Nanoxide electronics Alexey Kalabukhov Quantum Device Physics Laboratory MC2, room D515 Alexei.kalaboukhov@chalmers.se
Playing Lego with oxide materials: G. Rijnders, D.H.A. Blank, Nature 433, 369 (2005)
Materials: Perovskite oxides Insulating Metallic High-Tc superconductors LaAlO 3 Ferromagnetic La x Sr 1-x MnO 3 SrRuO 3 Ferroelectric PbZr y Ti 1-y O 3 ReBa 2 Cu 3 O 7-x All materials belong to one structural group Perovskites, ABO 3
Perovskite table of elements A B 3d -> 4d -> 4f -> Group I: A 1+ B 5+ O 2-3 : KTaO 3, NaTaO 3, LiNbO 3 Group II: A 2+ B 4+ O 2-3 : SrTiO 3, BaTiO 3, CaTiO 3 Group III: A 3+ B 3+ O 2-3 : LaAlO 3, NdGaO 3, GdFeO 3
Emerging phenomena FET, memory Charge: Metal-insulator transitions (FET, memory) Strain: Induced ferroelectric polarization Spintronics Spin: Induced magnetic order, magnetic interactions at interfaces Multiferroics
Outline: I: 2DEG between wideband gap insulators II: Multiferroic materials
Structural properties Perovskite: CaTiO 3 (L. Perovsky, 1839), face-centered cubic lattice A-site: Alkali metals, structural properties B-site: transition metals, electro-magnetic properties A O B O 2 Tolerance factor : ra ro 0.75 t f 1 2( r r ) B O A O Densest crystal lattice!
Electronic properties Oxygen atoms in octahedra act as point charges d-orbitals in the B-site split into two groups: e g and t 2g B-O 6 octahedron: B-O 6 d-orbitals: e g t 2g t 2g e g
Example: SrTiO 3 SrTiO 3 SrTiO 3-δ Annealing in vacuum at 900 C transparent, wide band gap insulator (E G =3.2 ev) The value of seeing nothing, J. Mannhart and D. G. Schlom, Science 430, p.620 (2004) Metallic, superconducting Tc ~ 0.3 K
Electrical doping in SrTiO 3 Doping by oxygen vacancies: SrTiO 3 -> SrTiO 3-δ + δv O 2+ + δ2e - 5-10% of oxygen vacancies! H.P.R.Frederikse, W.R.Hosler, Phys.Rev. 161, 822 (1967)
Thin film growth Epitaxy: growth of single-crystal films on substrate template. Requires good lattice match and chemical compatibility. Deposition methods: Molecular Beam Epitaxy (MBE) or Pulsed Laser Deposition (PLD) Atomic layer control: Reflection High-Energy Electron Diffraction (RHEED), in-situ with deposition
Deposition of thin films Pulsed Laser Deposition with atomic control: Reflection High Energy Electron Diffraction (RHEED) intensity oscillations: atomic layer-by-layer growth G.J.H.M. Rijnders et al. Materials Science and Engineering B 56 (1998)
2 µm 5 µm Control of SrTiO 3 surface Mixed: TiO 2 +SrO TiO 2 non-reconstructed TiO 2 reconstructed Annealed in O2 as-received BHF-etched flow, 950 C M.Kawasaki et al., Science 266, 1540(1994); G.Koster et al., Mat. Sci. Eng. B 56, 209(1998)
Surface termination and film growth Atomic Force Microscope image RHEED during growth Non-terminated No oscillations in the beginning! TiO 2 -terminated Layer-by-layer growth M.Kawasaki et al., Science 266, 1540 (1994)
Engineered oxygen vacancies PLD-RHEED of oxygen SrTiO 3 /SrTiO 3-x superlattice: High-resolution TEM: sharp boundaries between layers Oxygen vacancies are unstable: clustering, diffusion, etc D.A. Muller et al., Nature 430 (2004)
Part I: Electrostatic carrier doping in oxide interfaces. 2DEG at the LAO/STO interface
Electrostatic Carrier Doping Source Field effect experiment: V G Gate Insulator Sample SiO 2 : ε = 3.9, E BG = 7.5 MV/cm, n 2D 16x10 12 cm -2 SrTiO 3 : ε = 240, E BG = 1.5 MV/cm, n 2D 200x10 12 cm -2 d Drain Simple electrostatics: Q C V G 0 S C d VG EG d 0 S Q EG d 0 S EG d Q 0 EG Sheet carrier n2d es e concentration Limited by breakdown field: E BG
Thomas-Fermi screening Thomas-Fermi model: screening is about inter-atomic distance in metals! TF 4e a 2 0 n In metals, carriers are doped only in few atomic layers close to the interface. Oxides: low carrier densities -> higher tunability C. H. Ahn et al., Nature 424, 1015 (2003)
SrTiO 3 and LaAlO 3 LaAlO 3 : SrTiO 3 : V g = 5.6 ev a = 3.87 Å Both are wide band-gap insulators V g = 3.2 ev a = 3.91 Å High dielectric constant in STO (ε ~ 240 at 300 K) Good lattice match can probably make good interface!
