DOI: 10.1002/ admi.201400445Full Paper

Giant switchable Rashba effect in oxide heterostructures

Zhicheng Zhong*, Liang Si, Qinfang Zhang, Wei-Guo Yin, Seiji Yunoki and Karsten Held

Dr. Zhicheng Zhong, Mr. Liang Si, and Prof. Karsten HeldInstitute of Solid State Physics, Vienna University of Technology,A-1040 Vienna, AustriaE-mail: Zhicheng.Zhong@ifp.tuwien.ac.at

Prof. Qinfang Zhang Key Laboratory for Advanced Technology in Environmental Protection of Jiangsu Province, Yancheng Institute of technology, China

Prof. Wei-Guo YinCondensed Matter Physics and Materials Science Department, Brookhaven National, Laboratory, Upton, New York 11973, USA

Prof. Seiji YunokiComputational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-I0198, JapanComputational Materials Science Research Team, RIKEN Advanced Institute for Computational Science (AICS), Kobe, Hyogo 650-0047, JapanComputational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan

Keywords: oxide heterostructures, spin orbit coupling, rashba effect, ferroelectricity

One of the most fundamental phenomena and a reminder of the electron’s relativistic nature is

the Rashba spin splitting for broken inversion symmetry. Usually this splitting is a tiny

relativistic correction. Interfacing ferroelectric BaTiO3 and a 5d (or 4d) transition metal oxide

with a large spin-orbit coupling, Ba(Os,Ir,Ru)O3, we show that giant Rashba spin splittings

are indeed possible and even controllable by an external electric field. Based on density

functional theory and a microscopic tight binding understanding, we conclude that the electric

field is amplified and stored as a ferroelectric Ti-O distortion which, through the network of

oxygen octahedra, induces a large (Os,Ir,Ru)-O distortion. The BaTiO3/Ba(Os,Ru,Ir)O3

1

BNL-107478-2015-JA

heterostructure is hence the ideal test station for switching and studying the Rashba effect and

allows applications at room temperature.

1. Introduction

An electric field control of the spin degree of freedom is the key to spintronics and

magnetoelectrics.[1] In the prototypical spintronic device, the Datta-Das spin transistor,[2] an

electric field tunes the Rashba spin splitting and with that the spin precession frequency. The

precession in turn controls the spin polarized current between two ferromagnetic leads.

Microscopically, the Rashba spin splitting originates from the spin orbit coupling (SOC) in a

two dimensional electron gas (2DEG) with broken inversion symmetry perpendicular to the

2DEG plane.[3,4] It has been observed for metal surfaces,[5,6] semiconductor and oxide

heterostructures,[7-12] and even in polar bulk materials.[13] The Rashba effect splits parabolic

bands into two subbands with opposite spin and energy-momentum dispersions

E±(k)=(ħ2k2)/2m*±αR|k|. Here, m* is the effective mass, k the wave vector in the 2DEG plane,

and αR the Rashba coefficient which depends on the strength of SOC and inversion

asymmetry. An electric field modulates this inversion asymmetry and consequently the

Rashba spin splittings. The electric-field induced change of αR is however very weak: up to

10-2 eVÅ in semiconductor[7] or 3d transition metal oxide heterostructures.[8-10] A large, electric-

field switchable Rashba effects are also much sought-after in the research area of topological

insulators.[14-16]

Giant Rashba effects with αR of the order of 1eVÅ have been reported for metal surfaces, [6] Bi

adlayers[17] and bulk polar materials BiTeI.[13,18] The large αR here relies on the surface or

interface structural asymmetry, which hardly changes in an external electric field. To enhance

the tunability by an electric field, Di Sante et al. [19] hence suggested a ferroelectric

semiconductor GeTe and Kim et al. [20] an organic-inorganic hybrid metal. For GeTe, an

external electric field switches between paraelectric and ferroelectric phase, breaking

2

inversion symmetry and tuning on the Rashba spin splitting. At first glance, this perfectly

realizes an electric field control of a giant Rashba effect. However, there is an intrinsic

difficulty: A single material cannot be both, a conductor with large Rashba spin splitting and a

ferroelectric which necessarily is insulating.

