First-principles Study of Rashba Spin Splitting at Strained SrTiO3(001) Surfaces

We investigated the Rashba spin splittings in a compressive-strained SrTiO$_3$(001) ultra thin-film using first-principles calculations. The effect of the polarization due to the compressive strain leads to the 2DEG with large Rashba spin splittings, where the sheet carrier density is of the same order of magnitude as that of the heterostructure LaAlO$_3$/SrTiO$_3$ ($\sim10^{14}$ cm$^{-2}$). Some localized surface states (SSs) show the giant Rashba coefficient $\alpha_R$ larger than 100 meV$\cdot$\AA.


I. INTRODUCTION
Spin-to-charge conversion enables spin current to change charge current, and its phenomenon owing to the Rashba effect [1], that is, the inverse Rashba-Edelstein effect (IREE) [2,3] was observed at the n-type interface in the heterostructure LaAlO 3 /SrTiO 3 [4]. In a twodimensional electronic system with the spatial inversion symmetry breaking, the Rashba effect occurs and induces spin splittings. As the Rashba coefficient α R , the strength of the Rashba effect, becomes larger, the efficiency of the IREE may become higher [2]. In our previous study for the LaAlO 3 /SrTiO 3 , we found the possibility of large Rashba spin splittings at the oxide surfaces or interfaces due to the strain effects which may control the polarity [5].
The bulk SrTiO 3 has the strain-induced polarization, through which the strain can control the polarity [6], and therefore an SrTiO 3 surface with the strain-induced polarization is a promising candidate for large Rashba spin splittings. Actually, for the SrTiO 3 (001) surface, the Rashba spin splitting is so small that the k-cubic term is more dominant than k-linear term [7], while there is ferroelectric surfaces such as a BaTiO 3 surface [12,13], a compressive-strained SrTiO 3 (001) surface is also expected to have 2DEG as well as larger Rashba spin splittings.
In this paper, we investigated the 2DEG and Rashba spin splittings in a compressive-strained SrTiO 3 (001) ultra thin-film using first-principles calculations. The effect of the polarization due to the compressive strain induces the 2DEG with large Rashba spin splittings. Some localized surface states (SSs) can lead to the giant Rashba coefficient α R larger than 100 meV·Å.

II. COMPUTATIONAL
Our calculations were done by using OpenMX code [14], which implements density functional theory within the generalized gradient approximation (GGA) with PBE exchange correlation functional [15]. We adopted normconserving pseudopotentials with an energy cutoff of 300 Ry for charge density, including the 4s, 4p, and 5s for Sr; 3s, 3p, 3d, and 4s for Ti; 2s and 2p for O. In order to consider the spin splitting, the spin-orbit interaction was taken into account by a treatment of fully relativistic total arXiv:1807.07050v2 [cond-mat.mtrl-sci] 5 Aug 2018 2 angular momentum dependent pseudopotentials [16]. We used a 24 × 24 × 1 regular k -point mesh. The numerical pseudo atomic orbitals are as follows: the numbers of the s-, p-, and d -character orbitals are 3, 3, and 2, respectively, for Sr; 3, 3, and 2, respectively, for Ti; 3, 3, and 1, respectively, for O. We also used the effective screening medium (ESM) method to eliminate the dipole-dipole interaction between slab models [17].
Our computational models are slab models of a superlattice (SrTiO 3 ) n+0.5 with homogeneous SrO or TiO 2 terminated surfaces an experimental lattice constant of a 0 = 3.905Å [18]. We assumed the compressive strain (a 0 − a)/a, where a denotes the in-plane lattice constant.
The initial atomic configurations before the structural optimization are based on those of bulk SrTiO 3 with the compressive strain inducing the polarization.

III. RESULTS AND DISCUSSION
We found the stable atomic configuration with the metallic SSs, and confirmed that the 2DEG emerges when the polarization breaks the spatial inversion symmetry along the surface-perpendicular direction (z-axis, hereafter), that is, the polarization is nonzero. The effect of the polarization induces the 2DEG through the charge transfer, and actually it was reported that BaTiO 3 (001) surface has 2DEG by the similar mechanism [12,13].
First, for the SrO terminations, we investigated the case where metallic SSs appear. As shown in Fig. 1, as the number of layers in the model (or formula units n) or strain increases, the metallic SSs tend to be appear.
There are differences between the symmetry of the system in real space with and without metallic SS: The symmetric atomic configurations and atom-projected density of states (ADOS), or asymmetric ones. By analyzing the ADOS shown in Fig. 2, we confirmed that in the asymmetric case there are metallic SSs (Fig. 2(a)), while only insulating states exist in the symmetric case ( Fig. 2(b)).
The metallic SSs mainly consist of O-2p bands at one surface (p-type) and Ti-3d bands at the other (n-type).  Fig. 3(b). Our previous study about Bi/M surface alloys (M = Cu, Ag, Au, Fe, Co, Ni) implied that the localization of SSs may enhance α R [22].
A theoretical work [23] suggested an expression for α R : and assymetric charge density give finite α R . The electrons in more localized SSs feel a stronger electric field on atomic sites, which may make α R larger.

IV. CONCLUSION
We have performed first-principles density functional MEXT as a social and scientific priority issue (Creation of new functional devices and high-performance materials to support next-generation industries) to be addressed using the post-K computer (Project ID: hp170269). [