The LAO/STO interface Pulsed Laser Deposition of ultrathin LaAlO 3 film on SrTiO 3 substrate: High crystalline quality confirmed by electron microscopy: LaAlO 3 SrTiO 3 A. Ohtomo & H. Hwang, Nature 427 (2004) Image: E. Olsson & N.Ljustina, Chalmers
The LAO/STO interface High electrical conductivity and mobility: Two-dimensional superconductivity: Ferromagnetism: A. Ohtomo & H. Hwang, Nature 427 (2004) N. Reyren et al., Science 317 (2007) J. A. Bert et al., Nature Physics 7 (2011)
Thickness of the electron gas Atomic force microscope (AFM) images with conducting tip: C-AFM Experiment: C-AFM in the perpendicular direction: STO LAO C-AFM cross-section: thickness about 5 nm G. Herranz et al., Nature Materials 7 621 (2008)
QHE in the LaAlO 3 /SrTiO 3 2DEG F. Trier et al. (2016) http://arxiv.org/pdf/1603.02850 Gariglio, Fête and Triscone, J. Phys.: Condens. Matter 27 (2015) R xy Unconventional Quantum Hall Effect: 1 = 10 e 2 h for B < 6T, R 1 xy = 20 e 2 h for B > 6 T. Possible explanation: single quantum well with parallel subbands
LAO/STO and GaAs 2DEG s J. Mannhart and D. G. Schlom, Science 327, 1607 (2010) GaAs: single quantum well generated by band bending LAO/STO: multiple quantum wells due to electron correlations of the TiO 6 orbitals
Origin of the 2DEG in the LAO/STO Stacked sequence of AB-BO 2 layers in (001) direction Non-polar in STO (SrO 0 -TiO 20 ), polar in LAO (LaO 1+ -AlO 1-2 ) The interface is polar n-type : (TiO 2 -LaO) p-type : SrO-AlO 2 N. Nakagawa et al., Nature Mat. 5, 204 (2006)
Critical thickness effect Abrupt insulator metal transition at 4 unit cells of LAO film: Metallic Insulating S. Thiel et al., Science 313, 1942 (2006)
Defect mechanism t < 4 uc: Ti<->Al antisite defects t > 4 uc: oxygen vacancies on the LAO surface Ti-Al antisite defects: compensate polar discontinuity Oxygen vacancies: donate electrons and create 2DEG at the interface L. Yu & Alex Zunger, Nature Communications 5, 2014
Giant electric field effect Insulator metal transition using electric field in 3 uc thick film On/Off ratio about 10 7 Slow response oxygen vacancies rather electrons! S. Thiel et al., Science 313, 1942 (2006)
AFM Nano-lithography AFM tip is used to create conducting paths in insulating LAO/STO interface LAO film thickness is slightly below 4 uc - close to MIT Writing Conducting after applying field Insulating 3 uc LAO Erasing Linewidth 3 nm! C. Chen et al., Nature Materials 7, 298 (2008)
AFM Nano-lithography Tunneling junctions with 2 nm gap, FET three-terminal devices C. Chen et al., Science 323, 1026 (2009)
Summary LAO/STO Novel 2DEG with unconventional electronic properties Prototype of future oxide nano-electronics: devices beyond Moor s law Challenges: to increase electron mobility, fabrication on other substrates, e.g. silicon. Superconductivity and magnetism: unconventional pairing, topological superconductivity and quantum computing
Part II: Magnetoelectric coupling in oxide interfaces
Multiferroic materials Multiferroics: a combination of two (or more) ferroic properties: Ferroelectricity Ferroelasticity Ferromagnetism Important case: magneto-electric coupling (hard drives, spintronics, tunable electronic components). Co-existence of ferroelectric and ferromagnetic properties in a single phase is contradictory (FE are good insulators, FM are half-filled metals). N. A. Spaldin, M. Fiebig, Science 309, 391 (2005)
Ferroelectrics Important condition for ferroelectric behavior: Double-well potential energy as a function of cation position Similar to ferromagnetics, second-order phase transition at T < T C
Perovskite ferroelectrics FE polarization stems from B-O displacements Short range repulsions (electron clouds) non-fe symmetric structure Bonding considerations: B-O hybridization, controlled by A-cation size B cation usually has d 0 state - insulating Conducting electrons screen electric fields FE must be insulating