In this letter, we propose to realize a giant switchable Rashba effect by heterostructures

sandwiching a thin metallic film of heavy elements in-between ferroelectric insulators, see

Figure 1. The thin film provides a 2DEG with strong SOC, while the inversion asymmetry is

induced by the structural distortion of the ferroelectrics which is switchable by an electric

field. As prime examples, we study heterostructures of transition metals oxides,

Ba(Os,Ir,Ru)O3/BaTiO3. BaTiO3 is a well-established ferroelectric.[21] It has a simple high-

temperature perovskite structure, with Ba atoms at the edges, a Ti atom at the center and the O

atoms at the faces of a cube. Such a structure has an inversion symmetry center at the Ti site.

At room temperature, inversion symmetry is broken since a ferroelectric structural distortion

occurs with a sizable Ti-O displacement zTi-O along one of the cubic axes. BaOsO3 has been

recently synthesized; it is a metallic perovskite with four Os 5d electrons and no sign of

magnetism.[22] It has a perfect lattice match with BaTiO3. Both materials have the same cation,

Ba, which will substantially reduce interfacial disorder during epitaxial growth. For

BaOsO3/BaTiO3 we find an electric-field switchable Rashba spin splitting which is at least

one magnitude larger than the current experimental record.[7-10] The mechanism behind is

nontrivial and summarized in Figure 1. Substituting BaOsO3 by BaIrO3 and BaRuO3 yields a

similar, even somewhat larger effect; the heterostructure can also be further engineered by

varying its thickness and strain.

2. Method

We use density-functional theory (DFT) with generalized gradient approximation (GGA)

potential[23] in the Vienna Ab initio Simulation Package (VASP) [24,25] and fully relax all the

atomic positions, only fixing the paraelectric or ferroelectric symmetries. At zero temperature,

3

the ferroelectric distorted perovskite has the lower GGA energy, but -as in the bulk- the

undistorted paraelectric phase will prevail at elevated temperatures.

Based on the fully relaxed atomic structures, electronic band structures are calculated with the

modified Becke-Johnson (mBJ)[26] exchange potential as implemented in the Wien2k code,[27]

which improves the calculated bandgap of BaTiO3. The SOC is included as a perturbation

using the scalar-relativistic eigenfunctions of the valence states. Employing wien2wannier, [28]

we project the Wien2k bandstructure onto maximally localized Wannier orbitals,[29] from

which the orbital deformation is analyzed and a realistic tight binding model is derived.[30,31]

We also vary the thickness of the thin films, replace the BaOsO3 by BaRuO3 or BaIrO3, and

simulate the strain effect by fixing the in-plane lattice constant to the value of a SrTiO3

substrate. Correlation effects from a local Coulomb interaction are studied in the

Supplementary Material.

2. Results and discussion

2.1. Paraelectric phase

We first consider a (BaOsO3)1/(BaTiO3)4 heterostructure which consists of one BaOsO3 layer

alternating with four BaTiO3 layers. Bulk BaTiO3 is a d0 insulator: the empty Ti 3d states lie

about 3eV above the occupied O 2p states. Bulk BaOsO3 is a d4 metal: four electrons in the Os

5d orbitals of t2g character are 0.8eV above the filled O 2p states. Since BaOsO3 and BaTiO3

share oxygen atoms at the interface, the O 2p states align; and the Os 5d states will stay in the

energy gap of BaTiO3. Hence, the DFT calculated band structures of BaOsO3/BaTiO3 in

Figure 2 shows three Os t2g (xy, yz, xz) bands near the Fermi level; they are dispersionless

along the z direction (not shown). That is, the low energy electronic degrees of freedom are

confined by the insulating BaTiO3 layers to the OsO2 plane, forming a 2DEG. Already in the

high temperature paraelectric phase, this heterostructure confinement reduces the initial cubic

symmetry of the Os t2g orbitals in the bulk perovskite: At Γ the xy band in Figure 2(a) is 1.2eV

lower in energy than the degenerate yz/xz bands. Including the SOC, the yz/xz doublet splits

4

into two subbands with mixed yz/xz orbital character, see Figure 2(b). For the paraelectric

phase of Figure 2(a-c), the spin degeneracy is however still preserved.

To better understand the DFT results, we construct an interface hopping Hamiltonian H0i for

the 2DEG confined Os t2g electrons by a Wannier projection.[30,31] The energy-momentum

dispersion for the xy orbital is ε(k)xy=−2t1coskx−2t1cosky−4t3coskxcosky, while that of the yz is

ε(k)yz=−2t2coskx−2t1cosky (ε(k)yz is symmetrically related by ). The largest hopping t1=0.392eV

is along the direction(s) of the orbital lobes, t2=0.033eV and t3=0.094eV indicate a much

smaller hopping perpendicular to the lobes and along (1,1,0), respectively. The xy–yz/xz

orbital splitting at Γ is 2t1−2t2+4t3=1.1eV and arises from the anisotropy of the orbitals.

