Quantum oscillations in the surface excitations of ultrathin Mg(0001) films

Using reflection electron energy-loss spectroscopy (EELS), we unveil a direct correlation between the thickness-dependent oscillatory charge spilling of quantum-well states in epitaxial Mg(0001) films, and the linear dispersion coefficient of the monopole surface plasmon mode. In addition, the spectral intensities of the photoemission threshold excitation and multipole surface plasmon mode follow a similar but mutually anticorrelated quantum oscillatory pattern. These oscillatory features of the collective response are attributed to quantum oscillations in the ground-state charge-density profile, specifically its decay into the vacuum. Because the decay lengths can be controlled through the quantum-size effects and appropriate choice of the quantum-size boundary conditions, these insights are expected to be significant in the design of quantum-sized plasmonic devices.

Figure 1

(a) LEED pattern of a 6-ML Mg(0001) film after annealing to RT. (b) STM image, showing an atomically flat thin-film morphology [15].

Figure 2

Spectra of 4.5-ML (top), 7.5-ML (middle), and 12-ML (bottom) Mg films before (black circle) and after (red circle) linear background subtraction. The incident/scattering angles are represented by “${\theta }_{\mathrm{in}}$/${\theta }_{\mathrm{sc}}$.”

Figure 3

(a) EEL spectra of a nominally 4.5-ML-thick Mg film at different scattering angles and ${50}^{\circ }$ incident angle. The apparent broadening of the elastic tail at ${50}^{\circ }$ scattering angle is due to the fact that the scattering is specular in this particular geometry. (b) Fitting of the 4.5-ML Mg film spectrum at one specific scattering angle (corresponding to $q_{\parallel }\approx 0$ for the surface plasmon), after subtraction of a linear background. Components TE, SP, MP, and BP correspond to threshold excitation, monopole surface plasmon, multipole surface plasmon, and bulk plasmon, respectively.

Figure 4

Fitted spectra of 4.5-, 7.5-, and 12-ML Mg films at ${\theta }_{\mathrm{in}}$/${\theta }_{\mathrm{sc}}={50}^{\circ }/{62}^{\circ }$.

Figure 5

Loss energies from the four-component fits (see text) as a function of $q_{\parallel }$.

Figure 6

Dispersions of monopole surface plasmons in 4.5-, 7.5-, and 12-ML Mg films. Dashed lines are the result of polynomial fitting. The initial dispersion slopes are indicated by solid lines.

Figure 7

Thickness dependence of (a) the real part of $d({\omega }_s$), (b) the multipole mode intensity, and (c) the threshold excitation intensity. The intensities of the spectra in (b) and (c) are normalized by the total loss intensity. (d) Photoemission intensity at $E_F$ in normal emission, or DOS($E_F$), from Ref. [12]. (e) DOS($E_F$) and initial oxidation rate of ultrathin Mg(0001) films on W(110) from Ref. [28]. (f) Charge spilling parameter $\lambda$ from first-principles calculations for Mg(0001) on W(110) [13].

Figure 8

(a) Imaginary parts of calculated surface reflection coefficients for $r_s=2$ (green) and $r_s=4$ (red) with $q_{\parallel }=0.12{\text{Å}}^{-1}$ and $\gamma =0.1{\omega }_p$. The TE and MP contributions, determined via a least-squares fit of the calculated loss spectra, are indicated by the dotted lines. Note the relative redshift of the SP peak for $r_s=4$, consistent with Fig. 6. (b) Real and imaginary parts of surface dielectric $d$ functions for $r_s=2$ (green) and $r_s=4$ (red), adopted from [19]. Vertical lines mark the SP energy of bulk Mg, ${\omega }_s={\omega }_p/\sqrt{2}$.

Figure 9

(a) Attenuation of the differential Si LVV Auger spectra as a function of deposition time. (b) Characteristic linear segment plot used to determine the Mg deposition rate.

Figure 10

Surface plasmon linewidths as a function of $q_{\parallel }$ for a Mg single crystal [17] (left) and for thin Mg films (right).