Theoretical study of the role of the tip in enhancing the sensitivity of differential conductance tunneling spectroscopy on magnetic surfaces

Based on a simple model for spin-polarized scanning tunneling spectroscopy (SP-STS), we study how tip magnetization and electronic structure affects the differential conductance ($\mathit{dI}/\mathit{dV}$) tunneling spectrum of an Fe(001) surface. We take into account energy dependence of the vacuum decay of electron states and tip electronic structure either using an ideal model or based on ab initio electronic structure calculation. In the STS approach, topographic and magnetic contributions to $\mathit{dI}/\mathit{dV}$ can clearly be distinguished and analyzed separately. Our results suggest that the sensitivity of STS on a magnetic sample can be tuned and even enhanced by choosing the appropriate magnetic tip and bias set point, and the effect is governed by the effective spin polarization.

Figure 1

Sketch of the relative energetic position of sample and tip electronic structures. $P(E),n(E),m(E)$ of the Ni tip apex and the surface Fe atom, and their relation at applied bias voltage $V$ are shown. Depending on $V$, different electron states are involved in the tunneling process for calculating the tunneling current, while $V$ (bias set point) fixes the relative energetic position of tip and sample electron states when simulating differential tunneling spectra, i.e., $E_F^{\text{TIP}}=E_F^{\text{SAMPLE}}+\text{eV}$. The energy scale is shown in the bottom left part (1 eV), and according to that, the bias voltage in the figure is $+$1.0 V.

Figure 2

Simulated differential tunneling spectra (TOTAL) and their topographic (TOPO) and magnetic (MAGN) contributions (solid lines) $z=3.5$ Å above an Fe atom on the Fe(001) surface, assuming a maximally spin-polarized and electronically flat tip using Eqs. (14) and (16). Tip magnetization direction is antiparallel ($C=\text{cos}\phi =-1$) (left part) and parallel ($C=\text{cos}\phi =+1$) (right part) to that of Fe. Note that, in the two parts, the topographic contribution is the same, while the magnetic contribution changes sign, and the total $\mathit{dI}/\mathit{dV}$ curve changes accordingly. By modifying the magnetization direction of tip, the surface-state peak can be tuned. For comparison, spin polarization $P_S(E)$ and other electronic properties of the surface Fe atom $[n_S(E)+m_S(E)*\text{cos}\phi ],n_S(E),m_S(E)*\text{cos}\phi$, each multiplied by $e^{-2\kappa (E_F^S)z}$, are shown in both parts (dashed lines). These properties correlate well with the corresponding spectra (curves with the same color and symbol) (see text for details).

Figure 3

Simulated differential tunneling spectra 3.5 Å above an Fe atom on the Fe(001) surface and its convergence depending on the contribution from the number of Fe atoms in the summation over $\alpha$ in Eq. (14), i.e., from 1 Fe atom (1Fe, dotted line) in a $1\times 1$ surface unit cell (the spectrum is taken above this atom), from 9 Fe atoms (9Fe, dashed line) in a $3\times 3$ surface cell (the spectrum is above the central Fe), and from 25 Fe atoms (25Fe, solid line) in a $5\times 5$ surface cell (the spectrum is above the central Fe). Note that each surface Fe atom has the same local electronic structure. For the simulation, a maximally spin-polarized and electronically flat tip is applied using Eq. (14), and tip magnetization direction is antiparallel to that of Fe.

Figure 4

Simulated differential tunneling spectra (TOTAL, solid lines) and topographic contribution (TOPO, dashed lines) 3.5 Å above an Fe atom on the Fe(001) surface, using a model Ni tip (see text for details), and depending on the bias set point for the tip (curves with different colors). The chosen bias set points are given in parentheses. They fix the relative energetic position of tip and sample electron states (see Fig. 1). Tip magnetization direction is antiparallel ($C=\text{cos}\phi =-1$) (left part) and parallel ($C=\text{cos}\phi =+1$) (right part) to that of Fe. Note that the topographic contributions for the corresponding bias set point are the same for both tip magnetization directions, while the total $\mathit{dI}/\mathit{dV}$ curves change considerably, similarly to Fig. 2. This is due to $P_T(E)P_S(E)\text{cos}\phi$ variations depending on the bias set point, which are shown with dotted lines. Thus, by modifying the bias set point, the surface-state peak can be tuned.