Overall, the three parameter tight binding model in Figure 3(a) (dashed line) is consistent

with DFT in Figure 2(a). Next, we include the atomic SOC Hamiltonian Hξ=ξl·s, expressed in

the t2g basis with ξ=0.44eV for Os. It lifts the yz/xz degeneracy and yields good agreement

with DFT, cf. Figure 3(a) (solid line) and Figure 2(b).

2.2. Ferroelectric phase

In sharp contrast to the paraelectric case, ferroelectrically distorted BaOsO3/BaTiO3 exhibits

evident spin splittings in the presence of SOC, see Figure 2(f). Note, in the absence of SOC

the DFT band structure in Figure 2 (e) is still very similar to the paraelectric case in Figure 2

(a). The spin splitting of the xy band is small around Γ, but strongly enhanced up to 50meV

around the xy/yz crossing region as shown in Figure 2(g), cf. Table 1. The other two subbands

of yz/xz character also show a strong splitting around Γ. In this respect, the upper yz/xz

subband exhibits a standard Rashba behavior, see the magnification in Figure 2(h), where the

momentum offset k0=0.043Å, the Rashba energy ER=4 meV, and hence αR=2ER/k0=0.186 eVÅ.

The behavior of the lower yz/xz subband is more complex (distorted) due to the proximity of

the crossing region. A similar structure of the spin orbit splitting as well as a k-cubic splitting

has been reported for other t2g systems before [31-35].

5

These spin splittings arise from ferroelectric distortions which break the inversion symmetry.

Bulk BaOsO3 has no such ferroelectric distortions and is inversion symmetric with Os and O

atom in the same plane. Also for the paraelectric heterostructure, the OsO2 layer is still an

inversion plane. The ferroelectric heterostructure eventually breaks inversion symmetry. As

listed in Table 1, the averaged ferroelectric Ti-O displacement in BaTiO3 layers is around 0.14

Å, which efficiently induces a sizable Os-O displacement of 0.05 Å via the oxygen

octahedron network of the perovskite structure. This structural distortion modifies the crystal

environment of Os t2g orbitals and deforms the orbital lobes, see Figure 1.

In order to quantify the orbital deformation, we project the DFT results above onto maximally

localized Wannier orbitals and directly extract the key parameter: a directional, spin-

independent inter-orbital hopping γ=⟨xy|H|yz(R)⟩, were R is the nearest neighbor in x

direction. In k-space one gets as a matrix for the yz,xz,xy orbitals (independent of spin)(1)

(1)

.[31,32,36] We obtain γ=0.016 eV for the ferroelectric heterostructure, while for the paraelectric

case γ=0 due to inversion symmetry. Let us emphasize that γ is the relevant measure for the

orbital deformation and inversion symmetry breaking. In combination with the strong SOC of

OS 5d electrons, results in the present giant Rashba spin splitting.

The Hamiltonian H0i +Hξ+Hγ

already well describes the spin splittings of the xy orbital in

good agreement with DFT results, but underestimates the spin splittings of the yz/xz subbands

near Γ. The reason for this is that the atomic SOC is not an accurate description anymore

because the SOC of Os is too strong and the deviation from the inversion symmetry too large.

Hence, we need to go beyond the purely atomic SOC and include an inversion asymmetry

correction to the SOC matrix so that Hξ in the t2g basis (yz|↑⟩, yz|↓⟩, xz|↑⟩, xz|↓⟩, xy|↑⟩, xy|↓⟩)

reads

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(2)

For the bandstructure of Figure 3(b) we have taken γ'=0.022 eV from the Wannier projection,

yielding good agreement with the DFT results Figure 2(f).

2.3. Electric-field tunability

The Rashba spin splittings can be switched and tuned by an electric field because of the

ferroelectricity of BaTiO3. It is a nature of ferroelectrics that an external electric field can

reverse the polarization and structural distortion,[17,21,37-39] including that of the BaOsO3 layer.

Because of the BaOsO3 layer, the ferroelectricity of the heterostructure is not as strong as in

bulk BaTiO3; a smaller electric field than in the bulk (E=103V/cm) [39] is needed for going

through the ferroelectric hysteresis loop. Such an electric field can switch the Rashba

coefficient listed in Table 1, which are at least one order of magnitude larger than in

semiconductors[7] or 3d oxide heterostructures[8-10] . In particularly a recent proposal of 5d

KTaO3 surfaces, where surface symmetry broken is hardly tunable, requires almost four

orders of magnitude larger electric fields of ~ 107V/cm.[40] For applications it is of particular

importance that ER in now clearly exceeds 0.025 eV, the thermal energy at room temperature.

