Probing the Rashba effect via the induced magnetization around a Kondo impurity

When a single magnetic adatom is deposited on a surface of a metal, it affects the charge and spin texture of the electron gas surrounding it. The screening of the local moment by conduction electrons gives rise to the Kondo effect. Here we investigate the effect of the Rashba spin-orbit coupling on the local magnetization density of states (LMDOS) around a Cobalt impurity on an Au(111) surface in a magnetic field. We show that the in-plane component of the LMDOS is exclusively associated with the Rashba spin-orbit interaction. This observation can be experimentally exploited to confirm the presence of the Rashba effect on surfaces, such as Au(111), by performing spin-polarized scanning tunneling microscopy measurements around the Kondo impurity.

Figure 1

Spatial distribution of the radial component ${\mathbf{M}}_r$ (left panel) and of the total LMDOS $\mathbf{M}$ (right panel) at energy $E=-2$ meV below the Fermi surface, and for a magnetic field $B=3$ T applied along the $z$th direction. The smaller (orange) spheres indicate the position of the Au atoms on the Au(111) surface, and the large (black) sphere represents the magnetic adatom. The arrows indicate the amplitude and direction of the LMDOS.

Figure 2

The normalized DOS for the Au(111) surface obtained within the TBA. The two insets show the singularities at the band tails due to the Rashba SO interaction.

Figure 3

The energy dependence of the spin-dependent spectral function ${\mathcal{A}}_{\sigma }\left(\omega \right)$ of the local orbital around the Fermi level, calculated within the NRG approach. The splitting of the Kondo resonance is due to the external magnetic field, $B=3$ T. The inset shows the full energy dependence of ${\mathcal{A}}_{\sigma }\left(\omega \right)$. The parameters for the Anderson model are $V=0.25$ eV, $U=2.85$ eV, and ${\varepsilon }_d=-0.84$ eV.

Figure 4

(a) The spatial distribution of the $z$th component of the LMDOS, $M_z$, around the Kondo impurity at energy $E=-2$ meV, below $E_F$ and (c) the corresponding cuts at different energies. The impurity is located at the center. The pattern formed around the magnetic impurity has a hexagonal symmetry and exhibits oscillations with distance from the impurity, with a period depending on the energy. The bright (dark) color corresponds to maximum (minimum) value of $M_z$. (b) $M_z$ as a function of energy and distance from the impurity along the $x$ direction, and (d) the energy dependence of $M_z\left(E\right)$ calculated at the impurity site and the two nearest-neighbor sites.

Figure 5

(a) The spatial distribution of the in-plane x component of the LMDOS, $M_x$, around the Kondo impurity at energy $E=-2$ meV, and (c) the corresponding cuts (in the $x$ direction) at different energies. (b) $M_r$ as a function of energy and distance from the impurity along the $x$ direction, and (d) the energy dependence of $M_r\left(\omega \right)$ calculated at the nearest and next-nearest neighbor sites.