Quasiparticle interference scattering of spin-polarized Shockley-like surface state electrons: Ni(111)

We report on a detailed quasiparticle interference (QPI) scattering study of the Ni(111) surface by low-temperature scanning tunneling spectroscopy (LT-STS). While conventional constant-separation STS shows two broad features, which are interpreted as the ${\Lambda }_3$ bulk band and $sp$-like Shockley-type surface state ($sp$-SS), energy-dependent Fourier-transformed QPI maps reveal the band dispersion of the underlying surface electronic features. We find two electronlike branches in the $sp$-SS dispersion, which are interpreted as the exchange-split minority and majority spin part. The exchange splitting is determined to $\Delta E_{\mathrm{ex}}=100\pm 8$ meV. In addition, a holelike $d$-derived surface resonance is found. Band onsets and effective electron masses are determined by fitting the band dispersion with a parabola at small $k$ values. Hybridization effects with bulk electronic states are observed towards larger $k$ values. Prominent quantum confinement phenomena of the $sp$-SS are observed in STS data obtained within vacancy islands. The results can be interpreted within a one-dimensional quantum-well model.

Figure 1

(a) The STM topography of clean Ni(111) (scan parameters: $U=+1.0$ V, $I=300$ pA). Within the field of view the surface exhibits four atomically flat terraces, which are separated by three monatomic step edges. The three weakly protruding lines (arrows) are presumably caused by subsurface dislocations. Typically, QPI maps were obtained on large atomically flat surface areas, such as shown in the zoomed-in image in the inset. Constant-separation tunneling spectra were taken at defect-free regions, as marked by a solid blue dot in the inset of (a). (b) Typical tunneling spectrum of Ni(111); two broad maxima representing the ${\Lambda }_3$ bulk state and the Shockley-type $sp$-SS can be recognized (STS set-point parameters: $U=+1.0$ V; $I=3.0$ nA).

Figure 2

(a)–(f) QPI maps taken at energies indicated in the upper right and their respective FT (insets). Obviously, the real space QPI scattering wavelength continuously increases (corresponding to the reduction of the reciprocal scattering vector in the insets) as the energy is lowered from $+375$ meV (a) down to $-125$ meV (d). Note that the FT-QPI maps in (a) and (b) reveal two scattering wave vectors, as indicated by double-ring features in the reciprocal space. This double ring cannot only be resolved on flat terraces, but also close to step edges of the pristine Ni(111) surface. No particular pattern is detected at $-200$ meV (e). Below $-275$ meV another pattern with a specific wavelength and a related ring in the FT appears in (f). All the QPI maps were taken at the constant tunneling resistance of 0.1 G$\Omega$.

Figure 3

(a) Constant-current topograph of Ni(111) and (b) the simultaneously recorded QPI map at 300 meV (tunneling resistance: 0.1 G$\Omega$). The corresponding FT-QPI pattern is shown in (c). The radial average of the double-ring feature is displayed in (d). The data can nicely be fitted with two Gaussian peaks. Inverse FT-QPI patterns within a narrow range of frequencies around the inner red and the outer blue circle, $k_{\parallel ,\mathrm{in}}$ and $k_{\parallel ,\mathrm{out}}$, are presented in (e) and (f), respectively.

Figure 4

(a) Energy dispersion relation extracted from FT-QPI patterns. The two electronlike upward dispersing bands, which correspond to the double-ring FT-QPI features discussed in detail in Fig. 3, are interpreted as an $sp$-like Shockley surface state, $sp$-SS. This surface state is exchange split into a minority (red) and a majority (blue) spin part. The exchange splitting amounts to $\Delta E_{\mathrm{ex}}=(100\pm 8)$ meV (black arrows). For the majority part, a parabolic dispersion (light blue line) persists up to $+100$ meV. The holelike downward dispersion (black triangles) corresponds to a $d$-like surface resonance ($d$-SR). The fit (orange line) gives a band onset and the effective mass of $(-235\pm 5)$ meV and $m^{*}=(-0.36\pm 0.05)m_e$, respectively. Schematics of the majority and minority bands are shown in (b) and (c), respectively (see text for details).

Figure 5

(a) Topographic STM image of a Ni(111) surface, which has been Ar${}^{+}$ bombarded and annealed to intentionally create vacancy islands (scan parameters: $U=+1.0$ V, $I=300$ pA). (b) STS spectra taken at the center of vacancy islands with different sizes and on the flat Ni(111) surface, as marked by differently colored solid dots in (a) (STS set-point parameters: $U=-0.3$ V, $I=1.0$ nA). The arrows in (b) indicate peaks that originate from energy levels due to quantum confinement of the unoccupied $sp$-SS. The wavelengths of the resonances can be estimated on the basis of a simple quantum-mechanical model as illustrated in (c) with ${\lambda }_n=(n+1)/2$, where $n=0,2,4,6...$. The analysis of k${}_n$($E$${}_n$) with size dependence have been arranged into the Fig. 4 together with the dispersion relations, i.e., colored triangular, circular, and square dots. (d) Topography (top panel) and differential conductance $dI/dU$ maps (bottom three panels) taken at the 9.2 nm vacancy within the area indicated by a black rectangle in (a) at bias voltages that correspond to quantum states with $n=2$, 3, and 4, respectively. Only those states with an antinode of the $dI/dU$ signal in the center of the vacancy island, i.e., with even $n$, show up as peaks in the respective spectra shown in (b).