Magnetization-Direction-Dependent Local Electronic Structure Probed by Scanning Tunneling Spectroscopy

Scanning tunneling spectroscopy (STS) of thin Fe films on W(110) shows that the electronic structure of domains and domain walls is different. This experimental result is explained on the basis of first-principles calculations. A detailed analysis reveals that the spin-orbit induced mixing between minority $d_{xy+xz}$ and minority $d_{z^2}$ spin states depends on the magnetization direction and changes the local density of states in the vacuum detectable by STS. As a consequence nanometer-scale magnetic structure information is obtained even by using nonmagnetic probe tips.

Figure 1

(a) Topography and magnetic $dI/dU$ signal of $1.75\pm 0.1\mathrm{M}\mathrm{L}\mathrm{F}\mathrm{e}/\mathrm{W}(110)$ as measured with (b) a Gd coated ($U=0.7\mathrm{V}$), (c) a Fe coated ($U=0.7\mathrm{V}$), and (d) an uncoated W probe tip ($U=0.05\mathrm{V}$). (e) $dI/dU$ spectra of domains and domain walls.

Figure 2

Calculated LDOS at about $z=14\AA$ above the surface of $2\mathrm{M}\mathrm{L}\mathrm{F}\mathrm{e}/\mathrm{W}(110)$, measured from the center of the atom. The lower panel displays the normalized difference. For the calculation 3600 ${\mathbf{k}}_{\Vert }$ points have been used in a square centered at $\overline{\Gamma }$ with an area covering 25% of the BZ (see Fig. 3).

Figure 3

${\mathbf{k}}_{\Vert }$-resolved contributions to the minority LDOS for states with an energy of $E_{\mathrm{F}}+50\mathrm{m}\mathrm{e}\mathrm{V}$ displayed in the 2D-BZ. A disk of radius $\overline{\Gamma \mathrm{P}}$ centered around the $\overline{\Gamma }$ point with an area of 20% of the 2D-BZ has been chosen. States with larger $|{\mathbf{k}}_{\Vert }|$ contribute only insignificantly to the vacuum LDOS. (a) The LDOS for the out-of-plane direction, and (b) the difference $\Delta n$ between the LDOS $n$ for out-of-plane and in-plane magnetization directions. Yellow (red) corresponds to positive (negative) values of $\Delta n$. A total of 6000 ${\mathbf{k}}_{\Vert }$ points have been used to sample the disk.

Figure 4

Comparison of the band structure of the entire Fe DL film along the line $\overline{\Gamma \mathrm{P}}$ (cf. Fig. 3) (a) without and (b) with spin-orbit interaction. In (a) the full (chained) line represents the minority (majority) bands. The view of (b) is shown as a red box in (a). The vertical grey lines indicate the radius of the inner circle of Fig. 3. A total of 400 ${\mathbf{k}}_{\Vert }$ points along $\overline{\Gamma \mathrm{P}}$ have been used to plot the band structure.