Quantum well states with nonvanishing parallel momentum in Cu/Co/Cu(100)

Using low-temperature scanning tunneling spectroscopy we study quantum well states in the topmost copper layer of a Cu/Co/Cu(100) system above the Fermi energy. The emergence and the energetic positions of QWSs within this layer crucially depend on the interface quality tailored by the sample preparation method. Samples deposited at room temperature show a rough interface and lead to the well-known QWSs with only a momentum perpendicular to the interface. Atomically smooth interfaces for samples grown at $80\mathrm{K}$ exhibit states caused by stationary points with a large nonvanishing parallel momentum. Simulations taking into account the different band structures allow QWSs to be modeled from both stationary points and an identification of a crossover between bound and resonance states.

Figure 1

(a) A sketch of the Cu/Co/Cu(100) layered system including the STM tip in tunneling contact. The red line sketches an effective potential $V_{\mathrm{eff}}\left(z\right)$ that was derived from the transfer matrix method and the Cu/Co band structure. The blue line shows the wave function of a QWS. (b) Cross sections along the (011) direction of two isoenergetic surfaces at 0.5 and 1.5 eV above the Fermi energy of Cu (left) and spin-down Co (right). The arrows indicate the two stationary points on this isoenergetic surface in the (100) direction.

Figure 2

STM topographies after different preparation steps for the RT and LT growth: (a), (e) 10 ML of Co on a Cu(100) single crystal. (b), (f) The same surface after a 5 min annealing step at 450 K. (c), (g) After 12 ML of Cu no additional annealing is needed [1 V at 0.1 nA (RT)/0.5 nA (80 K)]. (d), (h) A more detailed view of the Cu layer reveals a segregation process of Co into the Cu film at room temperature. The same is observed for deposition at low temperature but up to five times less than in the room-temperature case [30 mV (RT)/10 mV at 1 nA (80 K)].

Figure 3

Electronic analysis of the QWSs. (a) Raw tunneling spectra of a Cu(100) bulk single crystal (black line) and of the Cu/Co/Cu heterostructure grown at RT (red line) ($-3$ V at 2 nA). (b) A section of the derivative of the differential conductivity over a monatomic step, shown in the topography at the bottom for the system grown at LT. (c) Two single spectra of the second derivative of the current, each taken at one of the two dots in the topography (3 V at 3 nA).

Figure 4

Statistical analysis of the energetic position of the QWS signatures. The energies accumulate to certain values, which are then attributed to the numbers of monolayers around the calibrated thickness from the evaporation. (a) and (c) show the analysis for the 12 ML copper grown at RT and LT, respectively, and (b) the analysis of the 9 ML film of copper prepared at LT.

Figure 5

Comparison between experimental data and numerical results for (a) the belly states and (b) the neck states. The experimental results are plotted as circles for the RT-grown structure and as triangles for the LT-prepared sample, the numerically obtained probability of the electron to be found inside the Cu well is shown color coded (scaled logarithmically). The black lines are a guide to the eye for the respective dispersion branches. The values for the sample grown at RT fit the dispersion for the belly while the values for the LT-grown sample clearly fail. On the contrary, the latter match the dispersion for the neck states in (b). In (c) the schematic formation of the two kinds of QWSs for the energies in (b) is shown. Below 1 eV we obtain bound states; above that resonant transmitting states are possible.