Furthermore, we also propose to take advantage of the ferroelectric hysteresis and the remnant

ferroelectric polarization, using our heterostructure as a spintronics memory device.

By changing temperature and inducing strain (see below) one can tune the amplitude of the

ferroelectric distortion and hence the Rashba splitting. At elevated temperatures, the system is

close to a second order ferroelectric transition. In this situation, we have a paraelectric with

huge dielectric constant so that an electric field can continuously change the amplitude of the

SOC splitting.

7

2.3. Heterostructure engineering

Besides applying an electric field, heterostructure engineering such as varying its thickness,

strain, crystalline orientation, and the material combination is a powerful way to tune the

Rashba spin splittings. First, we vary the thickness of BaOsO3 and BaTiO3. It is well known

experimentally and theoretically [21,41] that below a few nanometer thickness of the BaTiO3

film, the Ti-O displacement is reduced and eventually ferroelectricity vanishes. As shown in

Table 1, when decreasing the thickness of BaTiO3 and increasing that of BaOsO3, the Rashba

spin splittings is indeed substantially reduced. Second, ferroelectricity of BaTiO3 is sensitive

to strain.[42] Taking SrTiO3 as a substrate provides a 2.5% in-plane compressive strain. This

enhances the ferroelectric distortion as well as Rashba spin splitting, αR=0.417eVÅ in Table 1.

Given the giant Rashba splitting, photoemission and transport measurements should be able to

validate this effect by comparing thin films with different thickness and substrate. The same

physics is found in BaIrO3/BaTiO3 with αR=0.731eVÅ, see Table 1, and in BaRuO3/BaTiO3.

Substituting the transition metal shifts the Fermi energy and might also be preferable for

applications since some Os oxides are toxic. The BaRuO3/BaTiO3 heterostructure also offers a

platform to study the interplay of Rashba physics and electronic correlations. For instance,

novel phenomena are expected in mixed 3d-5d transition-metal materials and even without

magnetism, the correlation induced formation of local moments may lead to new SOC

splitting or its reduction.[43] Let us also note that a strong temperature dependence of the αR in

SrIrO3 was recently reported.[44] While, in this paper we focus on t2g electrons in oxide

heterostructures along in (001) orientation, a topological behaviour was reported in (111)

oxide heterostructures [45]. Hence, a nature idea and extension of the present paper is to

incorporate a ferroelectric material such as BaTiO3 in a (111) heterostructure for studying the

interplay of Rashba SOC and topology.

3 Conclusion

8

We propose to combine a transition metal oxide with large spin-orbit coupling such as

Ba(Os,Ir,Ru)O3 and a ferroelectric such as BaTiO3 in an oxide heterostructure for realizing

giant Rashba spin splittings that are switchable by an electric field. The physics behind is that

ferroelectric BaTiO3 amplifies the electric field through a distortion (polarization) of its TiO6

octahedra. This distortion very efficiently propagates to the OsO6 octahedron via the shared

oxygens, breaking inversion symmetry and deforming the Os orbital lobes. Together with the

strong SOC it leads to a giant switchable Rashba effect with, e.g., αR∼0.2 (0.4) eVÅ for

(strained) BaOsO3/BaTiO3 and αR∼0.7 eVÅ for BaIrO3/BaTiO3. This is at least one magnitude

larger than state-of-the-art, allowing intriguing application at room temperature. Moreover,

the ferroelectric hysteresis and remnant polarization leads to a memory effect which can be

exploited for spintronics memory devices.

Supporting InformationSupporting Information is available from the Wiley Online Library or from the author.

AcknowledgementsZZ acknowledges financial support by the Austrian Science Fund through the SFB Vi-CoM

F4103-N13, QFZ by NSFC (11204265), the NSF of Jiangsu Province (BK2012248), WY by

the U.S. Department of Energy under Contract No. DE-AC02-98CH10886, SY by Grant-in-

Aid for Science Research from MEXT Japan under the grant number 25287096 and by

RIKEN iTHES Project, and KH by the European Research Council under the European

Union’s Seventh Framework Program (FP/2007-2013)/ERC through grant agreement n.

