Designing the Rashba spin texture by adsorption of inorganic molecules

Using the physisorption and chemisorption of inorganic molecules on BiAg2/Ag(111) we demonstrate from first principles that the spin–orbit splitting and the spin direction of surface Rashba-split states can be manipulated selectively. Although NH3 is physisorbed, it nevertheless leads to a slight enhancement of the outward buckling of the surface Bi that increases the magnitude of the Rashba splitting. On the other hand, the weakly chemisorbed BH3 determines a strong inward relaxation of the surface Bi such that the occupied Rashba state shifts into Ag bulk states while a new unoccupied one is induced. Importantly, for the BH3–BiAg2/Ag(111) system the size of the out-of-plane spin polarization is significantly larger than the in-plane one at variance with the clean surface case.

Achieving control over the spin direction at surfaces offers the possibility to directly access a variety of physical properties in metallic [1], insulating [2] or semiconducting [3] systems and thereby opens new prospects in the field of spintronics. For instance, it provides the possibility to control the spin-direction in setups that utilize current induced spin-polarization or accumulation [4] or at interfaces to magnetic systems it can be exploited to exert spin-orbit torques in the magnetic layers [5]. Additionally, by tuning the magnitude of the out-of-plane spin polarization one can directly modify the strength of the Dzyaloshinskii-Moriya interaction in non-collinear magnetic systems [6].
In this respect, the spin-orbit coupling (SOC) plays a crucial role to manipulate the spin degree of freedom in spintronics [7]. In particular, the SOC is a crucial ingredient to describe the physical properties of the emerging classes of Rashba [8] and topological insulator (TI) [9] materials. More specifically, the Rashba-Bychkov [10][11][12] spin-orbit effect describes the spin-split electronic states of a spatial inversion asymmetric two-dimensional electron gas (2DEG) (for a recent review see, e.g., [13]). This effect opens the fascinating possibility to control the spin using only electric fields as initially suggested by Datta and Das for a spin field-effect transistor (FET) [14] and recently demonstrated for an all-electric spin FET device [15].
While the above mentioned applications focus on SOC effects in 2DEGs at interfaces, much attention also shifted to their manifestation in surface states. The first observation in this direction was made on the Au(111) surface [16], where a (spin) splitting of the surface state was observed that can be described in the Rashba model by the spin-splitting parameter k SO [17] of 0.012 » Å −1 . Subsequent studies using spin-and angle resolved photo emission spectroscopy (ARPES) measurements revealed large Rashba splittings at the low index surfaces of Bi [18], and Bi surface alloys [19,20]. For instance, a BiAg 2 /Ag(111) surface alloy exhibits a 'giant' spin splitting of k 0.13 SO  Å −1 . Importantly, for this system it was demonstrated that a significant outward relaxation of the Bi atom is the key ingredient that leads to a larger Rashba splitting as compared to a Bi(111) surface [21]. Generally, it was emphasized that the driving force of this Rashba splitting is the asymmetry of the surface state wave function in the core region [17,22].
As regarding the issue how to tune spin-orbit effects for surface systems, several experimental and theoretical studies have proposed that the strength of the Rashba splitting can be tuned via adatom adsorption [23][24][25][26][27] or by a stoichiometry change of the surface alloy [28]. Furthermore, it was shown that a graphene layer on the Ir(111) surface protects the Rashba-split surface state from air [29] and keeps k SO unaffected even when Au nanoclusters are deposited on the graphene layer [30], demonstrating that the 2DEG of the surface state can be isolated in a well-defined state. For adsorbed molecular systems such as C 60 , iron octaethylporphyrin (FeOEP) and 3, 4, 9, 10-perylene-tetracarboxylic acid (PTCDA) the ARPES measurements performed in [31] indicated that they also did not alter the Rashba splitting of the BiAg 2 /Ag(111) surface states due to a weak molecule-surface interaction. A recent study of PTCDA on PbAg 2 /Ag(111), however, reports changes in the substrate bandstructure [32]. Also on a TI surface such as Bi 2 Se 3 (111), Rashba split interface states can be induced by organic molecules depending on the strength of the molecule-substrate interaction [33]. Furthermore, for the cobalt phthalocyanine (CoPc)/Bi 2 Se 3 system a recent ARPES study demonstrated that the topological surface state is not present anymore in the first quintuple layer due to the molecule-surface hybridization, but nevertheless it is buried in the second quintuple layer [34].
While the above-mentioned studies were mainly focused on the size of the spin-orbit splitting, we show in this contribution that adsorbates can also be used to manipulate the spin-direction of the spin-texture in the 2DEG. In case of the Bychkov-Rashba effect, which is based on a uniform 2DEG in an electric field normal to the surface, the spins are oriented in the surface plane, perpendicular to the momentum direction. We demonstrate that the adsorption of inorganic molecules can be used to create in-plane surface potential gradients that induce a dominant out-of-plane spin polarization as illustrated in figure 1.
