Spin-polarized surface states close to adatoms on $\mathrm{Cu}\left(111\right)$

We present a theoretical study of surface states close to $3d$ transition-metal adatoms (Cr, Mn, Fe, Co, Ni, and Cu) on a $\mathrm{Cu}\left(111\right)$ surface in terms of an embedding technique using the fully relativistic Korringa-Kohn-Rostoker method. For each of the adatoms we found resonances in the $s$-like states to be attributed to a localization of the surface states in the presence of an impurity. We studied the change of the $s$-like densities of states in the vicinity of the surface-state band edge due to scattering effects mediated via the adatom’s $d$ orbitals. The results obtained clearly show that a magnetic impurity causes spin polarization of the surface states. In particular, the long-range oscillations of the spin-polarized $s$-like density of states around an Fe adatom are demonstrated.

Figure 1

Left panel: positions of maxima in the Bloch spectral functions near to the $\overline{\Gamma }$ point of the SBZ (dots). The solid line refers to a parabolic fit. It should be noted that only the first third of the SBZ is displayed $(\overline{K}\approx 0.65)$. Right panel: density of the surface states $(\mid k_{\Vert }\mid <0.15)$ close to a clean $\mathrm{Cu}\left(111\right)$ surface. The different values for the imaginary part of the energy used are displayed explicitly. The Fermi energy and the bottom of the surface-state band are indicated by a dashed and a dotted horizontal line, respectively.

Figure 2

Calculated spin-projected $s$-like density of states at the impurity positions. Insets: spin-projected total density of states of the adatoms. In each entry, the majority- and minority-spin DOS are depicted by dotted and solid lines, respectively.

Figure 3

Upper panel: calculated scalar-relativistic $d$-DOS of a single Cu impurity on a $\mathrm{Cu}\left(111\right)$ surface as partitioned into $d_{xz}$-, $d_{yz}$-, $d_{xy}$-, $d_{z^2}$-, and $d_{x^2-y^2}$-like contributions. Lower panel: relativistic (dash-dotted line) and scalar-relativistic $s$-DOS (see text) at the same site. The DOS presented in this figure are normalized to one spin projection.

Figure 4

Calculated minority-spin (upper panel) and majority-spin (lower panel) $s$-DOS at a site in the same plane as a single Fe impurity on a $\mathrm{Cu}\left(111\right)$ surface with respect to the distance between these two sites. The distance (in units of the two-dimensional lattice constant) is indicated in the legend of the lower panel.

Figure 5

Calculated minority-spin (solid line) and majority-spin (dotted line) $s$-DOS at $E-E_F=0.012$ Ry of a site positioned in the same plane but at a certain distance from a single Fe impurity on a $\mathrm{Cu}\left(111\right)$ surface. Inset: $s$-like magnetization density of states (MDOS).