atoms (upper panels) and for Co atoms (lower panels) in a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer. The layer subscripts are defined in Fig. 1.

Figure 4

(Color online) Dependence of local magnetic moments in ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer on the number of neighbors of opposite chemical type. Upper panels show ${\mu }_{\text{spin}}^{\left(p\right)}$, ${\mu }_{\text{spin}}^{\left(d\right)}$, and ${\mu }_{\mathrm{orb}}^{\left(d\right)}$ for Au; lower panels show differences $\Delta {\mu }_{\text{spin}}^{\left(p\right)}$, $\Delta {\mu }_{\text{spin}}^{\left(d\right)}$, and $\Delta {\mu }_{\mathrm{orb}}^{\left(d\right)}$ between moments for Co in a proper ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer and a ${\mathrm{Co}}_{11}{\mathrm{Co}}_4$ auxiliary system. Values for single-atom impurities are also shown.

Figure 5

(Color online) Number of holes, $n_h^{\left(d\right)}$, and magnetic dipole moment $7T_z^{\left(d\right)}$ for Au atoms (upper panels) and for Co atoms (lower panels) in a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer for different models of interdiffusion.

Figure 6

(Color online) Ratios $({\mu }_{\text{spin}}^{\left(d\right)}+7T_z^{\left(d\right)})∕n_h^{\left(d\right)}$ and ${\mu }_{\text{spin}}^{\left(d\right)}∕n_h^{\left(d\right)}$ for Au atoms (upper panels) and Co atoms (lower panel) in a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer for difference models of interdiffusion.

Figure 7

(Color online) Ratios ${\mu }_{\mathrm{orb}}^{\left(d\right)}∕({\mu }_{\text{spin}}^{\left(d\right)}+7T_z^{\left(d\right)})$ and ${\mu }_{\mathrm{orb}}^{\left(d\right)}∕{\mu }_{\text{spin}}^{\left(d\right)}$ for Au atoms (upper panels) and for Co atoms (lower panels) in a ${\mathrm{Co}}_{11}{\mathrm{Au}}_4$ multilayer for different models of interdiffusion.