More specifically, the basic aims of this study are to tailor the magnitude of the (1) Rashba splitting and (2) out-of-plane spin polarization. The key mechanism is to modify the size of the Bi outward relaxation upon the molecular adsorption and to induce in-plane potential gradients. In practice, we achieved these goals for two exemplary inorganic molecular systems with an opposite electronic character. More precisely, the ammonia molecule (NH 3 ) has a pyramidal structure in which the electronic states are sp 3 hybridized and contains an electronegative N atom with a lone electron pair that usually plays an important role in the molecular bonding to a surface of choice [35]. On the other hand, the planar borane molecule (BH 3 ) is sp 2 hybridized containing an electropositive B atom with less electronic density as compared to N in NH 3 (i.e., an empty p z orbital at B). On this basis, a considerable difference in the interaction between these two molecules and the BiAg 2 /Ag(111) surface is to be expected.
Using the computational setup described in the supplementary material available online at stacks.iop.org/ NJP/19/043017/mmedia, our ab initio calculations reveal that in the ground-state NH 3 adsorbs with the N at an fcc hollow site and BH 3 with its B atom in an hcp hollow site (see figure 2). Overall, the calculated adsorption energies [36] indicate that NH 3 is physisorbed (E 0.23 ads = eV) while BH 3 is weakly chemisorbed (E 0.50 ads = eV) on the BiAg 2 /Ag(111) surface alloy. A particularly important effect induced by both molecules on the BiAg 2 /Ag(111) surface is the structural change upon molecular adsorption, namely how BH 3 and NH 3 modify the magnitude of the outward relaxation of the surface Bi atom, d Bi . Despite of the weak interaction of NH 3 with this substrate, Bi is slightly pulled out of Å with respect to the clean surface buckling of 0.61Å. Note that this behavior is similar to that observed for organic molecules adsorbed on a magnetic substrate that induces an outward relaxation of the surface atoms (i.e., skyhook effect) that further modifies the strength of their magnetic exchange interactions [37]. On the contrary, BH 3 adsorption leads to ∼40% inward relaxation of the Bi resulting in d 0.37 In the view of the correlation between the size of the Rashba splitting and the degree of the outward buckling of the Bi outlined in [21], these structural changes of the surface layer raise the expectation that the Rashba effect on the BiAg 2 /Ag(111) can indeed be selectively tuned by the adsorption of the two molecular species NH 3 and BH 3 .
To investigate this issue in more detail, we focus now on the electronic structure of the hybrid moleculesurface systems as revealed by the calculated band structures obtained by taking into account the SOC. We first note that our theoretical band structure obtained for the clean BiAg 2 /Ag(111) surface (cs) is in good agreement with previous experimental and first-principles investigations [20,21]  Å −1 by about ≈10% as expected due to the enhanced outward relaxation of the Bi upon molecular adsorption. Remarkably, this increase of the Rashba spin splitting is as large as the whole spin-orbit splitting of the Au(111) surface state [16]. Overall, this behavior is a direct consequence of the fact that the increased outward buckling of the Bi added more p z and p x y , ( ) character to the occupied surface state, which has in case of the clean surface mainly (s p , z ) character 2 . This makes this surface state more asymmetric that is the key ingredient to obtain a sizeable Rashba splitting [17,22]. Additionally, the Rashba splitting of the first unoccupied surface state is k 0.09 SO NH ,unocc 3 = Å −1 being by 0.01Å −1 larger than that for the clean surface.
