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Ferroelectrics from first principles Designing ferroelectrics the improper way Nick Bristowe Functional Materials Group, University of Kent, UK CCP9 meeting, April 11th 2017 M Ferro-electric/magnets, Multiferroics Multiferroic:materialcombiningtwoormoreferroic parameters Ferromagnetic: ● N N N S S S N N N S S S Ferroelectric: M P Ferroelectric: P + - + - + + - - + + - - ● Hysteresis: Multifunctional magnetoelectrics (Generalized) Magnetoelectric: cross coupled response to electric and magnetic fields Non-volatile data-storage! Magnetoelectric: - + Polarization, P E H Claude Ederer First principles studies of multiferroic materials P M Magnetization, M Possibleapplications: i.e. control of the magnetic M (electric P) phase with an applied electric E (magneticRAM:electricwrite/magneticread H) field - Magnetoelectric - 4-statememory Perovskites e of A2+ Ti4+ O3 and A3+ Ti3+ O3 ([001]) ABX3 Widerangeofproperties Duetocouplingdegreesoffreedom P. Zubko et al. Annu. Rev. Condens. Matter Phys. 2, 141 (2011). Why are most perovskites NOT FE? ectricity as a lattice property CaTiO3 Purely tilted ground state PbTiO 3 as the ce distortion, Q, has identical symmetry properties polarization, i.e. Q∝ P, involve smallFE atomic distortions Pure ground state Ti paraelectric e group Pm3m neering Physics ! P + – tetragonal-ferroelectric Space group P4mm 42 Why are most perovskites NOT FE? Structuralinstabilitiesfromsimplecubic CaTiO3 Purely tilted ground state PbTiO3 Pure FE ground state lattice property Ferroelectricity as a lattice property entical symmetry properties as the involve small atomic FEdistortions (ferroelectric) polar distortion P Oxygen M(f+) FE lattice distortion, Q, has identical symmetry properties as the FEatomic (ferroelectric) distortions Octahedral Tilts polarization, i.e. Q∝ P, involve small Pb polar distortion R(f-) Ti + – O Phonons courtesy of Ph Ghosez P + – Why are most perovskites NOT FE? Competing FE and AFD lattice instabilities Energy landscape 1 1 2 E = A0 P + B0 P 4 + C12φ12φ22 2 4 1 2 1 4 + A1φ1 + B1φ1 + C01φ12 P 2 2 4 1 1 2 + A2φ2 + B2φ24 + C02φ22 P 2 2 4 FE (P) AFD-M (f1) AFD-R (f2) Tilting often wins! € FE and AFD usually competing through bi-quadratic coupling (C01,C02>0) signiÆcance occurs in perovskites used for microwave dielectric applications. Colla et al. (1993) have shown that the sign Why are most perovskites NOT FE? 2. Octahedral tilt sy As previously noted, o of the A-site cation co change in A–X bond ways in which the o different coordination Theyoftentiltinstead The coordination num nation sphere has b common tilt systems ( A standard notation hedral tilting distortio alternative, but equa AFD (M-point) : f+ AFD (R-point) : fAleksandrov (1976). F Glazer notation throug Figure 1 and Woodward Acta Cryst. B57 725 (2001) a tilt system by rotati Distribution of Lufaso tilt systems among known perovskites with a single octahedral cation. orthogonal Cartesian a 726 Lufaso and Woodward ✏ Prediction of the crystal structures signiÆcance occurs in perovskites used for microwave dielectric applications. Colla et al. (1993) have shown that the sign Why are most perovskites NOT FE? 2. Octahedral tilt sy As previously noted, o of the A-site cation co change in A–X bond ways in which the o different coordination Theyoftentiltinstead The coordination num nation sphere has b common tilt systems ( A standard notation hedral tilting distortio alternative, but equa AFD (M-point) : f+ AFD (R-point) : fAleksandrov (1976). F Glazer notation throug Figure 1 and Woodward Acta Cryst. B57 725 (2001) a tilt system by rotati Distribution of Lufaso tilt systems among known perovskites with a single octahedral cation. orthogonal Cartesian a 726 Lufaso and Woodward Detour: Why is Prediction of the crystal structures Pnma