Ferromagnets Second-order phase transition at T=T c : Hysteresis loop T < T c T > T c Nicola A. Hill J. Phys. Chem. B, Vol. 104, No. 29, 2000
Origin of ferromagnetism Magnetic dipoles moments of atoms line up below T C First five d electrons have parallel spins (minimizes exchange energy) Maximum moment for d 5 Nicola A. Hill J. Phys. Chem. B, Vol. 104, No. 29, 2000
Manganites: La 1-x Sr x MnO 3 Only Mn 3+ : antiparallel alignment is favorable, resulting in antiferromagnetic arrangement Mn 3+ and Mn 4+ : strong positive interaction and ferromagnetic ordering of spins ( double exchange ), colossal MR La 3+ Mn 3+ O 3 2- -> La 3+ 1-xSr 2+ xmn 3+ 1-xMn 4+ xo 3 2- Electronic configuration of LaMnO 3 Charge transfer between Mn 3+ and Mn 4+
Multiferroic ME Ferroelectricity: d 0 B-cations, insulating Ferromagnetism: d 5 B-cations, half metallic Only few magnetic ferroelectrics known! Solutions: chemical doping, strain, interface interactions
Magnetoelectric effect... ), (... ), (... 2 1 2 1 ), ( 0 0 0 0 0 i ij j ij S i i j ij j ij S i i j i ij j i ij j i ij i S i i S i E H M H E M H E P H E P E H M M E E H M E P F H E F Landau theory, expansion of the free energy: Magneto-electric coupling: electric field to re-orient the magnetic polarization and vise versa P H M E, Linear ME effect L. D. Landau and E. M. Lifshitz, Electrodynamics of continuous media Pergamon, Oxford (1960).
Magnetoelectric effect Upper bound for the linear ME coupling: ij E M ii jj W.F. Brown R. M. Hornreich S. Shtrikman Phys. Rev. 168, 574 577 (1968) ME effect is strong only in materials with high electrical and magnetic susceptibility, e.g. in multiferroics Multiferroic ME Direct coupling: Ferroelectric <-> Ferromagnetic Composite ME Indirect coupling: Ferroelectric <-Piezoelectric-> Ferromagnetic
Example I: strained EuTiO 3, theory EuTiO 3 : Anti-ferromagnet T C ~ 5 K, paraelectric When bi-axially strained: can be ferromagnetic and ferroelectric (theory), see strain phase diagram: C.J. Fennie, K.M. Rabe, PRL 97, 267602 (2006)
Example I: strained EuTiO 3,experiment Substrate consideration: Growth by Molecular Beam Epitaxy: No available substrates to induce compressive strain DyScO 3 : at the boundary of AFM-FM transition with tensile strain H. Lee et al., Nature 466 (2010)
Example I: strained EuTiO 3,experiment Ferroelectric loops: Ferroelectic below 250 K Magnetization v.s. temperature: Very weak ferromagnet below 5 K H. Lee et al., Nature 466 (2010)
Example II: BiFeO 3 /BiCrO 3 superlattice BiFeO 3 : The only multiferroic material at room temperature, but it is anti-ferromagnetic Can be ferromagnetic if Fe replaced by 50 % Cr (ordered!) PLD of BiFeO 3 /BiCrO 3 superlattice High-resolution TEM image N. Ichikawa et al., Appl.Phys.Express 1, 101302 (2008)
Example II: BiFeO 3 /BiCrO 3 superlattice Weak ferromagnetic behavior: Piezoelectric properties by AFM: Co-existence of weak ferromagnetism and weak ferroelectricity Low break-down voltages, doping due to oxygen vacancies Deviation from ordered periodicity in Cr/Fe sites N. Ichikawa et al., Appl.Phys.Express 1, 101302 (2008)
Example III: Interface coupling Magneto-electric device: coupling at the interface Ferroelectric anti-ferromagnetic coupling: BiFeO 3 Magnetization in FM layer is coupled to AFM by exchange bias mechanism Application of electric field results in FM switching R. Ramesh and N. Spaldin, Nature Materials 6, 21 (2007)
Example III: Interface coupling Soft FM layer on the top of BiFeO 3 film: Resistace v.s. magnetic field in-plane direction: Magnetoresistance reversal by 180 under applied electric field Direct proof of magneto-electric coupling J.T. Heron et al., PRL 107, 217202 (2011)
Example IV: LuFeO 3 /LuFe 2 O 4 LuFe 2 O 4 Ferrimagnetic, not ferroelectric LuFeO 3 Ferroelectric, not ferromagnetic
LuFeO 3 /LuFe 2 O 4 Only indirect evidence of magneto-electric coupling: LuFe 2 O 4 / LuFeO 3 superlattice is ferroelectric and ferromagnetic above room temperature: How to measure ME coupling directly?
Summary