306447. Calculations have been done on the Vienna Scientific Cluster (VSC).

Received: ((will be filled in by the editorial staff))Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))

[1] I. Žuti ć, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004).

9

[2] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).

[3] E. I. Rashba, Sov. Phys. Solid State 2, 1109 (1960).

[4] R. Winkler, Spin Orbit Coupling Effects in Two-Dimensional Electron and Hole

Systems (Springer, 2003).

[5] S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev. Lett. 77, 3419 (1996).

[6] C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D. Pacilé, P. Bruno, K. Kern,

and M. Grioni, Phys. Rev. Lett. 98, 186807 (2007).

[7] J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Phys. Rev. Lett. 78, 1335 (1997).

[8] A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancellieri, and J.-M. Triscone,

Phys. Rev. Lett. 104, 126803 (2010).

[9] M. Ben Shalom, M. Sachs, D. Rakhmilevitch, A. Palevski, and Y. Dagan, Phys. Rev.

Lett. 104, 126802 (2010).

[10] H. Nakamura, T. Koga, and T. Kimura, Phys. Rev. Lett. 108, 206601 (2012).

[11] P. D. C. King, R. C. Hatch, M. Bianchi, R. Ovsyannikov, C. Lupulescu, G. Landolt,

B. Slomski, J. H. Dil, D. Guan, J. L. Mi, et al., Phys. Rev. Lett. 107, 096802 (2011).

[12] P. D. C. King, R. H. He, T. Eknapakul, P. Buaphet, S.-K. Mo, Y. Kaneko,

S. Harashima, Y. Hikita, M. S. Bahramy, C. Bell, et al., Phys. Rev. Lett. 108, 117602 (2012).

[13] K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe,

K. Koizumi, S. Shin, H. Miyahara, A. Kimura, et al., Nat. Mat. 10, 521 (2011).

[14] M. Bahramy, B. Yang, R. Arita, and N. Nagaosa, Nat. Commun. 3, 679 (2012).

[15] S. Nakosai, Y. Tanaka, and N. Nagaosa, Phys. Rev. Lett. 108, 147003 (2012).

[16] T. Das and A. V. Balatsky, Nat. Commun. 4, 1972 (2013).

[17] H. Mirhosseini, I. V. Maznichenko, S. Abdelouahed, S. Ostanin, A. Ernst, I. Mertig,

and J. Henk, Phys. Rev. B 81, 073406 (2010).

[18] J.-J. Zhou, W. Feng, Y. Zhang, S.-A. Yang, and Y. Yao, Scientific Reports 4, 3841

(2014).

10

[19] D. Di Sante, P. Barone, R. Bertacco, and S. Picozzi, Advanced Materials 25, 509

(2013), ISSN 1521-4095.

[20] M. Kim, J. Im, A.J. Freeman, J. Ihm, H. Jin, PNAS 111, 6900 (2014).

[21] M. Dawber, K. M. Rabe, and J. F. Scott, Rev. Mod. Phys. 77, 1083 (2005).

[22] Y. Shi, Y. Guo, Y. Shirako, W. Yi, X. Wang, A. A. Belik, Y. Matsushita, H. L. Feng,

Y. Tsujimoto, M. Arai, et al., Journal of the American Chemical Society 135, 16507 (2013).

[23] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

[24] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).

[25] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).

[26] F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).

[27] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An

Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties

(Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001), ISBN 3-9501031-1-2.

[28] J. Kuneš, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, Computer Physics

Communications 181, 1888 (2010).

[29] A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari,

Computer Physics Communications 178, 685 (2008), ISSN 0010-4655.

[30] Z. Zhong, Q. Zhang, and K. Held, Phys. Rev. B 88, 125401 (2013).

[31] Z. Zhong, A. Tóth, and K. Held, Phys. Rev. B 87, 161102 (2013)

[32] G. Khalsa, B. Lee, and A. H. MacDonald, Phys. Rev. B 88, 041302R (2013).

[33] H. Nakamura, T. Koga, and T. Kimura, Phys. Rev. Lett. 108,

206601 (2012).

[34] P. D. C. King , S. McKeown Walker, A. Tamai, A. de la Torre, T. Eknapakul, P.

Buaphet, S.-K. Mo,

W. Meevasana, M.S. Bahramy, and F. Baumberger Nat. Commun. 5, 3414 (2014).

11

[35] Panjin Kim, Kyeong Tae Kang, Gyungchoon Go, and Jung Hoon Han Phys. Rev. B

90, 205423 (2014)

[36] L. Petersen and P. Hedagard, Surf. Sci. 459, 49 (2000).

