Spin-split bands of metallic hydrogenated ZnO $( 10 1 ¯ )$ surface: First-principles study

Recent developments in spintronics rely on new pathways for exploiting carrier spins in semiconductors without magnetic materials or external magnetic fields, primarily by utilizing the effect of spin orbit interactions (SOIs).^1–3 This method is promising because the SOI enables the generation and manipulation of electron spin solely through an external electric field. Current-induced spin polarization⁴ and the spin Hall effect⁵ are important examples of spintronics phenomena, where the SOI plays an important role. Especially the Rashba effect⁶ attracted much attention for the important role it plays in spintronics device operations such as the spin-field effect transistor (SFET).⁷ 

The Rashba effect has been widely studied on a variety of metal surfaces^8,9 and in ultrathin metal^10,11 films exhibiting large spin splitting. However, the functionality of such systems as spintronics devices is limited by spin-degenerate bulk currents induced by metallic substrates On the other hand, the discovery of the Rashba effect on the surfaces of semiconductors such as Bi/Si(111),^12–14 Bi/Ge(111),¹⁵ Ti/Si(111),^16,17 and Pt/Si(111)¹⁸ shows non-metallic spin-split bands that contribute only little to spin transport. For spintronics applications, metallic surface-state bands are required to induce significant spin transport. Therefore, it is highly desirable to establish semiconductor surfaces exhibiting metallic spin-split bands.

The ZnO wurtzite structure is a promising candidate material for spintronics since the high quality of the two-dimensional electron gas system has been experimentally observed,¹⁹ and it exhibits large carrier concentration and high carrier mobility.²⁰ In a past study, we have found that the Rashba splitting is observed in the bulk and surface systems of ZnO.^21,22 Furthermore, it was reported that a metallic surface-state is observed^23,24 when a ZnO (⁠$10 1 ¯ 0$⁠) surface is hydrogenated, indicating that this system can produce significant spin transport. On the other hand, the ZnO (⁠$10 1 ¯ 0$⁠) surface is energetically stable as the electrostatic instability of two polar surface terminations^25,26 can be avoided. Therefore, for spintronics applications, it is crucial to investigate the spin-split band of metallic hydrogenated ZnO (⁠$10 1 ¯ 0$⁠) surface.

In this paper, we use first-principles density-functional theory (DFT) calculations to show that spin-split bands are achieved using a metallic hydrogenated ZnO (⁠$10 1 ¯ 0$⁠) surface. We find that a metallic surface-state band with dominant Zn-s and p orbitals shows Rashba spin splitting with strong anisotropic character. We also find that these spin-split bands have Rashba-like spin spin textures exhibiting small out-of-plane spin components. We determine the origin of these spin textures by using a simplified Hamiltonian derived from the group theory and provide further analyses by evaluating the electric polarization around the surface.

First-principles electronic-structure calculations based on the DFT were carried out within a generalized gradient approximation (GGA)²⁷ using OpenMX code.²⁸ In our past study, it was found that the optimized lattice parameters of bulk wurtzite ZnO are a = 3.284 Å and c/a = 1.615,²¹ where a and c are the in-plane and out-of-plane lattice constant, respectively. Surface calculations were carried out by using a slab model consisting of 20-bilayers with a thickness of 56.88 Å [Fig. 1(a)]. The vacuum length was set to be more than 15 Å in order to avoid interactions between neighboring slabs. In the hydrogenated surface systems, the binding energy of hydrogen termination on the surface was calculated by using the relation²⁹ 

where E_Tot(surf + H), E_Tot(surf), and E_Tot(H) are the total energies of surfaces with H atoms, clean surfaces, and isolated H atoms, respectively, and N(H) is the number of H atoms in one supercell. We fully relaxed these structures until the force acting on each atom was less than 1 meV/Å. In our DFT calculations, norm-conserving pseudo-potentials³⁰ were used. The wave functions were expanded by a linear combination of multiple pseudo-atomic orbitals (LCPAOs), which were generated using a confinement scheme,^31,32 defined as Zn6.0-s²p²d², O5.0-s²p²d¹, and H5.0-s²p¹. For example, in the case of a Zn atom, Zn6.0-s²p²d² means that in this confinement scheme the cutoff radius is 6.0 Bohr^31,32 and two primitive orbitals for the s, p, and d components are used. SOI was included in these fully relativistic calculations, and the spin textures in k-space of the surface Brillouin zone [Fig. 1(b)] were calculated using the k-space spin density matrix of the spinor wave function.³³ 