most common? ✏ Pnma most stable N Miao et al structural phase as a successive ns in the cubic . fic Pnma ground R+ 4 instabilities t is not a priori ation of tilts is the structures of icted to M+ 3 and ation of tilts, the er the symmetry Figure 4. The calculated gains of energy, with respect to the ideal Miao, Bristowe et al JPCM 26 035401 (2014) cubic SrRuO3 phase taken as reference, for different relaxed phases, Pnma most stable N Miao et al structural phase as a successive ns in the cubic Duetoother motions (nottilts!) . fic Pnma ground R+ 4 instabilities t is not a priori ation of tilts is the structures of icted to M+ 3 and ation of tilts, the er the symmetry ->couplingsat play? Figure 4. The calculated gains of energy, with respect to the ideal Miao, Bristowe et al JPCM 26 035401 (2014) cubic SrRuO3 phase taken as reference, for different relaxed phases, Trilinear terms N Miao et al f structural phase as a successive rns in the cubic ). ific Pnma ground d R+ 4 instabilities it is not a priori ination of tilts is t the structures of tricted to M+ 3 and nation of tilts, the wer the symmetry ystem will further other modes that ally understood as d are rationalized ical Goldschmidt ubic perovskites ation is small and Miao, Bristowe et al JPCM 26 035401 (2014) Figure 4. The calculated gains of energy, with respect to the ideal + cubic SrRuO phase taken :asfreference, for differentAnti-polar relaxed phases, AFD 3(M-point) : X5z labeled in terms of the compatible tilt pattern. Eoxygen corresponds to the gain of energy that can be achieved from the relaxation of oxygen atomic positions only. Ecation corresponds to the supplemental gain of energy that can be achieved when allowing for additional concomitant cation motions. In this latter case, the oxygen distortions are modified through the coupling with cation motions: the dashed line identifies the reduced gain of energy 0 (Eoxygen ) produced by pure oxygen motions in this fully relaxed phase. All the previous calculations are done when keeping the unit cell fixed. E corresponds to the additional gain of energy when AFD (R-point) : fx- Can we cooperatively couple AFD with FE? Turn anti-polar X mode to polar mode? Considerdigitalsuperlattice LayersofA andA’ inalternate(001)planes canbegrownlayer-by-layer(e.g.PLDMBE) ornaturallyordered(e.g.doubleperovskites) (thesameconceptwillworkonthicker superlattices,andotherlayeredmaterials e.g.RP,DJ,Aurivilius) Rotationally driven ferroelectricity digitalsuperlattice 2 2 AFD motions AFD motions P4/mmm structure P4/mmm structure E = λφ xy− φ z+ Pxy Pxy OnlyingredientisPnma typerotationsandlayering Breathing Jahn-Teller Pxy Charge and orbital Bousquet et al Nature 452 732 (2008), Fukushima et al PCCP 13 12186 (2011), Rondinelli et al Adv Materials 24 1961 (2012) (Hybrid) Improper Ferroelectricity Shift the well to lower energy through the coupling with other phonon modes Hybrid improper ferroelectricity “Hybrid” = requires two independent order parameters belonging to a different subspaces 1 1 E = A0 P 2 + B0 P 4 + C12φ12φ22 2 4 1 1 2 + A1φ1 + B1φ14 + C01φ12 P 2 2 4 1 1 + A2φ22 + B2φ24 + C02φ22 P 2 2 4 Trilinear +λφ1 φ2 P coupling term - lf1f2 acts as an effective field shifting P well to lower energy - Switching P requires reversing either f1 or f2 (and perhaps M) Figure courtesy of Ph Ghosez Experimental signatures ARTICLES PUBLISHED ONLINE: 12 JANUARY 2015 | DOI: 10.1038/NMAT4168 Experimental demonstration of hybrid improper ferroelectricity and the presence of abundant charged walls in (Ca,Sr)3Ti2O7 crystals Yoon Seok Oh1,2†, Xuan Luo3, Fei-Ting Huang1,2, Yazhong Wang1,2 and Sang-Wook Cheong1,2,3* On the basis of successful first-principles predictions of new functional ferroelectric materials, a number of new ferroelectrics PHY I C A L rotation, R E Vhybrid I E Wimproper LETTERS