[37] S. Mathews, R. Ramesh, T. Venkatesan, and J. Benedetto, Science 276, 238 (1997).

[38] C.-G. Duan, S. S. Jaswal, and E. Y. Tsymbal, Phys. Rev. Lett. 97, 047201 (2006).

[39] R. Tazaki, D. Fu, M. Itoh, M. Daimon, and S. ya Koshihara, J. Phys.: Condens. Matter.

21, 215903 (2009).

[40] K. V. Shanavas, and S. Satpathy, Phys. Rev. Lett. 112, 086802 (2014).

[41] J. Junquera and P. Ghosez, Nature 422, 506 (2003).

[42] K. J. Choi, M. Biegalski, Y. L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche, Y. B.

Chen, X. Q. Pan, V. Gopalan, et al., Science 306, 1005 (2004).

[43] W.-G. Yin, X. Liu, A. M. Tsvelik, M. P. M. Dean, M. H. Upton, J. Kim, D. Casa,

A. Said, T. Gog, T. F. Qi, et al., Phys. Rev. Lett. 111, 057202 (2013).

[44] L. Zhang, Y. B. Chen, J. Zhou, S.-T. Zhang, Z. bin Gu, S.-H. Yao, and Y.-F. Chen,

arXiv 1309.7566 (2013).

[45] Di Xiao, Wenguang Zhu, Ying Ran, Naoto Nagaosa, and Satoshi Okamoto, Nat.

Commun. 2, 596 (2011)

12

Figure 1. Schematics of the mechanism behind the giant switchable Rashba effect: (1) An

external electric field is amplified and stored as a ferroelectric distortion, in particular Ti-O

displacements. (2) These displacements entail, via the oxygen octahedron network of the

perovskite heterostructure, Os-O or (Ir,Ru)-O displacements. (3) As a consequence of the Os-

O displacements the Os orbitals deform, which reflects the broken inversion symmetry. This

orbital deformation and the strong SOC of Os finally lead to a giant Rashba spin splittings

that is switchable by an electric-field.

13

Figure 2. DFT calculated band structures of (BaOsO3)1/(BaTiO3) 4 multilayers for the

paraelectric (c) and ferroelectric structure (d). The paraelectric heterostructure breaks cubic

but not inversion symmetry so that the Os xy orbital splits off from two degenerate yz/xz

orbitals without SOC (a); including SOC further lifts the yz/xz degeneracy (b). The

ferroelectric state further breaks inversion symmetry, which essentially does not change the

bandstructure in the absence of SOC (e) but leads to substantial spin splittings in the presence

of SOC (f). The spin splitting at the xy−yz crossing region is magnified in (g), while the

standard Rashba spin splitting ER with momentum offset k0 around Γ of the upper yz/xz mixed

orbital is magnified in (h). The two Rashba subbands have opposite spin-directions, which are

in the xy plane and perpendicular to the momentum; e.g. in (g,h) the spins are oriented parallel

and antiparallel to the y axis. For the bandstructure of Ba(Ir,Ru)O3/BaTiO3 and different layer

thicknesses, see Supplementary Material.

14

Figure 3. Tight binding bandstructure of the three Os t2g orbitals for (a) the paraelectric case

with and without SOC and (b) the ferroelectric case with SOC and asymmetry parameter

γ=0.016 eV taken from the Wannier projection.

15

Table 1. Polar distortions and Rashba spin splittings of (BaOsO3) n/(BaTiO3)m multilayers,

alternating n layers of BaOsO3 and m layers of BaTiO3. Second and third column: averaged

displacement of Os-O and Ti-O along z as calculated by DFT. Forth column: strength of the

interface asymmetry term γ obtained from the Wannier projection. Fifth to seventh column:

DFT calculated parameters characterizing Rashba effects: momentum offset k0, Rashba energy

ER, and Rashba coefficient αR of the upper yz/xz subband around Γ as defined in Figure 2(h).

