Classical and cubic Rashba effect in the presence of in-plane 4f magnetism at the iridium silicide surface of the antiferromagnet GdIr2Si2

Abstract

We present a combined experimental and theoretical study of the two-dimensional electron states at the iridium-silicide surface of the antiferromagnet GdIr 2 Si 2 above and below the Néel temperature. Using angleresolved photoemission spectroscopy (ARPES) we find a significant spin-orbit splitting of the surface states in the paramagnetic phase. By means of ab initio density-functional-theory (DFT) calculations we establish that the surface electron states that reside in the projected band gap around the M point exhibit very different spin structures which are governed by the conventional and the cubic Rashba effect. The latter is reflected in a triple spin winding, i.e., the surface electron spin reveals three complete rotations upon moving once around the constant energy contours. Below the Néel temperature, our ARPES measurements show an intricate photoemission intensity picture characteristic of a complex magnetic domain structure. The orientation of the domains, however, can be clarified from a comparative analysis of the ARPES data and their DFT modeling. To characterize a single magnetic domain picture, we resort to the calculations and scrutinize the interplay of the Rashba spin-orbit coupling field with the in-plane exchange field, provided by the ferromagnetically ordered 4 f moments of the near-surface Gd layer.

Spin-Orbit Interaction Effect on Surface Electronic Structure of GdX2Si2 Compound

“…The GGA+U method was used for strongly correlated 4f-states of gadolinium [14,15], with U = 6.7 eV and J = 0.7 eV [16]. The Brillouin zone was sampled with a 12124 and 12121 k-point grids in the case of the bulk and slab calculation, respectively [2,3,6]. According to these works, the theoretical calculations based on these techniques were in good agreement with the experimental data and provided an accurate description of the electronic structure.…”

“…The influence of the d-shell filling on the spin-orbit interaction was studied through a comparison of the intrinsic spin-orbit splitting of the electron and hole states at the Brillouin zone center for the coupled compounds GdAu 2 Si 2 -GdIr 2 Si 2 [6] and GdAg 2 Si 2 -GdRh 2 Si 2 [2,4]. The electronic configuration in each couple is characterized by filling of 5d-and 4d-shells in GdAu 2 Si 2 -GdIr 2 Si 2 and GdAg 2 Si 2 -GdRh 2 Si 2 couples, respectively.…”

“…Lately, the type REX 2 Si 2 compounds, where RE is a rare-earth element and X is a transition element, have been intensively investigated [1][2][3][4][5][6][7]. The silicon (001) surface of this compounds offers a platform for systematic studies of spin-orbit interactions, including the Bychkov-Rashba effect [8].…”

“…These systems are characterized by the intensity control of the spin-orbit interaction due to changes within one group of transition elements. Thus, the spin-orbit interaction is low in Co-based compounds, while in Ir-based compounds this interaction is more intensive [6]. The electronic structure of GdRh 2 Si 2 and GdIr 2 Si 2 compounds is investigated in detail in [2,4,6] using theoretical calculations and experimental data.…”

“…Thus, the spin-orbit interaction is low in Co-based compounds, while in Ir-based compounds this interaction is more intensive [6]. The electronic structure of GdRh 2 Si 2 and GdIr 2 Si 2 compounds is investigated in detail in [2,4,6] using theoretical calculations and experimental data. In our recent research [6], we show that the surface state of GdIr 2 Si 2 compound significantly modifies during the spin-orbit interaction, which is not intrinsic to related compounds with a lower intensity of the spin-orbit interaction.…”