Research: Observation of a cubic Rashba effect in the surface spin structure of ternary rare-earth materials

In this work, we show that the spin structure of the surface-electron state trapped at the Si-terminated surface of the layered antiferromagnet TbRh₂Si₂ exhibits an unusual spin texture characterized by a triple winding of the electron spin along the fourfold-symmetric constant energy contour. This surface state spreads over four atomic layers that create the non-centrosymmetric surface block Si-Rh-Si-Tb. There, this 2D state experiences both spin-orbit coupling due to the Rh atoms and exchange magnetic interaction with the ordered Tb 4f magnetic moments.

We find that the spin-orbit interaction on the Rh atoms leads to an in-plane spin-momentum locking with a triple winding of the electron spins caused by an exotic cubic Rashba mechanism. Its essential property is a fast rotation of the electron spin along the Fermi surface, which is three times faster than in the classical Rashba effect.

This exotic spin structure apparently survives and remains intact when the material transfers from the paramagnetic (PM) to the antiferromagnetic (AFM) phase. In the latter, the Tb 4f magnetic moments become magnetically ordered perpendicular to the surface and create a strong exchange magnetic field. The triple winding of the electron spins within the surface turns out to be rather robust, although the spin-orbit coupling at the Rh atoms is substantially weaker than the out-of-plane exchange field due to the Tb 4f magnetic moments.

Our spin- and momentum-resolved photoelectron spectroscopy measurements are compared to calculations of the spin photocurrent within an ab-initio one-step theory of photoemission that fully support the obtained findings. Additionally, we have developed a relativistic k.p model that proves that the unusual spin pattern originates from a cubic Rashba effect and makes our results accessible for a broad audience.

D. Yu. Usachov, I. A. Nechaev, G. Poelchen, M. Güttler, E. E. Krasovskii, S. Schulz, A. Generalov, K. Kliemt, A. Kraiker, C. Krellner, K. Kummer, S. Danzenbächer, C. Laubschat, A. P. Weber, J. Sánchez-Barriga, E. V. Chulkov, A. F. Santander-Syro, T. Imai, K. Miyamoto, T. Okuda, D. V. Vyalikh,
Cubic Rashba Effect in the Surface Spin Structure of Rare-Earth Ternary Materials,
Phys. Rev. Lett. 124, 237202 (2020)