PRL 114, 035701 (2015) have been experimentally discovered. Using trilinear coupling of two types of Soctahedron ferroelectricity has been theoretically predicted in ordered perovskites and the Ruddlesden–Popper compounds (Ca3 Ti2 O7 , Ca3 Mn2 O7 and (Ca/Sr/Ba)3 (Sn/Zr/Ge)2 O7 ). However, the ferroelectricity of these compounds has never been experimentally confirmed and even their polar nature has been under debate. Here we provide the first experimental demonstration of roomtemperature switchable polarization in bulk crystals of Ca3 Ti2 O7 , as well as Sr-doped Ca3 Ti2 O7 . Furthermore, (Ca,Sr)3 Ti2 O7 is found to exhibit an intriguing ferroelectric domain structure resulting from orthorhombic twins and (switchable) planar polarization. The planar domain structure accompanies abundant charged domain walls with conducting head-to-head and insulating tail-to-tail configurations, which exhibit a conduction di�erence of two orders of magnitude. These discoveries provide new research opportunities, not only for new stable ferroelectrics of Ruddlesden–Popper compounds, but also for meandering conducting domain walls formed by planar 1,2,* polarization. 1 1 3 4 week ending 23 JANUARY 2015 Negative Thermal Expansion in Hybrid Improper Ferroelectric Ruddlesden-Popper Perovskites by Symmetry Trapping T M. S. Senn, 1 A. Bombardi, C. A. Murray, C. Vecchini, A. Scherillo, X. Luo,5 and S. W. Cheong5,6 Diamond Light Source Limited,energy Harwell Science and Innovation Campus, Didcot OX11 0DE, United Kingdom here have been numerous attempts at computational ferroelectric barriers (for example, 20 meV for BaTiO 3 2 materials design based on first-principles calculations for (ref. 18),of 30 Chemistry, meV for PbTiOInorganic 25 meV for hexagonal Department Laboratory, University of Oxford, 3 (ref. 19) andChemistry Vol 452 | 10 April 2008 | doi:10.1038/nature06817 new functional materials1,2 . A large number of ferroelectric/ RMnO3 (R = rare earths) (ref. 20 and N. A. Spaldin, private South Parks Road, Oxford OX1 3QR, United Kingdom 3–7 piezoelectric materials have been computationally predicted , communication), the calculated switching barriers of 200 meV 3 5,8–13 Hampton Road, Teddington TW11 0LW, United Kingdom some of which have been experimentally confirmedNational . For Physical for Ca3 Mn2Laboratory, O7 and ⇠100 meV for (Ca/Ba) 3 (Sn/Zr) 2 O7 are still 15,17 4 example, the presence of ferroelectricity and strong coupling too largeRutherford to switch polarization for this Didcot reason, theOX11 0QX, United Kingdom ISIS, STFC, Appleton. Primarily Laboratory, between magnetism and ferroelectricity were theoretically validity of hybrid improper ferroelectricity in A3 B2 O7 has been 5 21–23 Laboratory Materials and Department of Physics, Pohang University of Science and Technology, predicted in EuTiO3 (ref. 3) and FeTiO3 (ref. for 4). Pohang The polar Emergent hotly debated . transition of the compounds was experimentally confirmed8,9 . Here we report the first experimental of hybrid Pohang demonstration 790-784, Korea 6 Some half-Heusler semiconductors are predicted to be new improper ferroelectricity in bulk single crystals of (Ca,Sr)3 Ti2 O7 . Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, 7 piezoelectrics with large polarizations . The theoretical prediction Electric polarization versus electric field P(E) hysteresis loops Piscataway, New polarization Jersey 08854, of stabilizing ferroelectricity in strained Srn+1 Tin O3n+1 (n 3; ref. 6) clearly show the existence of switchable with a USA was also experimentally confirmed in biaxially strained films, which unexpectedly low switching electric field.2014; Moreover, in-plane piezo(Received 9 September published 22 January 2015) exhibit switchable polarization at low temperatures10 ; Srn+1 Tin O3n+1 response force microscope (IP-PFM) images reveal intriguing films with large n such as SrTiO3 , corresponding to the n = 1 ferroelectric domain structures comprising abundant meandering We present newcharged results on the microscopic nature of the ferroelectricity mechanisms in Ca3 Mn2 O7 and member, do show ferroelectricity at room temperature11–13 . domain walls. To understand the origin of the unexpectedly Geometric ferroelectrics are improper Ca ferroelectrics where low switching electric field and abundancethe of charged walls, we Ti O . To the first approximation, wetheconfirm hybrid improper ferroelectric mechanism recently 3 2 7 geometric structural constraints, rather than typical cation–anion propose a classification of eight types of ferroelectric and four types by Benedek and Fennie for by these compounds. However, in Ca Mn2 O7 we 1 2 paring, induce ferroelectric polarization14proposed . Hybrid improper of ferroelastic domain1walls meansRuddlesden-Popper ofDawber crystallographic symmetry. Eric Bousquet *, Matthew *{, Nicolas Stucki2, Céline Lichtensteiger23, Patrick Hermet , Stefano Gariglio2, ferroelectricity, one kind of geometric ferroelectricity, results on this classification, between we individual 2 suggest that 1 switching find that there is a Based complex competition lattice modes of different symmetry which leads to a phase & Philippe Ghosez Jean-Marc Triscone from the combination of two or more non-ferroelectric structural of elementary tilting modes results in the low switching electric LETTERS Improper ferroelectricity in perovskite oxide artificial superlattices Alternative to tilts? Tri-linearcouplingoflatticemodes: E-field E ∝ λ R1 R2 P R1? R2? N WantRtostronglycoupletoelectronic degreesoffreedom: S orbital magnetic charge Jahn-Teller distortion Manganite systems 6 GOODENOUGH LaMnO3/BiMnO3$ The“Q2”distortion: Annu. Rev. Mater. Sci. 1998.28:1-27. Downloaded from www.annualreviews.org Access provided by Imperial College London on 01/28/16. For personal use only. Goodenough,Annu.Rev.Mater.Sci.2811998 YMnO3/BiMnO3$ YMnO3/LaMnO3$ Orthorhombicwithtwoshort, mediumandlongbondlengths A3+Mn3+O3/A’3+Mn3+O3 eg 3+ : d4 Mn 3+ e.g.Mn Q MJT 2 modes Q Figure 2 The E vibrational g 2 dx2-y2 and Q3 of an octahedral-site complex. dz2 complex is independent of ✓, which means that the p ground state correspondsdz2 dx2-y2 to any point on the circle of radius ⇢ = = g/ C, where C is the stiffness t2g constant associated with the vibrations. This situation corresponds to a dynamic coupling of the e electrons to the modes Q2 and Q3 and is referred to as a dynamic J-T stabilization of vibronic states. In order to obtain a static J-T deformation, it is necessary to introduce anharmonic terms into the potential energy and/or higher-order directly coupling terms.connected The ground state ofto an octahedral Bandgap JT distortion complex then becomes Marcus Schmitz et al., unpublished 1E = 2 [C/2 + (A3 B3 ) cos 3✓], 5. where A3 is generally positive (4). Although a point-charge calculation gives B3 > 0, covalent considerations favor square-coplanar bonding, which makes B3 < 0 and hence unambiguously favors a static deformation to tetragonal ! Jahn-Teller distortion Manganite systems 6 GOODENOUGH LaMnO3/BiMnO3$ The“Q2”distortion: Goodenough,Annu.Rev.Mater.Sci.2811998 R-point M-point Annu. Rev. Mater. Sci. 1998.28:1-27. Downloaded from www.annualreviews.org Access provided by Imperial College London on 01/28/16. For personal use only. MJT YMnO3/BiMnO3$ YMnO3/LaMnO3$ Orthorhombicwithtwoshort, mediumandlongbondlengths RJT A3+Mn3+O3/A’3+Mn3+O3 eg 3+ : d4 Mn 3+ e.g.Mn Q MJT 2 modes Q Figure 2 The E vibrational g 2 dx2-y2 and Q3 of an octahedral-site complex. dz2 complex is independent of ✓, which means that the p ground state correspondsdz2 dx2-y2 to any point on the circle of radius ⇢ = = g/ C, where C is the stiffness t2g constant associated with the vibrations. This situation corresponds to a dynamic coupling of the e electrons to the modes Q2 and Q3 and is referred to as a dynamic J-T stabilization of vibronic states. In order to obtain a static J-T deformation, it is necessary to introduce anharmonic terms into the potential energy and/or higher-order directly coupling terms.connected The ground state ofto an octahedral Bandgap JT distortion complex then becomes Marcus Schmitz et al., unpublished 1E = 2 [C/2 + (A B ) cos 3✓], 5. 