Oxide Interfaces: Perspectives & New Physics

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1 Oxide Interfaces: Perspectives & New Physics Seminar, University of Illinois September 24, 2007 Sashi Satpathy University of Missouri, Columbia Funding: DOE, AFOSR, PRF, MURB, DFG

2 History of semiconductor physics One should not work with semiconductors, that is a filthy mess; who knows if they really exist Pauli 1931

3 First Semiconductor Transistor (1947) Bardeen, Brattain, and Shockley Bell Labs (1947) A picture of the first transistor ever assembled, invented in Bell Labs in It was called a point contact transistor because amplification or transistor action occurred when two pointed metal contacts were pressed onto the surface of the semiconductor material. The contacts, which are supported by a wedge shaped piece of insulating material, are placed extremely close together so that they are separated by only a few thousandths of an inch. The contacts are made of gold and the semiconductor is germanium. The semiconductor rests on a metal base.

4 High Quality Oxide Interfaces SrTiO 3 LaTiO 3 Examples of systems: SrTiO 3 /LaTiO 3 (interfacial 2DEG) LaMnO 3 /SrMnO 3 (spin-polarized 2DEG?) CaRuO 3 /CaMnO 3 (metal in contact with an antiferromagnet) SrTiO 3 /LaAlO 3 (polar heterostructure) SrTiO 3 /LaVO 3 (polar heterostructure) FM/SC interfaces, etc. High-resolution scanning electron microscopy image of a lattice-matched SrTiO 3 /LaTiO 3 superlattice, grown with pulsed laser deposition. Ref: Ohtomo et al., Nature 419, 378 (2002)

5 Epitaxial Oxides Credit: Christen, Oak Ridge National Lab, 12/2006

6 Theoretical Methods Electronic structure of solids: Interacting many-body problem Density-Functional Theory Local Density Approximation (LDA, LSDA) Generalized Gradient approximation (GGA) LDA/GGA + Hubbard U Models: Hartree-Fock, Dynamical mean field theory (DMFT) More accurate methods: exact diagonalization, Quantum Monte Carlo (Limited to small systems)

7 Density-functional Theory Key point (Kohn, Sham, Hohenberg, 1965): The ground-state energy of the interacting electrons can be found by solving a one-particle Schrödinger equation with an effective potential: H i = i i H = h2 2m 2 + V eff (x, y,z) Solution of the mean-field one-particle equations LMTO (Linear muffin-tin orbitals method) {most physical, computationally fast} LAPW (Linear augmented plane waves) {most accurate} Pseudopotential plane waves method {easiest to formulate} Different religions, same God.

8 I. The LaTiO 3 /SrTiO 3 Interface: 2D Electron Gas LaTiO 3 SrTiO 3 Ohtomo et al., Nature 419, 378 (2002)

9 Superconducting interface between insulating oxides: 2DEG Ref: Reyren et al., Science 317, 1196 (2007)

10 Quantum Hall effect in the 2DEG at the oxide interfaces Ref: Tsukazaki et al., Science 315, 1388 (2007)

11 Bulk electronic structure of SrTiO 3 and LaTiO 3 LaTiO 3 : Mott insulator - Occupied Ti(d 1 ) - Half-filled Hubbard band - antiferromagnetic insulator SrTiO 3 : Band insulator - Empty Ti(d 0 ) band La La x Sr x Sr 1-x 1-x TiO TiO 3 3 FIG: Resistivity data indicating the Metal-Insulator transition as a small number of holes are doped via Sr substitution Ref: Tokura et al, PRL 70, 2126 (1993)

12 The LaTiO 3 /SrTiO 3 Interface: 2D Electron Gas SrTiO 3 LaTiO 3 Zoran Popovic Paul Larson Electronic Structure Calculations Density-Functional Theory Methods: LMTO, LAPW

13 SrTiO 3 /(LaTiO 3 ) 1 /SrTiO 3 : Basic result from DFT 2DEG The V-shaped potential and the electron density profile near the interface from DFT Popovic and Satpathy, PRL 94, (2005)

