Abstract
We present a combined experimental and theoretical study of the two-dimensional electron states at the iridium-silicide surface of the antiferromagnet ${\mathrm{GdIr}}_{2}{\mathrm{Si}}_{2}$ above and below the N\'eel temperature. Using angle-resolved 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 $\overline{\mathrm{M}}$ 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 N\'eel 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 $4f$ moments of the near-surface Gd layer.
Highlights
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
Spin-orbit coupling (SOC) in a noncentrosymmetric environment leads to the momentum-dependent splitting of otherwise spin-degenerate electron-energy bands that is known as Rashba SOC effect [1–3]
We focus on the new antiferromagnetic material GdIr2Si2 [21], where the spin properties of the surface electron states at its iridium-silicide surface are governed by both SOC and exchange magnetism of similar strength, that is in difference to TbRh2Si2 mentioned above [7]
Summary
Spin-orbit coupling (SOC) in a noncentrosymmetric environment leads to the momentum-dependent splitting of otherwise spin-degenerate electron-energy bands that is known as Rashba SOC effect [1–3]. For GdIr2Si2, we will explore both the cubic and the classical Rashba effect and study how the spin structure of the surface states will be affected when the strong and robust in-plane magnetism from the Gd 4 f moments sets in. We have evaluated the spin structure of the surface electron states in the AFM phase when the staggered magnetization is directed along the [100] and [110] directions within the basal ab plane We considered these two limiting cases for the following reason: In light of our recently performed time-resolved experiments on the antiferromagnet GdRh2Si2 [32], the direction of the Gd 4 f moments reveals a temperature dependence which changes the easy magnetization axis. Thorough DFT modeling of different domain scenarios and comparison to our experimental results gives strong evidence that at 23 K the easy magnetization axis is along the [110] direction
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