It is important to note that this outcome of our ab initio study is in contrast to the experimental results obtained for a physisorbed π-conjugated organic molecule such as CuPc on PbAg 2 /Ag(111) [32] or C 60 on Bi 2 Se 3 (111) [33], which indicated that the Rashba spin-split surface electronic states were not modified by the molecular adsorption. Qualitatively, we assign this strikingly different behavior to the specific nature of the molecular electronic states that mediates the molecule-surface interaction: while for CuPc and C 60 the dispersion interaction is related to delocalized π molecular electronic states, the NH 3 interacts with the BiAg 2 / Ag(111) surface mainly via the lone pair localized at the nitrogen atom. Overall, this difference leads to a surface structural change in the case of the inorganic NH 3 molecule while this effect is not present for the organic ones. In the case of BH 3 (see figure 3(c)) the occupied BiAg 2 /Ag(111) surface state is pushed into the projected Ag bulk states (see figures 2 and 3 in the supplementary material) upon molecular adsorption due to the significant inward relaxation of the Bi atom by ∼40%. Hence, this observation implies that the chemisorbed BH 3 allows to selectively move the occupied surface state away from the Fermi energy E F . The Rashba splitting of the unoccupied surface state is preserved upon BH 3 adsorption with a spin splitting comparable with that of the clean surface. Remarkably, the weakly chemisorbed BH 3 on BiAg 2 /Ag(111) induces a Rashba-like (linear in k) spin-splitting of an unoccupied surface state at ≈1eV above the Fermi energy that was 3rd order spin split in the case of the clean BiAg 2 /Ag(111) surface. Note that this new Rashba-like surface state is characterized by k 0.09 SO BH ,unocc2 3 = Å −1 being similar to the occupied Rashba split state of the clean surface 3 . Again, as in the case of the physisorbed NH 3 , the impact of the weakly chemisorbed BH 3 on the Rashba-split surface states of the BiAg 2 /Ag(111) substrate is qualitatively different with respect to behavior evidenced in [32,33] for organic molecules. In particular, the inorganic BH 3 molecule leads to an inward relaxation of the surface Bi atoms in constrast to the outward relaxation of the Pb ones for PTCDA on PbAg 2 /Ag(111) [32]. Moreover, even if it is weakly chemisorbed, BH 3 induces a new unoccupied Rashba spin-split surface state on BiAg 2 /Ag(111) similarly to the strongly chemisorbed sulphurated H 2 Pc organic molecule on Bi 2 Se 3 (111) [33]. Generally, these results of our first-principles study clearly illustrate the versatility of the inorganic molecules to chemically functionalize the electronic structure of a hybrid molecule-surface Rashba system.
To gain a further insight into the origin of the differences between the electronic structure of the clean BiAg 2 /Ag(111) surface alloy and those of the hybrid molecule-surface systems we firstly investigated the electronic structure related to the molecule-surface hybridization (the hybridization effect) or the Pauli repulsion-induced charge rearrangement at the molecule-surface interface (the Pauli repulsion effect). Then, we analyzed these results with respect to the effect of the molecular-induced structural changes via the rehybridization of the surface atoms states (the geometrical effect) on the calculated band structure obtained for the geometries of the hybrid systems with the molecules removed (see figures 3(d) and (e)).
For the NH 3 -induced geometry, figure 3(d) clearly indicates that the calculated band structure is very similar to that of the hybrid molecule-surface system shown in figure 3(b). This observation suggests that the corresponding changes in the band structure are mainly a geometrical effect. More specifically, the splitting of the occupied surface state amounts to k 0.10 SO NH induced,occ 3 = -Å −1 as in the case of the NH 3 -surface system. Moreover, the Rashba splitting of the unoccupied state is reduced to k 0.08 SO NH induced,unocc 3 = -Å −1 , which coincides with the value obtained for the clean surface. This observation leads to the conclusion that for the physisorbed NH 3 on the BiAg 2 /Ag(111) surface the increased Rashba splitting of its unoccupied surface state is related to an interfacial charge rearrangement due to the Pauli repulsion effect as indicated by the charge density difference plot shown in figure 4(a).  (111), (d) the NH 3 -induced clean surface geometry and (e) the BH 3 -induced clean surface geometry. The orbital character of the electronic states for a contribution larger than 8% for the surface layer atoms is indicated as follows: s (black), p x (red), p y (green) and p z (blue). 3 We also note in passing that in general the dispersion of the Rashba split surface states is slightly anisotropic in the k-space but a detailed analysis of this feature of the calculated band structures for both molecule-surface systems is beyond the scope of this study.
In case of the BH 3 -induced geometry, the band structure displayed in figure 3(e) indicates that the occupied Rashba split surface state is also moved into the projected Ag bulk states as already noticed for the moleculesurface system. Surprisingly, this observation implies that for the chemisorbed BH 3 on BiAg 2 /Ag(111) this shift of the occupied Rashba split surface state is predominantly a geometrical effect related to the significant inward relaxation of the Bi atoms. Besides this, as in the case of the NH 3 -induced surface geometry, the unoccupied Rashba split surface state also shows a reduced splitting of the size of k 0.08  figure 4(b), this behavior is essentially related to a hybridization effect due to the mixing of the molecule and surface electronic states.
