Unoccupied surface and interface states in Pd thin films deposited on Fe/Ir(111) surface

We present a systematic first-principles study of the electronic surface states and resonances occuring in thin films of Pd of various thicknesses deposited on a single ferromagnetic monolayer of Fe on top of Ir(111) substrate. This system is of interest since one Pd layer deposited on Fe/Ir(111) hosts small magnetic skyrmions. The latter are topological magnetic objects with swirling spin-textures with possible implications in the context of spintronic devices since they have the potential to be used as magnetic bits for information technology. The stabilization, detection and manipulation of such non-collinear magnetic entities require a quantitative investigation and a fundamental understanding of their electronic structure. Here we investigate the nature of the unoccupied electronic states in Pd/Fe/Ir(111), which are essential in the large spin-mixing magnetoresistance (XMR) signature captured using non spin-polarized scanning tunnelling microscopy [Crum et al., Nat. Commun. {\bf 6} 8541 (2015); Hanneken et al., Nat. Nanotech. {\bf 10}, 1039 (2015)]. To provide a complete analysis, we investigate bare Fe/Ir(111) and Pd$_{n=2,7}$/Fe/Ir(111) surfaces. Our results demonstrate the emergence of surface and interface states after deposition of Pd monolayers, which are strongly impacted by the large spin-orbit coupling of Ir surface.


I. INTRODUCTION
Understanding the surface electronic structure is one of the key ingredients for designing and developing new functionalities in information technology. Recently, it was demonstrated that the electronic states residing on a surface hosting non-collinear magnetic states can give rise to a large magnetoresistance effect, which was coined the spin-mixing magnetoresistance (XMR) effect [1] or non-collinear magnetoresistance (NCMR) [2]. The current flow between the substrate and a non-magnetic electrode was found to depend strongly on the spinmixing induced by the misalignment of the magnetic moments and on the presence of spinorbit interaction in the probed magnetic electrode. This effect is thus different from the giant magnetoresistance (GMR) [3,4] or tunneling magnetoresistance (TMR) effects [5], requesting two magnetic electrodes during measurements.
While the surface state of clean fcc-Ir(111) substrate is occupied [26], it is unoccupied in fcc-Pd(111) [25]. This aspect is interesting since Ir and Pd are neighbors in the periodic table. In fact, if one exchanges Ir with another neighboring element from the periodic table being valence-isoelectronic to Pd, e.g. Pt, the unoccupied surface state is restored at 0.5 eV above the Fermi energy [30,31]. Because of the weaker ionic potential of Pd compared to that of Pt, the unoccupied surface state of the former is located at a higher energy (1.3 eV) [25]. The system Pd/Fe/Ir(111) provides the playground to investigate how the interplay of interface and confinement effects with magnetism, inducing a spin-dependent shift of the potential, affects the aforementioned surface electronic features.
By depositing Pd on top of the ferromagnetic Fe grown on Ir(111) surface and by focusing 2 our first-principles study on the unoccupied states related to the observed large XMR effect, we find interface states confined within PdFeIr interfaces besides an unoccupied surface state of Pd. The latter is demonstrated by observing its stability upon the increase of the thickness of Pd films. We analyze the impact of SOI and find that it can project into a given spin-channel, confined states originally living in the opposite spin-channel.
The article is structured as follows. First, we describe the methodology and the computational details followed for the simulations then present our results and discussions. Previous experimental studies have shown the possibility of growing Pd in either hcp-or fcc-stacking on top of fcc-Fe/Ir(111) surface [2,14]. As shown in Refs. [10], there are differences in the electronic structure between these two stacking leading to a shift of the unoccupied electronic features. To make our study concise, we focus here on the fcc-stacking of Pd as a follow up of our previous study [1]. We address initially the two-dimensional Bloch spectral function of fcc-Pd/Fe/Ir(111) surface and discuss the nature of the different unoccupied states showing high intensity at Γ, the center of the two-dimensional Brillouin zone. By investigating the case of bare fcc-Fe/Ir(111) surface, which was shown to host a lattice of skyrmions in its ground state [32][33][34], and considering thicker Pd films deposited on that surface, we aim at distinguishing the states stemming from Pd. Our conclusions are summarized in the last section.

II. METHOD
We use the full-potential Korringa-Kohn-Rostocker Green function method [35] including SOI as implemented within density functional theory. The exchange and correlation effects are treated in the local spin-density approximation as parametrized by Vosko, Wilk and Nusair [36]. We consider slabs of 44 layers to model the ferromagnetic Pd nMLs /Fe/Ir(111), we have considered a semi-infinite Ir (111) substrate using the decimation technique [37,38] to avoid any size effect that can blind our conclusions. Also, we have performed singleshot calculations without spin-orbit coupling in order to assess its effect on the k-dependent density of states. In the discussion focusing on the unoccupied states, all energies shown are positive and given with respect to the Fermi energy.  The decay of a state into vacuum is k-dependent and approximately proportional to e − 2m 2 +k with being the state's energy given with respect to the height of the potential barrier [40]. Therefore, it is expected that the states contributing most to the STM spectra are close to the center of the Brillouin zone, which motivates the focus of our following discussion on the surface-projected band structure at the Γ point. Indeed, one notices that away from Γ, the electronic states experience a strong decay into the vacuum. For the Fe ML ( Fig. 3 (b)), the most intense unoccupied minority-spin bands are located substrate [30,31]. This contrasts with the other intense states, which are of resonant nature since they live in a"sea" of surface-projected bulk-bands. substrate's orbitals provide the best matching to the vacuum's symmetry, which is invariant to rotations normal to the surface [41].

