Coupling exchange interaction (SOI) and spin-orbit interaction (XCI) provides the foundation for many prospective spin-based information technology applications. For example, it was suggested that the strength of SOI at a ferromagnet/heavy-metal (FM/HM) interface is decisive for the efficiency of writing magnetic bits in spin-orbit-torque MRAM devices [1].

Exploring the electronic structure is the key to access the factors underlying the coupling of SOI and XCI. We use spin- and angle- resolved inverse photoemission to study the interplay of SOI and XCI in the unoccupied electronic structure at the interface of a low-dimensional FM on a HM substrate. The prototypical FM/HM hybrid system Ni/W(110) exhibits exchange-split Ni-related states that become strongly influenced by SOI. A balanced ratio of SOI and XCI results in a magnetization- and k-dependent quenching or enhancement of the spin splitting. This remarkably large interplay of SOI reflected in the adlayer states contrasts previous studies of the occupied electronic structure of the same system, where the observations were attributed solely to either SOI or XCI [2].

Using density-functional-theory (DFT) calculations, we investigate the underlying drivers responsible for the experimentally observed coupling of SOI and XCI. We find that hybridization between adsorbate and substrate states, along with the strongly localized wave functions at the heavy W nuclei, cause the strong influence of SOI within the Ni-related exchange-split states.

[1] I.M. Miron et al., Nature, 476 189 (2011)

[2] A. Nuber, PhD Thesis (University of Würzburg, Germany, 2011)

Although NiCo₂O₄ thin film is shown to possess perpendicular magnetic anisotropy [1], we have observed in-plane spin polarization of NiCo₂O₄ thin film in spin polarized inverse photoemission spectroscopy (SPIPES). The unoccupied states of NiCo₂O₄, above Fermi level, were observed to have unequal density of states for spin majority and spin minority carriers in SPIPES, and the spectra obtained from the SPIPES have spectral features that can be compared to the XMCD spectra. The in-plane spin polarization of NiCo₂O₄ is found to decrease with increasing temperature, as expected. In addition to the temperature dependent change in spin polarization, we observed that there is change in the surface electronic properties of NiCo₂O₄ from conducting to insulating when the temperature is increased. X-ray photoemission spectroscopy (XPS) studies show that there exist no appreciable binding energy changes of Ni 2p_3/2 and Co 2p_3/2 core levels with change in temperature (T) when the NiCo₂O₄ film exists in conducting phase. However, when the NiCo₂O₄ films became insulating, the core level binding energies changed reversibly with change in temperature during annealing and cooling cycles. The core level binding energy (BE) change with temperature (T) is found to closely follow a modified Arrhenius type model. The proposed model is also followed by Co 2p_3/2 and Fe 2p_3/2 core levels in temperature dependent XPS of insulating CoFe₂O₄ thin films.Our studies indicate that thermal effects and oxygen defects should play the roles in changing both magnetic and electronic properties of NiCo₂O₄ thin films with temperature.

The BiAg₂ and PbAg₂ surface alloys exhibit giant Rashba splittings [1-4]. The related TlAg₂ surface alloy is expected to show states with smaller but still large Rashba splittings due to the lower atomic number of Tl. However, this alloy forms only small patches with long-range structural order [5]. For higher coverages of Tl on Ag(111), a smooth and stable wetting layer forms with a moiré superstructure due to the lattice mismatch between Tl and Ag. We present a study of the unoccupied electronic structure of this superstructure by spin- and angle-resolved inverse photoemission. The experimental results are accompanied by DFT calculations. We observe surface states and an image-potential resonance located several Å in front of the surface. Surprisingly, one surface state exhibits almost no Rashba splitting even though it is located around the Tl atoms. This result is explained by the orbital symmetry of the respective state. For the image resonance, we find hybridization with a downward dispersing Tl state leading to spin-dependent spectral intensities that vary strongly close to the hybridization point. This observation, both in experiment and bandstructure calculations, is supported by charge distribution calculations showing an expeditious change from the image resonance to the Tl-induced surface state depending on k_||.

[1] C. R. Ast et al., Phys. Rev. Lett. 98, 186807 (2007)

[2] G. Bihlmayer, S. Blügel, and E. V. Chulkov, Phys. Rev. B 75, 195414 (2007)

[3] S. Wissing et al., Phys. Rev. Lett. 113, 116402 (2014)

[4] L. El-Kareh et al., New J. Phys. 16, 045017 (2014)

[5] P. Härtl, S. Schemmelmann, P. Krüger, M. Donath, and M. Bode, submitted to Phys. Rev. B

Tamm and Shockley states, these two paradigmatic concepts are used to describe surface states not only in electronic systems but also in photonic and phononic crystals. The Re(0001) surface was found to host both types of electronic surface states in neighboring, but qualitatively different gaps [1]. Interestingly, spin-orbit interaction generates a double W-shaped energy vs k_||dispersion by mixing both types of states and lifting their spin degeneracy. We employ a combination of spin- and angle-resolved photoemission, tight-binding model calculations, and density functional theory that accounts for the photoemission process to establish reliable criteria for distinguishing between the two types of surface states. Our approach leads to a coherent understanding of the mechanism of spin-orbit interaction in such a situation.

From a detailed investigation of the Re(0001) surface along the ΓM and ΓK high-symmetry directions [2], we obtain Rashba parameters of 0.32 and 0.34 eVÅ along the two respective directions. This indicates a slight warping of the surface state. Regarding the aforementioned state’s spin polarization: at variance with theoretical predictions for a perfect hcp(0001) of rhenium [3], we do not find any out-of-plane spin polarization. This is attributed to monatomic steps of a real Re(0001) surface with alternating terminations, leading on average to an effective sixfold surface symmetry and vanishing net out-of-plane spin polarization.

[1] M. Holtmann et al., Phys. Rev. B 105, L241412 (2022)

[2] M. Holtmann et al., Phys. Rev. B 107, 165420 (2023)

[3] A. Urru and A. Dal Corso, Surf. Sci. 686, 22 (2019)