First, we investigate the stability of the relaxed geometry. In the ZnO (⁠$10 1 ¯ 0$⁠) surface, one of the nearest-neighbor bonds in the fourfold coordination of the Zn and O atoms is broken. Therefore, it is expected that H atoms saturate the two dangling bonds during hydrogenation. Previous experimental studies have found that there are two types of energetically stable hydrogen chemisorption:²³ (i) H atoms are adsorbed on both the Zn and O sites forming a ZnO(⁠$10 1 ¯ 0$⁠)-2H surface, and (ii) H atoms are adsorbed only on the O sites forming a ZnO(⁠$10 1 ¯ 0$⁠)-H surface. Here, we find that both ZnO(⁠$10 1 ¯ 0$⁠)-2H and ZnO(⁠$10 1 ¯ 0$⁠)-H surfaces are energetically stable with the binding energies of 3.75 and 3.15 eV per H atom, respectively. In the case of a clean surface, we find that the length of Zn-O bond in the uppermost surface along the [0001] direction is 1.883 Å, which is smaller than in bulk system (1.954 Å) [TABLE I]. However, this bond lengthens to 2.162 Å and 2.132 Å   for ZnO (⁠$10 1 ¯ 0$⁠)-2H and ZnO (⁠$10 1 ¯ 0$⁠)-H, respectively, under hydrogenation.

Because of the in-plane and out-of-plane atomic relaxation at the surface, the Zn-O dimer tilts from the surface plane. As shown in Table I, in the case of the ZnO(⁠$10 1 ¯ 0$⁠)-2H surface, we find that relaxation of the Zn and O atoms in the in-plane direction is 0.15 Å and -0.11 Å, respectively, while it is found to be -0.31 Å and -0.045 Å, respectively, in the out-of-plane direction. These values are larger than those of clean surface [Δy(Zn) = 0.19 Å, Δy(O) = -0.03 Å; Δz(Zn) = -0.28 Å, Δz(O) = -0.035 Å ]. In contrast, in the case of ZnO(⁠$10 1 ¯ 0$⁠)-H surface, in-plane atomic relaxation reduces [Δy(Zn) = 0.07 Å, Δy(O) = -0.045 Å ], whereas out-of-plane atomic relaxations increases [Δz(Zn) = − 0.37 Å, Δz(O) = -0.069 Å ]. Therefore, it can be concluded that hydrogenation significantly changes the surface geometry.

Because the surface geometry is strongly affected by hydrogenation, it is expected that the electronic structure be strongly modified. In the case of ZnO (⁠$10 1 ¯ 0$⁠)-2H surface, we find that the band structures resemble those of an insulator with a significant band gap [Fig. 2(b)], similar to those of the clean surface [Fig. 2(a)]. However, in the case of ZnO (⁠$10 1 ¯ 0$⁠)-H surface, the band structures show a metallic character, where the surface states bands across the Fermi level [Fig. 2(c)]. We calculated the partial density of states (PDOS) projected onto the surface atoms and confirmed that in the case of a clean surface, the unoccupied states mainly originate from the Zn-s and p orbital, while the occupied ones originate from the O-p orbital [Fig. 3(a)]. However, in the case of ZnO(⁠$10 1 ¯ 0$⁠)-H surface, an odd number of electrons are transferred from hydrogen atoms to the surface, leading to the partially filled electronic states.^23,29 As a result, strong hybridization between H-s and O-p orbitals is introduced, which shifts the position of O-p orbitals to be lower energy. Consequently, metallization is induced where the surface states at the Fermi level are predominately filled by Zn-s and p orbitals [Fig. 3(c)]. On the other hand the system changes to an insulating state when all dangling surface bonds are saturated by hydrogen atoms. This is because the excess charge electron at the surface is transferred to a surface Zn ion, forming a new, stable Zn-H bond.³⁴ This is confirmed by our calculated PDOS, where the occupied states are predominately filled by the orbitals character of H-Zn bond atoms, while the unoccupied ones remains unchanged [Fig. 3(b)].

Next, we study the effect of SOI on hydrogenated surface systems. Here, we focus on the metallic surface-state bands of the ZnO (⁠$10 1 ¯ 0$⁠)-H surface. As shown in Fig. 4(a), a substantial Rashba splitting is observed in the surface states along the $Γ ¯$-$X ¯$ direction, whereas it is extremely small in the $Γ ¯$-$Y ¯$ direction, indicating that the Rashba splitting is strongly anisotropic. We find strongly localized spin textures where the out-of-plane S_z component of spin is small [Fig. 4(b)], while the [Fig. 4(c)-4(d)]. Our calculations of the atomic spin decomposition confirm that these localized spin textures mainly originate from the contribution of Zn atoms in the first surface bilayer [Fig. 4(e)], which is consistent with the result of the PDOS.

To understand the origin of spin textures, we consider SOI of surface states based on group theory.^35–38 In our past study, we clarified that the ZnO (⁠$10 1 ¯ 0$⁠) surface belongs to the symmetry point group C_s, where the mirror reflections in operation in this symmetry transform (x, y, z) to (−x, y, z).²² In this case, SOI can be expressed as²² 

where k_x and k_y are the wave vectors in the x and y directions, respectively; σ_x, σ_y, and σ_z are Pauli matrixes; and α₁, α₂, and α₃ are coupling constants that define the spin-orbit strength. Here, α₁ is characterized by the in-plane electric field E_y because of the polarity of the present system, whereas α₂ and α₃ relate to the out-of-plane electric field E_z that originates from the surface effect.

