Noble metal surfaces such as gold feature a Shockley surface state and a layer of electrons confined to the topmost atomic layers. The broken crystal inversion symmetry at the surface generates a strong perpendicular electric field, lifting the spin degeneracy and splitting the electronic state into two distinct rings, each with an opposite in-plane spin direction. This spin-splitting phenomenon is known as the Rashba effect.

Historically, conflicting assignments have emerged from prior literature regarding the absolute spin direction (clockwise vs. counterclockwise) owing to variations in experimental setups and analysis conventions. The IMS team aimed to overcome these ambiguities by using a refined, high-efficiency imaging technique.

The experiments employed a unique twin-hemispherical analyzer PMM at UVSOR, capable of capturing a snapshot of a wide, two-dimensional (2D) energy and spin-resolved map of electron momentum (k). Soft X-rays with a grazing incidence, p-polarized configuration were used as the excitation source. Crucially, the system included a spin rotator placed before a 2D spin filter (Ir(001) crystal). The spin rotator enabled the acquisition of two images with opposite spin sensitivity without moving the sample, allowing for fast, sign-calibrated mapping.

The resulting spin-resolved large k-space images provided unambiguous confirmation of the disputed spin assignment. When viewed from the vacuum side, the outer electron band rotated clockwise (cw), and the inner band rotated counterclockwise (ccw). This confirmed the spin-splitting texture characteristics of the Rashba effect.

Furthermore, by illuminating the surface with s-polarized vacuum ultraviolet (VUV) light at normal incidence, the dominant 6s and 6p atomic orbitals constituting the surface states were successfully identified. This orbital identification was validated by confirming an orbital selection rule: the photoelectron intensity dropped to zero for electrons emitted perpendicular to the electric-field vector of the incident photon.

By establishing a robust, image-based assignment of both spin and orbital textures, this study provides a reliable quantum reference dataset for materials science in the future. The refined PMM methodology allows fast, simultaneous, and sign-calibrated mapping of complete 2D spin and orbital textures. This highly efficient method can be extended to build a consistent “atlas” of spin textures, representing a fundamental step for the design and development of spintronic devices that utilize electron spin for novel functionalities.

(Written by F. Matsui on behalf of all authors)

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