3 3 Producesdifferentorbitalorderings, where A3 is generally positive (4). Although a point-charge calculation gives andhencespinorderings B > 0, covalent considerations favor square-coplanar bonding, which makes 3 B3 < 0 and hence unambiguously favors a static deformation to tetragonal ! Alternative to tilts – Jahn-Teller distortion Tri-linearcouplingoflatticemodes: E ∝ λ R1 R2 P E-field Alternative to tilts – Jahn-Teller distortion pss Phys. Status Solidi RRL 9, No. 1, 62–67 (2015) / DOI 10.1002/pssr.201409470 Tri-linearcouplingoflatticemodes: High-temperature ferroelectricity www.pss-rapid.com E-field and strong magnetoelectric effects E ∝ R1 R2 P in a hybrid organic–inorganic perovskite framework λ Ying Tian1, Alessandro Stroppa*, 2, Yi-Sheng Chai1, Paolo Barone2, Manuel Perez-Mato3, Silvia Picozzi2, and Young Sun*, 1 N S 1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China 2 CNR-SPIN, L’Aquila, Italy 3 Departamento de Fisica de la Materia Condensada, Facultad de Ciencia y Tecnologia, UPV/EHU, Bilbao, Spain Received 10 October 2014, revised 3 November 2014, accepted 10 November 2014 Published online 18 November 2014 orbital magnetic Keywords metal-organic framework, multiferroic, magnetoelectric effect, hydrogen bond * Corresponding authors: e-mail [email protected], [email protected] Potentialapplications:magnetoelectrics,electrochromic,MITs,transistors….?? A Cu-based organic–inorganic perovskite framework exhibits high-temperature ferroelectricity with strong magnetoelectric effects. Both electric field control of magnetization and magnetic field control of polarization are realized. Theoretical calculations suggest that a new mechanism of hybrid improper ferroelectricity arising from the Jahn–Teller distortions of magnetic metal ions and tilting of the organic cations are responsible for the peculiar multiferroic behaviors. SimilarmechanismproposedinrelatedMOFs formultiferroic magnetoelectric applications [1] Stroppa et al., Adv.Mater.25,2284(2013) [2] Tian etal.,Phys.StatusSolidiRRL9,62(2015) bulk modulus B = (c11 +2c12 )/3 of cubic SrRuO3 to be 172 GPa. No experimental data are a comparison, but bulk modulus values of 200 a have been reported in previous LSDA calculation the equation of states [25], which likely overesti MJT isallowed,andalwaysappears,inPnma perovskites [1,2] to the typical overbinding tendency of the LSDA Lattice-driven Jahn-Teller distortion Figure 2. The calculated phonon dispersion curves and phonon density of states of cubic SrR MJT 0–X–M–0–R–M − of the cubic Brillouin zone. The total DOS and the projected DOS of oxyge plotted using a solid line (in black), a dashed line (in blue), a dottedinstabilities line (in green) and shor 4. Antiferrodistortive anda dist JT xy xy frequencies indicate imaginary values. E ∝ λM φ A phases Axy Φxy- As previously discussed, the cubic structure points, attesting tha exhibits strong antiferrodistortive instabilities, ass exchange–correlatio rotations of the oxygen octahedra. If, in line with Finally, the ela we restrict ourselves to the oxygen rotations ass were computed wit + M+ that such r 3 and R4 modes and consider method [37]. For c appear along any of the three cubic directions, elastic constants: c six distinct basic tilt patterns (spanning the six-1 312.8 GPa, 