Tuning the spin signal from a highly symmetric unpolarized electronic state

A remarkably large spin signal is observed on nonmagnetic W(110) for a highly symmetric unoccupied state with no intrinsic spin polarization. The magnitude and, more importantly, the sign of this spin signal, measured by spin- and angle-resolved inverse photoemission for normal electron incidence, can be tuned in a user-defined manner by variation of the photon-detection angle and/or by rotating the spin-polarization direction of the incident electrons. Using calculations of the orbitally decomposed spectral densities, this effect is traced back to a mixing of different symmetries within the respective state. This explanation is underlined by the behavior of a second electronic state of pure symmetry, which does not show such a spin signal. In general, the spin signals of electronic states are not only influenced by their intrinsic spin polarization but also by the choice of symmetry-breaking experimental parameters in combination with the particular orbital characters of the states under investigation. The latter permits one to tune the spin signal in magnitude and sign.

Figure 1

(a) LEED pattern of clean W(110) for an electron energy of 63 eV. The surface Brillouin zone is shown as an overlay. The $x$ and $y$ axes are chosen along the $\overline{\Gamma }\overline{\mathrm{N}}$ and the $\overline{\Gamma }\overline{\mathrm{H}}$ symmetry lines, respectively. (b) Experimental geometry of the spin-resolved IPE experiment. Arrows of rotation denote positive direction of rotation. (c) Spin-integrated IPE spectrum (sum over all counters) for $\theta =0{}^{\circ }$. The gray-shaded area highlights the energy region in which W1 and W2 appear.

Figure 2

(a) Experimental geometries of counters C1, C2, and C3, with photon-detection angles specified. (b)–(d) Spin-resolved normal-incidence IPE spectra of W(110) and corresponding spin-asymmetry data for $\varphi =0^{\circ }$ (sensitive to the spin-polarization components $P_y$ and $P_x$) and $\varphi ={90}^{\circ }$ (sensitive to $P_y$). Panels with nonzero spin asymmetry are highlighted by frames with thicker linewidth. (e) Spin asymmetry of W1 vs azimuthal angle $\varphi$ for spin polarization $\mathbf{P}$ perpendicular to the plane of incidence.

Figure 3

Calculated electronic structure of W(110) along $\overline{\Gamma }\overline{\mathrm{N}}$. Spectral densities $n(E,{\mathbf{k}}_{\parallel })$ (a) for a bulk layer and (b) for the topmost surface layer, sharing a common color scale (dark is small values and bright is large values). (c) Spin difference $n_{\uparrow }(E,{\mathbf{k}}_{\parallel })-n_{\downarrow }(E,{\mathbf{k}}_{\parallel })$ of the spin-projected surface spectral density, illustrated in red (blue) where spin-up (spin-down) intensity prevails (white denotes zero spin difference). (d) Orbital decomposition of the spectral density (surface and subsurface layer) with assigned symmetry representation.

Figure 4

Spin-resolved IPE spectra of W(110) for various angles of electron incidence $\theta$ along $\overline{\Gamma }\overline{\mathrm{N}}$ ($\varphi =0^{\circ }$), sensitive to the Rashba component $P_y$ of the spin polarization. Photons are detected by counters C1 (left) and C2 (right). For C2 (symmetric position with respect to $\theta$), the spin-integrated spectra for $+\theta$ and $-\theta$ are equivalent.