Eighth column: spin splitting around the crossing region of xy and yz orbitals as in Figure

1(g). To demonstrate the effects of heterostructure engineering, we also list the results of

BaOsO3/BaTiO3 strained by a SrTiO3 substrate, as well as BaRuO3/BaTiO3 and

BaIrO3/BaTiO3. Band structures are given in Supplementary Material.

n:m Os-O (Å) Ti-O (Å) γ (eV) k0(Å-1) ER (eV) αR (eVÅ) ERxy (eV)

1:3 BaOsO3/BaTiO3 0.038 0.065 0.011 0.025 0.001 0.08 0.031

1:4 0.049 0.103 0.016 0.043 0.004 0.186 0.053

2:3 <0.010 <0.010 0.003 0 0 - 0.004

2:4 0.024 0.071 0.010 0.035 0.002 0.114 0.018

1:3 strained 0.095 0.223 0.030 0.105 0.021 0.396 0.102

1:4 strained 0.099 0.229 0.031 0.115 0.024 0.417 0.106

1:4 BaIrO3/BaTiO3 0.115 0.119 0.021 0.145 0.053 0.731 0.051

1:4 BaRuO3/BaTiO3 0.082 0.119 0.015 0.128 0.016 0.250 0.007

Supporting Information

Giant switchable Rashba effect in oxide heterostructures

16

Zhicheng Zhong*, Liang Si, Qinfang Zhang, Wei-Guo Yin, Seiji Yunoki and Karsten Held

S1. Correlations, metallicity and magnetism

While the 5d orbitals are extended in space and hence only show a weak Coulomb interaction

in comparison with 3d orbitals, the strong spin-orbit coupling (SOC) might lead to a band

narrowing. This can push 5d transition metal oxide into the regime of strong correlations,

leading to spin-orbit Mott insulators.[S1] Such an unconventional insulator with canted

antiferromagnetism has been observed in bulk Sr2IrO4 [S1] as well as in SrIrO3

(monolayer)/SrTiO3 multilayers.[S2,S3] These Sr compounds exhibit a moderate IrO6 octahedron

rotation which plays the key role in their insulating and magnetic behavior. In contrast, Ba

compounds are cubic-like in the absence of the octahedron rotation, and hence electronic

correlation are expected to be reduced.

To study possible correlation effects, metallicity and magnetism in Ba compounds, we

consider various magnetic configurations and perform generalized gradient approximation

(GGA) plus spin-orbit coupling (SOC) and GGA+SOC+U calculations without and with an

on-site Coulomb repulsion U=2 eV, respectively. First of all, in contrast to the case of Sr

compounds, ferromagnetic states are always energetically more favorable than

antiferromagnetic states. Since no antiferromagnetic Slater gap opens, we do not observe any

insulating behavior.

As listed in the Table S1, GGA+SOC gives very weak magnetism for bulk BaOsO3 and

BaIrO3 (the corresponding magnetic energy is smaller than 1meV/unit cell), and moderate

magnetic moments for BaRuO3, in a good agreement with experimental values. In

comparison, including an on-site Coulomb repulsion U overestimates magnetism as indicated

by the large local magnetic moments. This discrepancy might arise from two possible reasons:

(i) The effect of U is smaller in Ba compounds due to the reduced IrO6 octahedron rotation;

(ii) DFT+U is based on a Hartree-Fock static mean field approximation which usually

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overestimates ordering, in particular in the experimental parameter regime of small magnetic

moments. We also performed DFT+ dynamical mean field theory (DMFT) for

BaOsO3/BaTiO3 , and do not find ferromagnetism, consistent with experiment and our paper.

Please note a full consideration of spin-orbit coupling and correlation in DFT+DMFT is still a

challenging topic, and we have not included the SOC in the DFT+DMFT calculation.

From the comparison with the experimental bulk results we suggest that GGA+SOC is better

suited for the Ba compounds than GGA+SOC+U. For the BaOs(Ir)O3/BaTiO3 multilayers, we

also obtain always a metallic behavior. The ferromagnetic moment is very weak in

GGA+SOC, stretching the limits of what can still be resolved. For example, for

BaOsO3/BaTiO3, the ferromagnetic solution is only 0.2 meV (corresponding to 20 K) lower in

energy than the paramagnetic one. This implies that while there might be ferromagnetism at

low temperatures, the multilayers can be expected to be paramagnetic around room

temperature. This makes BaOsO3/BaTiO3 and BaIrO3/BaTiO3 ideal Rashba 2DEG systems as

stated in the main text. In contrast, for BaRuO3/BaTiO3, there is a moderate magnetic

moment, and it might be suitable for studying the interplay of magnetism and Rashba effect.

S2. DFT Bandstructures

For lack of space, we have only shown the DFT bandstructure of (BaOsO3) 1/(BaTiO3) 4

multilayers in Figure 2 of the main text. We have however systematically studied (i) the effect

of changing the number of BaOsO3 and BaTiO3 layers, (ii) the effect of strain achieved by

growing the heterostructure on a SrTiO3 substrate as well as (iii) replacing Os by Ir or Ru.