Minority
In order to unveil the origin of these states, we provide in Fig. 4  with respectively 80% and 70% of their total amplitude in IrFePd trilayer as can be seen in Fig. 5 Once more, this is explained by their orbital nature, which dictates the tunneling amplitude. degenerate bands at 1.34 eV get splitted by nearly 0.2 eV due to the large spin-orbit coupling introduced by the Ir substrate (see also Fig. 5(b)). As mentioned earlier, these states stem mainly from Ir and Fe hybrid states. Thus, SOI allows to promote an initially resonant state into an interface state at the edge of the gap of the surface-projected band structure.
A similar behavior can be observed for bare Fe/Ir(111) surface by comparing Fig. 6(a) to Fig. 6(b). The band at 1.34 eV splits by approximately the same amount obtained for Pd/Fe/Ir(111). Also, the band at 0.68 eV in Pd/Fe/Ir(111) obtained when including SOI seems to be the result of the splitting of the band originally present at 0.64 eV without SOI (compare Fig. 3(b) with Fig. 6(b)). This can be better seen in Fig. 5(a). The splitting is about 0.1 eV, which indicates that the SO-driven splitting is state dependent. Note that in this region Pd states contribute a lot and since Pd is lighter than Ir, a lower impact of SOI is expected.
Majority-spin channel. Here is it interesting to look at the band structure of Pd/Fe/Ir (111) surface first when SOI is switched off (Fig. 7). Only one intense unoccupied resonant state is found at Γ point around 0.41 eV. This state is attributed mainly to the hybridization of p z and d z 2 orbitals of Fe and Pd, and therefore has the right symmetry to survive across the vacuum (see Fig. 7(d)).
By switching on SOI (Fig. 3(e-g), all the bands get pushed to higher energies and one notices the appearance of other surface and resonant states at the Γ point. We distinguish two surface states located within the band gap of the surface-projected band structure with energies 1.27 eV and 1.45 eV. Similarly to what has been predicted in half metals [42], these two states originate from the minority-spin channels (see previous discussion) and are projected via SOI into the majority-spin channel. As mentioned above they originate from the hybridization of d xz and d yz orbitals of Ir and Fe.
The SOI-driven projection mechanism can be grasped by recalling the first order effect of SOI on the electronic structure. The off-diagonal elements of spin-orbit potential in the spinor basis Even in an energy window initially without majority-spin states, a component of the spinor gets finite after solving the previous equation in first-order (therefore the index (1)): Thus a weak image of the band structure of the minority-spin channel can be realized in the majority-spin channel (and vice-versa). A quadratic dependence with respect to SOI is expected since the LDOS is related to |Ψ| 2 . As can be seen from the denominator of Eq.3, the weight of the states will be enhanced close to those k-points where the unperturbed spin-dependent bands cross.
In addition to the aforementioned surface states we note the presence of resonant states To complete our analysis, we increased the number of Pd layers deposited on the substrate.
With this, we explore the stability of the features observed with a single Pd overlayer. Also, this allows to better identify the electronic states that belong to Pd and neither to Fe nor to Ir. We note that Fe/Ir(111) covered with Pd films thicker then the so-far discussed single Pd ML can host magnetic skyrmions as already demonstrated for Pd 2MLs /Fe/Ir(111) [1,2,10]. When increasing the thickness of Pd films, the XMR signal detecting the presence of magnetic skyrmions will then be mostly coming from the Pd layers. Interestingly, the surface-projected band structure of Pd films plotted in Fig. 8 bears several similarities to that of the single Pd-overlayer. For instance, the minority-spin interface resonant state originating from hybridization of the electronic states of Pd and Fe at the Γ point located at 0.68 eV in the single Pd overlayer seems to shift to a higher energy, around 1 eV and stays there independently from the thickness of Pd. Contrary to the former, the latter state is insensitive to the presence of SOI and becomes a surface state that lies in the band gap of the surface-projected band structure when the number of Pd layers on Fe/Ir(111) substrate is greater than 2. Furthermore, we notice that the position of this state is very similar to the one of the surface state of Pd(111) surface located at 1.3 eV as measured by angle-resolved photoemission [25]. Moreover, we note that the states found at 1.27 eV and 1.45 eV in Pd/Fe/Ir(111) survive at the IrFePd interface even for thicker Pd films but, and as expected, their intensity on the Pd surface decreases strongly. These states are located either in the minority-spin or in the majority-spin channel. We investigated their origin and characterized their orbital nature, which dictate the tunneling matrix elements requested in transport experiments based on STM and, thus, are important for the recently discovered XMR-effect.
We found that the spin-orbit coupling of the Ir substrate not only splits some of these states but also shift them while modifying the curvature of the bands, which affect the electron effective mass and therefore the decay of the states in the vacuum. Interestingly the spin-orbit interaction projects some of the resonant states of the minority-spin channel to the energy-band gap of the majority-spin channel, promoting them then to interface states.