Asymmetric band gaps in a Rashba film system

The joint effect of exchange and Rashba spin-orbit interactions is examined on the surface and quantum well states of ${\mathrm{Ag}}_2\mathrm{Bi}$-terminated Ag films grown on ferromagnetic Fe(110). The system displays a particular combination of time-reversal and translational symmetry breaking that strongly influences its electronic structure. Angle-resolved photoemission reveals asymmetric band-gap openings, due to spin-selective hybridization between Rashba-split surface states and exchange-split quantum well states. This results in an unequal number of states along positive and negative reciprocal space directions. We suggest that the peculiar asymmetry of the discovered electronic structure can have significant influence on spin-polarized transport properties.

Figure 1

Scheme of (a) and (d) spin-polarized QWS interacting with (b) and (e) Rashba-split surface states. Depending on the QWS spin orientation, spin-selective hybridization with the surface states results in (c) and (f) asymmetric $(\mathbf{k}$ vs $-\mathbf{k})$ band structures.

Figure 2

(a) Photoemission spectra for 15 ML Ag/Fe(110) along the $\overline{\mathrm{M}}-\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ direction. (b) and (c) Photoemission spectra for ${\mathrm{Ag}}_2\mathrm{Bi}$/15 ML Ag/Fe(110) along $\overline{\mathrm{M}}-\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ with collinear SQA of QWS and Rashba-split states, for opposite magnetization, $M^{+}$ and $M^{-}$, of the Fe film. (d)–(f) Second derivative spectra of the regions enclosed by the dashed lines in panels (a)–(c). The photon energy is 50 eV.

Figure 3

Second derivative photoemission spectra of ${\mathrm{Ag}}_2\mathrm{Bi}$/15 ML Ag/Fe(110) with SQA of QWS collinear with Rashba states, measured with magnetization (a) $M^{+}$, (b) $M^{-}$, and (c) their difference. Second derivative photoemission spectra of ${\mathrm{Ag}}_2\mathrm{Bi}$/15 ML Ag/Fe(110) with SQA of QWS orthogonal to the Rashba states, for (d) $M^{+}$, (e) $M^{-}$, and (f) their difference.

Figure 4

Constant energy cut for the ${\mathrm{Ag}}_2\mathrm{Bi}$/11 ML Ag/Fe(110) film, taken at 0.54 eV binding energy with magnetization (a) $M^{+}$ and (c) $M^{-}$ aligned along the vertical axis. (b) and (d) Schemes corresponding to (a) and (c). The photon energy is 50 eV.

Figure 5

(Left panel) Band structure of a 9-ML Ag(111) film on an Fe substrate with a ${\mathrm{Ag}}_2\mathrm{Bi}$ surface alloy on top. Ag and Bi states are marked with circles and diamonds, respectively. Open and solid symbols indicate different spin orientations. Gray lines show Fe bands. (Right panels) Charge density of the QWS at the $\overline{\mathrm{\Gamma }}$ point for two different energies. Gray regions indicate the Fe layers.

Figure 6

Model band structure of the system along $\mathbf{k}$ (a) parallel and (b) perpendicular to the magnetization direction. (c) CISP for current along the $y$ axis $\left(S_{xy}\right)$ and current along the $x$ axis $\left(S_{yx}\right)$. (d) Calculated AMR ratio as a function of binding energy.

Figure 7

Sketch of the experimental geometries used for the angle-resolved photoemission experiments. (a) The measured electrons are emitted in the plane containing the surface normal and the $\mathrm{Fe}\left[1\overline{1}0\right]$ axis. The photoemission measurement probes in reciprocal space the $\overline{\mathrm{M}}-\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ direction of the Ag(111) films, which corresponds to the $\mathrm{Ag}\left[11\overline{2}\right]$ axis. (b) The measured electrons are emitted in the plane containing the surface normal and the $\mathrm{Fe}\left[001\right]$ axis. The photoemission measurement probe in reciprocal space the $\overline{\mathrm{K}}-\overline{\mathrm{\Gamma }}-\overline{\mathrm{K}}$ direction of the Ag(111) films, which corresponds to the $\mathrm{Ag}\left[1\overline{1}0\right]$ axis. The electron wave vector is perpendicular to the magnetization axis in the first case and parallel to it in the second case. (c) and (d) Fe $3p$ photoemission spectra measured in the geometries of panels (a) and (b), respectively, for the opposite sign of the magnetization $(M^{+},M^{-})$.

Figure 8

Spin-resolved (solid red and open red symbols) and spin-integrated (solid black circles) photoemission spectra in normal emission for a 11 atomic layer Ag(111) film grown on Fe(110).

Figure 9

Constant energy cuts for a ${\mathrm{Ag}}_2\mathrm{Bi}$/11 ML Ag/Fe(110) film, taken at binding energies (a) 0.34, (b) 0.70, (c) 0.92, (d) 1.12, (e) 1.28, and (f) 1.42 eV. The photon energy is 50 eV. The magnetization is aligned along the vertical axis.

Figure 10

(a) Constant energy cut through the band stucture shown in Fig. 6 of the main text at 0.4 eV. Two arclike features result from crossings of bands of opposite spin. (b) Band surface of the inner feature shown in (a). Energies $0.4\pm 0.1\mathrm{eV}$ are shown on the vertical axis. (c) Schematic presentation of the transport arising from the state at the touching point of this band surface in a cylinder geometry. $\mathbf{M}$ is the magnetic field from the Fe film.