14 Electron density profile from EELS Ti(+3) Two layers Experiment One layer of LaTiO 3 Theory Ref: Ohtomo et al., Nature 419, 378 (2002)

15 Electron confinement at the interface: No lattice relaxation 2DEG Electron charge-density contours

16 Effect of lattice relaxation Single LaTiO 3 Interface layer + SrTiO 3 TiO SrO 2 TiO SrO 2 TiO 2 SrO O(-) + LaO (Positively charged plane) Ti(+) Ti and O atoms relax to generate a dipole moment that screens the interface electric field LAPW results: Larson et al, unpublished

17 Lattice Relaxation screens the electric field Screening in solids: Electronic + lattice SrTiO 3 is close to a ferroelectric transition, with very large dielectric constant. relaxed unrelaxed DFT: Static dielectric constant ~ 23 (electrons only) unrelaxed ~ 70 (electrons + lattice) relaxed

18 The 2DEG at the interface 30 Å

19 Interface Subbands

20 GaN/Al x Ga 1-x N Interface: Highest-density 2DEG in the semiconductor system FIG: Electric fields calculated from DFT

21 2DEG at the GaN/Al x Ga 1-x N Interface (Expt vs. Theory) Density of the 2DEG ~ cm -2 (semiconductor interface) ~ 1 x cm -2 (GaN/AlGaN) ~ 3 x cm -2 (LaTiO 3 /SrTiO 3 interface) Al concentration x SS, Popovic, Mitchel, JAP 95, 5597 (2004)

22 Jellium model for the 2DEG at the Oxide Interface Ref: Thulasi, Ph. D. thesis (MU, 2006); Thulasi and Satpathy, PRB (2006) Sunita Thulasi Schematics of the 2DEG formed at the oxide interface. The charged La atom forms a positive sheet charge, localizing a 2DEG in its neighborhood. V-shaped external potential: Problem: Study the ground-state properties using Hartree-Fock and DFT methods.

23 Two-Dimensional Airy electron gas in the jellium model H = H ke + H ee + H ext + H eb = h2 2m * One-particle states are the Airy functions in the V-shaped potential well h 2 2m d 2 + V (z) =, V (z) = F z 2 dz k n >= 1 A eir k. r n (z) i 2 i + e2 2 N i=1 z i +H ee Hartree-Fock: occ + F >= a r r k n k n vac > E HF =<F H F >

24 DFT Calculation of the 2DEG Kohn-Sham equations Use von Barth-Hedin expression for V xc and solve self-consistently Ground-state Energy Potential and electron density

25 Spatial extent of the 2DEG: Jellium model vs. Expt (Jellium DFT) Calculated density profile of the 2DEG, compared to the EELS data. Expt: Ohtomo et al., Nature (2002)

26 II. CaRuO 3 /CaMnO 3 : A metal-on-magnetic insulator interface Ref: Tokura et al. (2006), Takahashi (2001) FerroMagnetism exists at Interface Only AFM insulator Magnetization per interface atom (μ B ) CaMnO 3 M ~ 0.85 μ B per interface atom Para metal CaRuO 3 Q. Is the suppressed magnetic moment due to the formation of magnetic domains or something more interesting might be going on at the interface?

27 CaMnO 3 /CaRuO 3 Interface Q. What is the origin of the suppressed magnetization at the interface? Ranjit Nanda Q. Can we control the interface magnetism by controlling the leaked metallic electrons? Expt: K. S. Takahashi, M. Kawasaki, and Y. Tokura, Appl. Phys. Lett. 79, 1324 (2001)

28 Potential barrier and charge leakage at the interface DFT Results Lang and Kohn, PRB (1970) Exponential leakage of electron gas similar to a Jellium surface Potential is similar to that of metal-vacuum interface W surface: Jones, Jennings, and Jepsen, PRB (1984) V (z) = {1 exp[ (z z 0)]}/[2 (z z 0 )], z > z 0 U 0 /{Aexp[ B(z 0 z)]+1}, z < z 0

