Co monolayers and adatoms on Pd(100), Pd(111), and Pd(110): Anisotropy of magnetic properties

We investigate to what extent the magnetic properties of deposited nanostructures can be influenced by selecting as a support different surfaces of the same substrate material. Fully relativistic ab initio calculations were performed for Co monolayers and adatoms on Pd(100), Pd(111), and Pd(110) surfaces. Changing the crystallographic orientation of the surface has a moderate effect on the spin magnetic moment, a larger effect on the orbital magnetic moment, but sometimes a dramatic effect on the magnetocrystalline anisotropy energy and on the magnetic dipole term $T_{\alpha }$. The dependence of $T_{\alpha }$ on the magnetization direction $\alpha$ can lead to a strong apparent anisotropy of the spin magnetic moment as deduced from the x-ray magnetic circular dichroism sum rules. For systems in which the spin-orbit coupling is not very strong, the $T_{\alpha }$ term can be understood as arising from the differences between components of the spin magnetic moment associated with different magnetic quantum numbers $m$.

Figure 1

Structure diagrams for a Co monolayer on Pd(100), Pd(111) and Pd(110). The blue and yellow circles represent the Co and Pd atoms, respectively. The orientation of the $x$ and $y$ coordinates used throughout this paper is also shown.

Figure 2

Dependence of the MAE for Co monolayers and adatoms on the difference of orbital magnetic moments for respective magnetization directions. The dashed line represents Bruno's formula in Eq. (3).

Figure 3

Spin-polarized DOS for Co monolayers and adatoms on Pd surfaces (in states per eV). Full lines represent DOS related to Co atoms, dashed lines represent DOS related to Pd atoms which are nearest neighbors to Co atoms, dotted lines represent DOS for bulk Pd.

Figure 4

Dependence of the MAE on the position of the top of the valence band. For systems on Pd(110), the anisotropy energies $E^{\left(x\right)}-E^{\left(z\right)}$ and $E^{\left(y\right)}-E^{\left(z\right)}$ are investigated separately. The left panel is for monolayers, the right panel is for adatoms. The meaning of the lines is the same for both panels (see the legend).

Figure 5

Difference between total energies for in-plane and out-of-plane magnetization for a Co adatom on Pd (100), (111), and (110) surfaces (optimized geometry). Points are results of the calculation, dashed lines are sinusoidal fits. The orientation of the $x$ and $y$ axes is as in Fig. 1.

Figure 6

Sum of the spin magnetic moments at the Co adatom and at those substrate Pd atoms which are enclosed in hemispherical zones of the given radii, for four embedded cluster sizes (identified by numbers of Pd atoms contained in them).

Figure 7

The MAE of a Co adatom in an hcp position on Pd(111) for different sizes of the embedded clusters.