As already discussed in literature [20,38], the clean BiAg 2 /Ag(111) surface is described by an anisotropic 2DEG characterized by an asymmetric out-of-plane potential as well as an in-plane structural inversion asymmetry (SIA) leading to a strong enhancement of the Rashba effect compared to that measured for Au(111) [16]. In particular, in contrast to the Rashba model that favors an in-plane spin polarization of the surface states, an asymmetric in-plane surface potential gradient due to SIA determines also a sizeable out-of-plane spin polarization P z [20]. In contrast to the small out-of-plane polarization P z of the clean surface (see figures 5(a) and (b)), our first-principles calculations indicate that both physisorbed NH 3 and chemisorbed BH 3 molecules considered in our study can specifically enhance the asymmetry of the in-plane surface potential and therefore they can tune the magnitude of P z of the corresponding hybrid molecule-surface systems. More specifically, in the case of NH 3 /BH 3 on BiAg 2 /Ag(111) this effect is illustrated for the surface Bi and Ag atoms in figures 5(c) and (d)/(e) and (f), respectively. Interestingly, a quantitative analysis of the out-of-plane spin polarization along the M G and K G directions for the occupied states of the BH 3 -BiAg 2 /Ag(111) system revealed that P 70% z BH 3  (see figure 5(f)) while the in-plane one P 50% of the clean surface [20], our ab initio results suggest that indeed a weakly chemisorbed molecule can be employed to change the dominant in-plane spin polarization of the clean surface to out-ofplane for the hybrid system. Note that in the case of the physisorbed NH 3 molecule on BiAg 2 /Ag(111), P 20% z NH 3  (see figure 5(d)) and P 65% xy NH 3  (see figure 5(c)) for the occupied states. To summarize, in this theoretical study we demonstrated that for the BiAg 2 /Ag(111) surface alloy the fingerprint features of its Rashba spin-split surface states can be specifically modified via physisorbed as well as chemisorbed inorganic molecules. More precisely, the physisorbed NH 3 on BiAg 2 /Ag(111) induces an increase of the outward buckling of the surface Bi atoms that in turn strengthens the Rashba splitting of the occupied surface state (i.e., it is a geometrical effect) while the Rashba splitting of the unoccupied one is enlarged due to the molecular-induced weak interfacial charge reordering (i.e., it is a Pauli repulsion effect). On the other hand, the weakly chemisorbed BH 3 leads to an inward relaxation of the Bi atoms such that the occupied Rashba spin-split surface state is shifted in the projected Ag bulk states. Interestingly, the interaction of BH 3 with BiAg 2 /Ag(111) also determines an additional spin splitting of an unoccupied surface state that for the clean surface was not Rashba spin split by SOC.  figure 2 by dashed lines. Note that the weak charge rearrangement at the NH 3 -surface interface due to the Pauli repulsion is a fingerprint for a physisorption bonding mechanism. In contrast, the BH 3 -surface system exhibits a significant charge rearrangement typical for chemisorption that especially involves a charge gain in the p z atomic-like state of boron. 4 For the BH 3 -induced geometry the calculated band structure indicates that P 50% Finally, a striking outcome of our first-principles study is that both molecule-BiAg 2 /Ag(111) systems induce a tunable out-of-plane spin-polarization P z normal to the surface. In this regard it is important to note that for the BH 3 -BiAg 2 /Ag(111) system the magnitude of the out-of-plane spin polarization P z is larger than the inplane one. To conclude, our ab initio results are the first and necessary step to unveil how physisorbed as well as chemisorbed inorganic molecule-surface systems can be designed to rationally modify specific properties such as the orientation of the spin polarization for a fine control of the spin transport in spintronics devices.
Acknowledgments SB, NA and VC gratefully acknowledge financial support from the Volkswagen-Stiftung through the 'Optically Controlled Spin Logic' project and by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 1238 (Project C01). The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN [39] at Jülich Supercomputing Centre (JSC). GCS is Figure 5. (a) The in-plane P xy and (b) out-of-plane P z spin polarization as defined in [21] for the clean BiAg 2 /Ag(111) surface modeled by a symmetric slab. (c) The in-plane P xy and (d) out-of-plane P z spin polarization for the NH 3 -BiAg 2 /Ag(111) hybrid system. (e) The in-plane P xy and (f) out-of-plane P z spin polarization for the BH 3 -BiAg 2 /Ag(111) hybrid system. Note that the out-of-plane P z for BH 3 -BiAg 2 /Ag(111) is significantly larger than the in-plane P xy one or as compared to the clean surface case. The large out-of-plane spin polarization of the second unoccupied surface state of the NH 3 -BiAg 2 /Ag(111) system close to G will not be considered here as in terms of transport experiments it is too far away from the Fermi energy. Red (blue) represents a positive (negative) spin magnetization larger than 2% and the size of the symbols is proportional to the magnitude of the calculated spin polarization. the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF). The authors gratefully acknowledge the computing time granted by the JARA-HPC Vergabegremium and VSR commission on the supercomputer JUROPA/JURECA [40] at Forschungszentrum Jülich.