In the case of hydrogenated surface systems, the Hamiltonian [Eq. (2)] unchanged since the mirror symmetry plane M is invariant [Fig. 1(a)]. However, the contribution of the electric field to the spin-orbit strength (α₁, α₂, and α₃) may differ from those of the clean surface. This is because atomic relaxation induced by the formation of stable O-H and Zn-H bonds strongly affects to the electric polarization at the surface. In fact, Deinert and coworkers²⁴ predicted that interaction of H atoms with ZnO(⁠$10 1 ¯ 0$⁠) surface leads to the change of normal and lateral electrostatic surface potential.

In the case of ZnO (⁠$10 1 ¯ 0$⁠)-2H surface, we observed an increase of surface atomic relaxation in the in-plane and out-of-plane directions, which in turn leads to an increase of the electric polarizations and fields in both in-plane and out-of-plane directions. Conversely, we observed a decrease of surface atomic relaxation on the ZnO (⁠$10 1 ¯ 0$⁠)-H surface in the in-plane direction but an increase in the out-of-plane direction. Consequently, the electric field becomes small in the in-plane direction, while it enhances in the out-of-plane direction. As a result, large band splitting is observed in the $Γ ¯$-$X ¯$ direction due to the first and second term of Eq. (2) [Fig. 4(a)] but the out-of-plane S_z component of spin becomes small [Fig. 4(b)], due to the first term in Eq. (2). It can therefore be concluded that the above spin-orbit Hamiltonian of the surface state accurately describes the calculated results.

Since the spin textures are strongly localized at the first two bilayers [Fig. 4(e)], it is expected that the electric polarization be strongly localized at the surface region. To confirm this, we calculate the layer-dependence of the electric polarization by using a point charge model (PCM) for Zn²⁺ and O²⁻ ions in every bilayer. The polarization difference relative to the ideal surface system is expressed by^21,22

where c/a and u are the lattice constant ratio and internal parameter for a given optimized structure, respectively, and u_ideal = 0.375.

As shown in Fig. 5, strong electric polarization is identified near the first bilayer. In the case of ZnO (⁠$10 1 ¯ 0$⁠)-2H surface, we find that the electric polarization in the in-plane ΔP_y and out-of-plane ΔP_z directions are -0.115 C/m² and 0.102 C/m², respectively, which are larger than those of clean surface [-0.08 C/m² and 0.07 C/m²].²² The larger value of the in-plane electric polarization ΔP_y indicates that the electric field in the in-plane direction E_y is enhanced, which is expected to induce a large out-of-plane S_z component of the spin. In contrast to the ZnO (⁠$10 1 ¯ 0$⁠)-2H surface, in-plane electric polarization ΔP_y decreases on the case of ZnO (⁠$10 1 ¯ 0$⁠)-H surface [ΔP_y = -0.03 C/m²], resulting in small out-of-plane S_z component of the spin [Fig. 4(b)]. This shows that the spin textures in Figs. 4(b)-4(d) are well explained by the PCM.

Thus far, we have found that hydrogen termination on the ZnO (⁠$10 1 ¯ 0$⁠) surface induces a Rashba effect with a strong anisotropic character. Here, we find that the Rashba coupling parameter (α_R) has some substantial values, estimated from the band dispersion in Fig. 4(a). The calculated value of α_R in the $Γ ¯$-$X ¯$ direction is 5.23 meVÅ, which is 11 times larger than that in the $Γ ¯$-$Y ¯$ direction (0.47 meVÅ). This value is smaller than that of recently reported Rashba materials, i.e., BiTel (α_R = 3.8 meVÅ)³⁹ and GeTe (α_R = 4.9 meVÅ).⁴⁰ However, due to the metallicity of the present system, a more significant spin transport can be expected, which enhances the functionality for spintronics device applications. Furthermore, the strong anisotropic character of Rashba splitting predicted in the present study should ensure that carriers have an extended spin lifetime,^41–43 which is promising for energy-saving spintronics devices.²² Therefore, this finding opens a possibility to realized spintronics devices using oxide electronic surface materials.

In conclusion, we have studied the spin-split band of metallic hydrogenated ZnO (⁠$10 1 ¯ 0$⁠) surface with first-principles DFT calculations. We found that a metallic surface-state band with a dominant Zn-s and p orbitals exhibits Rashba spin splitting with a strong anisotropic character. We also found that these spin-split bands have Rashba-like spin textures. Recently, hydrogenated surface systems were extensively studied.^23,24,29 Our calculation study clarified that hydrogenation on surface systems plays an important role in SOI.

This work was supported by Kanazawa University SAKIGAKE Project. Part of this research was funded by the MEXT HPCI Strategic Program. This work was partly supported by Grants-in-Aid for Scientific Research (Nos. 25390008, 25790007, 25104714, 26108708, and 15H01015) from the Japan Society for the Promotion of Science (JSPS). The computations in this research were performed using the supercomputers at the Institute for Solid State Physics (ISSP) at the University of Tokyo.