29 Charge leakage from the metallic to the insulator side Interface Dipole moment Exponential leakage of electron gas similar to a Jellium surface Lang and Kohn, PRB (1970)

30 Energetics (LSDA results) AFM FM FM-II Minimum energy structure

31 DFT Results: Electron distribution at the interface interface Leaked electrons

32 Mn (d) electron states in the solid e g t 2g Mn (d)

33 Magnetic Interactions: Superexchange and Double Exchange Superexchange t U Double Exchange (Anderson, Hasegawa, Zener, De Gennes, 1950s) itinerant electron Hopping forbidden e g X e g Hopping allowed t e g e g Mn core spins Mn t 2g Mn t 2g Mn t 2g Mn t 2g Canting angle of the Mn core spins Simple model: Anderson-Hasegawa (1950) =>

34 Canting does survive in a lattice and also Coulomb does not kill the canting Two-site model: Anderson-Hasegawa (1950) ==> Results of exact diagonalization Ref: Mishra, SS, Gunnarsson, PRB 55, 2725 (1997)

35 Buridan s ass is the common name for the thought experiment which states that an entirely rational ass, placed exactly in the middle between two stacks of hay of equal size and quality, will starve since it cannot make any rational decision to start eating one rather than the other.

36 Q. How are the competing interactions accommodated at the interface layer? Ans: A spin-canted state forms. No. of electrons in e g level = x e g t 2g Compute canting angle by minimizing total energy: H k = ( k) ( k) ( k) ( k) (k) = 2t cos( /2) f (k) A single MnO 2 plane at the interface (k) = 2t sin( /2) f (k) f (k) = cos k x a + cos k y a

37 Canted State in the interfacial CaMnO 3 layer canted AFM First layer: electron concentration x ~ 0.1 => canted state Second layer: x ~ 0.01 => AFM state remains unchanged Expt: Mag. Mom. at the interface is 0.85 B => canting FM FIG: Dependence of canting on electron concentration (x) in the layer Nanda, SS, Springborg, PRL (2007) Conclusion: Canted antiferromagnet at the interface.

38 III. Spin polarized 2DEG: The LaMnO 3 /SrMnO 3 system Spin-up Spin-down Spin-polarized 2DEG Potential V(z) seen by electrons near the interface

39 Control of interface magnetism by strain Magnetic exchange across the interface Double exchange ~ t (Ferro) Superexchange ~ -t 2 /U (Anti-ferro) t Bhattacharya/ Eckstein structure grown on SrTiO 3 compressive tensile strain Expt: Yamada, APL 89, (2006)

40 IV. Polar Interfaces Coulomb divergence (Harrison 1978) Ge GaAs - + Coulomb divergence solved by atomic diffusion at the interface. But does that really happen or do we have electronic reconsruction?

41 LaAlO 3 /SrTiO 3 Eckstei n, Nat. Mater. July 2007 Thiel et al, Science (2006) 2DHG 2DEG Q. What is the origin of the 2DEG at the interface? (polarity issues) Superconducting 2DEG Reyren et al., Sci ence 317, 1196 (2007) Q. How much of the effect is intrinsic to the interface and how much is extrinsic, such as oxygen vacancy? Q. Why is 2DEG metallic, while 2DHG is insulating? Q. Is the 2DEG any different from that in the semiconductor interfaces? (correlated system)

42 Conclusion New class of perovskite oxide interfaces -- New physics of 2DEG? Examples: SrTiO 3 /LaTiO 3 /SrTiO 3 (High density 2DEG at interface) CaMnO 3 /CaRuO 3 (Interfacial magnetism controlled by leaked electrons) LaMnO 3 /SrMnO 3 /LaMnO 3 (spin polarized 2DEG --new system ever? ) LaAlO 3 /SrTiO 3 (how does polarity affect interface states) Rapid progress in growth of high-quality, lattice-matched oxide interfaces is poised to bring in a new era Potential for new physics and new device applications