Table I of the main text summarizes the main parameters for the Rashba effect. For the four

most relevant other multilayers, we here supplement the DFT bandstructure in Figure S1 and

S2.

Figure S1(a) shows the bandstructure for two BaOsO3 layers alternating with BaTiO3, instead

of a single one. Here, the Os-O displacement is reduced by a factor of two, and the Rashba

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parameters are consequently smaller but still sizable. Since the unit cell contains two Os sites,

there are 2×3 Os t2g bands near the Fermi level. Because of the anisotropy nature of t2g

orbitals, orbital selective quantum well states will be formed: yz/xz bands exhibit a large

quantization of the energy levels, whereas xy bands exhibit a much smaller level spacing.[S7]

In Figures S1 (b), we show the bandstructure for a calculation where we have taken the in-

plane lattice parameters of SrTiO3, which corresponds to growing (BaOsO3) 1/(BaTiO3) 4 on a

standard SrTiO4 substrate. This strain substantially increase the Os-O displacement to 0.1 Å

and the Os t2g orbital deformation γ to 0.03eV, leading to an even larger Rashba splitting ER=

0.417eVÅ which can also be seen in the DFT bandstructure of Figure S1(b).

Figure S2 show the bandstructures of BaIrO3/BaTiO3 and BaRuO3/BaTiO3, for the

paramagnetic phase though for the compound ferromagnetism might possibly prevail up to

room temperature. The Rashba spin splitting for BaIrO3/BaTiO3 is largest among all studied

multilayers. Qualitatively we obtain similar Rashba effects in the Os, Ir and Ru compounds,

albeit of course the filling of the bands is quite different. The different filling allows for

studying the Rashba spin splitting in the three distinct t2g orbitals experimentally.

[S1] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, and T. Arima,

Science 323, 1329 (2009).

[S2] J. Matsuno, K. Ihara, S. Yamamura, H. Wadati, K. Ishii, V. V. Shankar, H.-Y. Kee, and

H. Takagi, arXiv: 1401.1066 (2014).

[S3] K.-H. Kim, H.-S. Kim, and M. J. Han, arXiv: 1402.2503 (2014).

[S4] Y. Shi, Y. Guo, Y. Shirako, W. Yi, X. Wang, A. A. Belik, Y. Matsushita, H. L. Feng,

Y. Tsujimoto, M. Arai, et al., Journal of the American Chemical Society 135, 16507 (2013).

[S5] M. A. Laguna-Marco, D. Haskel, N. Souza-Neto, J. C. Lang, V. V. Krishnamurthy,

S. Chikara, G. Cao, and M. van Veenendaal, Phys. Rev. Lett. 105, 216407 (2010).

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[S6] C.-Q. Jin, J.-S. Zhou, J. B. Goodenough, Q. Q. Liu, J. G. Zhao, L. X. Yang, Y. Yu,

R. C. Yu, T. Katsura, A. Shatskiy, et al., Proceedings of the National Academy of Sciences

105, 7115 (2008).

[S7] Z. Zhong, Q. Zhang, and K. Held, Phys. Rev. B 88, 125401 (2013).

Figure S1: DFT bandstructure of (BaOsO3)2/(BaTiO3)4 (a) and strained (BaOsO3)1/(BaTiO3) 4

(b) for the ferroelectrically distorted structure. The strain is achieved by a SrTiO3 substrate.

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Figure S2: DFT bandstructure of (BaIrO3)1/(BaTiO3)4 (a) and (BaRuO3)1/(BaTiO3)4 (b)

multilayers for the ferroelectrically distorted structure.

Table S1: Local magnetic moments of bulk BaOs(Ir,Ru)O3 and BaOs(Ir,Ru)O3/BaTiO3

multilayers. Our DFT+ dynamical mean field theory (DMFT) calculations also find BaOs

O3/BaTiO3 is paramagnetic.

BaOsO3 BaIrO3 BaRuO3 BaOsO3/ BaTiO3 BaIrO3/ BaTiO3 BaRuO3/ BaOsO3

Experiment Paramagnetic[S4] 0.03[S5] 0.8[S6] - - -

GGA+SOC 0.06 0.01 1.14 0.029 0.061 0.988

GGA+SOC+U 1.296 0.121 1.524 1.347 0.484 1.375

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