Spin-Flip and Element-Sensitive Electron Scattering in the ${\mathrm{BiAg}}_2$ Surface Alloy

Heavy metal surface alloys represent model systems to study the correlation between electron scattering, spin-orbit interaction, and atomic structure. Here, we investigate the electron scattering from the atomic steps of monolayer ${\mathrm{BiAg}}_2$ on Ag(111) using quasiparticle interference measurements and density functional theory. We find that intraband transitions between states of opposite spin projection can occur via a spin-flip backward scattering mechanism driven by the spin-orbit interaction. The spin-flip scattering amplitude depends on the chemical composition of the steps, leading to total confinement for pure Bi step edges, and considerable leakage for mixed Bi-Ag step edges. Additionally, the different localization of the occupied and unoccupied surface bands at Ag and Bi sites leads to a spatial shift of the scattering potential barrier at pure Bi step edges.

Figure 1

(a) Monoatomic steps perpendicular to the $\mathrm{\Gamma }M$ ($A$) and $\mathrm{\Gamma }K$ ($B$) directions. The atomically resolved image (bottom) shows the Bi sites as protrusions. Set point: $I=0.59\mathrm{nA}$, $V_b=1000\mathrm{mV}$ (top) and 28 mV (bottom). (b) Atomic structure of the different step edges derived from the images in (a). Bi atoms of the lower (upper) terrace correspond to orange (brown) circles, and Ag atoms to white (grey) circles, respectively.

Figure 2

Electron scattering from $A$ steps. (a) $dI/dV$ spectra acquired along a line crossing several steps (topography and line profile shown on top). Set point: $I=1.6\mathrm{nA}$, $V_b=-2.0\mathrm{V}$. (b) Fourier transform of the $dI/dV$ spectra along the $x$ axis acquired on the left and right terraces. The scattering vectors $q$ for the $D_1$ and $D_2$ branches are indicated as open red circles. (c) Comparison of the experimental scattering vectors and calculated band structure. The color and size of the points in the band structure correspond to the sign and magnitude of the spin polarization in the ${\mathbf{k}}_{\parallel }\times \mathbf{z}$ direction, respectively.

Figure 3

(a) Dispersion and spin polarization for a selected branch of the unoccupied bands. (b) Spin density of the state marked by an arrow in (a). The cutting plane is chosen through the Bi atom, in the center of the unit cell. (c) Orbital-resolved band structure along $\mathrm{\Gamma }K$. The size of the symbols indicates the Bi $p_z$ (left), $p_x$ (middle), and $p_y$ (right) contribution to the state. Opposite spin directions are shown by full and empty symbols. Similar results are obtained for the $\mathrm{\Gamma }M$ direction.

Figure 4

(a) $dI/dV(x)$ for the $N=2$ resonance of the unoccupied (closed symbols) and occupied band (open symbols) for resonators of the two step types ($L=70\AA$ for $A$ type, and 75 Å for $B$ type). The fit of the unoccupied state with Fabry-Pérot resonances is shown for free ${\varphi }_{l,r}$ (solid line) and fixed ${\varphi }_{l,r}=-\pi$ (dashed line) [21]. The center of the terrace ($x_c$) and step edges are indicated by black and green vertical dashed lines, respectively. The step direction, atomic arrangement, and potential barriers are sketched on top. (b) $\mathrm{DOS}(z)$ integrated over the $z=\text{constant}$ plane parallel to the surface for the two surface states, calculated using the method of Ref. [30].