Simulation of spin-polarized scanning tunneling spectroscopy on complex magnetic surfaces: Case of a Cr monolayer on Ag(111)

We propose a computationally efficient atom-superposition-based method for simulating spin-polarized scanning tunneling spectroscopy (SP-STS) on complex magnetic surfaces based on the sample and tip electronic structures obtained from first principles. We go beyond the commonly used local density of states (LDOS) approximation for the differential conductance $dI/dV$. The capabilities of our approach are illustrated for a Cr monolayer on a Ag(111) surface in a noncollinear magnetic state. We find evidence that the simulated tunneling spectra and magnetic asymmetries are sensitive to the tip electronic structure, and we analyze the contributing terms. Related to SP-STS experiments, we show a way to simulate two-dimensional differential conductance maps and qualitatively correct effective spin-polarization maps on a constant current contour above a magnetic surface.

Figure 1

Projected charge and magnetization DOS of the surface Cr atom of the sample Cr/Ag(111), the tip apex Cr atom of the Cr/Fe(001) tip,[22] and the flat tip.

Figure 2

Comparison of single point differential conductance tunneling spectra calculated from numerical differentiation of the tunneling current $I\left(V\right)$, and $dI/dV$ calculated according to Eq. (16), and its contributing terms, the virtual differential conductance $dI/dU(V,V)$, the background term $B\left(V\right)$, and the tip-derivative term $D_T\left(V\right)$. The model CrFe tip apex is 3.5 Å above a surface Cr atom and its magnetization direction is parallel to that of the underlying surface Cr atom. The inset shows the ratio of $B\left(V\right)/I\left(V\right)$.

Figure 3

Comparison of simulated single point differential conductance tunneling spectra following Eq. (16), probed with the flat magnetic tip and the model CrFe tip, 3.5 Å above a surface Cr atom. Parallel (P) and antiparallel (AP) tip magnetization directions are set relative to the underneath surface Cr atom. For the flat magnetic tip, two different vacuum decays, $\kappa \left(U\right)$ and $\kappa (U,V)$ are assumed using Eqs. (12) and (9), respectively. The vertical dotted line at $-$1.2 V shows the bias position of the identified STS peak coming from the electronic structure of the CrFe tip.

Figure 4

Comparison of magnetic asymmetries 3.5 Å above a surface Cr atom probed with the flat magnetic tip and the model CrFe tip. $A^{\mathrm{Flat},\kappa \left(U\right)}$, $A^{\mathrm{Flat},\kappa (U,V)}$, and $A^{\mathrm{CrFe},dI/dV}$ are calculated from the corresponding P and AP spectra shown in Fig. 3. For the CrFe tip, we compare the magnetic asymmetry expressions defined in Eqs. (27, 28, 29, 30, 31).

Figure 5

(Top left) Surface geometry of 1 ML Cr on Ag(111). The Cr and Ag atoms are denoted by spheres colored by green (medium gray) and purple (dark gray), respectively, while the magnetic moments of individual Cr atoms are indicated by (red) arrows. The ($\sqrt{3}\times \sqrt{3}$) magnetic unit cell is drawn by yellow (light gray) color. The surface Cr positions are denoted by “x.” (Bottom left) Constant current contour about 3.5 $\AA$ above the surface with $I_{\mathrm{TOTAL}}(V_{\mathrm{stab}}=+1V)=54$ nA calculated with the flat magnetic tip using $\kappa (U,V)$, Eq. (9). The tip magnetization direction (${\underline{M}}_{\mathrm{TIP}}$) is indicated by an arrow. (Middle column) Simulated 2D differential conductance maps $dI/dV(x,y,V=+0.5$V$)$ (top middle: min. 15.8, max. 16.5 nA/V), and $dI/dV(x,y,V=+0.6$V$)$ (bottom middle: min. 22.9, max. 23.6 nA/V), while the tip is following the constant current contour at the bottom left of the figure. Minimum (MIN) and maximum (MAX) values are indicated. (Right column) Simulated effective spin polarization (ESP) maps on the same current contour following Eq. (29), ESP$(x,y,V=+0.5$V$)$ (top right), and ESP$(x,y,V=+0.6$V$)$ (bottom right). Black contours correspond to zero ESP, and the regions with positive (+) and negative (−) ESP are indicated. The surface magnetic unit cell is drawn by a yellow (light gray) rhombus on each 2D map.