101.8 G M+ R+ of the Pm3̄m 3 4 reducible representation to the Voigt–Reuss can be combined to generate various tilted struc bulk modulus B = ( Figure 3. A schematic illustration of relevant phonon modes of group theory analysis, Howard and Stokes [49] d to be 172 GPa. N SrRuO3 . Black arrows indicate the atomic motions. Sr atoms (inQ2 the existence of 15 distinct combinations o Doesnothavetoappearasanelectronicinstability! red) at the corners, Ru atoms (in green) at the centers and O atoms comparison, but bu patterns that, when condensed within the Pm3̄m (in blue) at the face centers of the perovskite cubic cell. The have been reported i lower the symmetry to distinct subgroups. T wavevectors are also given in parentheses for corresponding modes. the equation of stat HerewedefineaJahn-Tellerdistortion: oxygen-tilted structures are usually specified us to the typical overbi bythesymmetryofthemode(Q2),whetheritiselectronicallyorlatticedriven Glazer notations [48] such as a0 b+ c , in whi literals refer to the three cubic directions and [1] Carpenter & Howard, Acta Cryst. B 65, 134 (2009) we also performed the phonon calculation with the LSDA 4. Antiferrodistor superscripts refer to the condensation of no [2] Miao, Bristowe, Xu, Verstraete & Ghosez, JPCM 26 035401 (2014) P1: psa/dpk P2: ARK/plb June 3, 1998 14:4 27. Downloaded from www.annualreviews.org ge London on 01/28/16. For personal use only. 6 QC: ARK Annual Reviews AR059-01 GOODENOUGH Figure 2 The Eg vibrational modes Q2 and Q3 of an octahedral-site complex. complex is independent of ✓, which means that the p ground state corresponds to any point on the circle of radius ⇢ = = g/ C, where C is the stiffness constant associated with the vibrations. This situation corresponds to a dynamic coupling of the e electrons to the modes Q2 and Q3 and is referred to + Highlight three P-JT couplings Symmetryanalysissupportedbyfirstprinciplescalculations(PBEsol+U and/orB1WC) 1)Superlattices (d1-d0) Titanates:ATiO3-RTiO3 2)Superlattices (d2-d2) Vanadates:RVO3-R’VO3 3)Epitaxialbulk(alldfillings) ferrites,titanates,manganites … − xy xy E ∝ λ M JT φ P Bristowe, Varignon, Fontaine, Bousquet & Ghosez, Nat. Commun. 6, 6677 (2015) E ∝ λ M JT Pz RJT Varignon, Bristowe, Bousquet & Ghosez, Sci Reports 5, 15364 (2015) E ∝ λ M JT Pxy Axy Varignon, Bristowe & Ghosez, Phys. Rev. Lett 116, 057602 (2016) Highlight three P-JT couplings Symmetryanalysissupportedbyfirstprinciplescalculations(PBEsol+U and/orB1WC) 1)Superlattices (d1-d0) Titanates:ATiO3-RTiO3 2)Superlattices (d2-d2) Vanadates:RVO3-R’VO3 3)Epitaxialbulk(alldfillings) ferrites,titanates,manganites … − xy xy E ∝ λ M JT φ P Bristowe, Varignon, Fontaine, Bousquet & Ghosez, Nat. Commun. 6, 6677 (2015) E ∝ λ M JT Pz RJT Varignon, Bristowe, Bousquet & Ghosez, Sci Reports 5, 15364 (2015) E ∝ λ M JT Pxy Axy Varignon, Bristowe & Ghosez, Phys. Rev. Lett 116, 057602 (2016) R is a trivalent ferromagnetic and ferroelectric insulating ground state. a rich variety of The electronic structure exhibits an intricate orbital and 3 3 oped manganites charge ordering which is argued to be at the heart of the ype AFM metallic observed ferromagnetism. A symmetry lowering struca CE-type AFM tural distortion enabling this particular orbital ordering Ground-state 2+ =Sr,Ba,(Ca) A with two different (Inallcases!) lumnar [11]), and 3.5+ ” and “antiferro” Ti =Ti TABLE I: Key quantities for a selection of ATiO3 -RTiO3 sud electronic phase R3+=La,Pr,Sm Y, - MonoclinicP21symmetry perlattices including amplitude Q (Å) of lattice distortions n the A and R Tm,(Lu) − (in-phase Φ+ z and anti-phase Φxy AFD motions, polar- mode Insulating disordered (such Pxy , Jahn-Teller mode appearing at the M -point of the cu- Ferroelectric ch as for Ba and bic Brillouin zone MJT , breathing Jahn-Teller BJT ), polari- mpare the physics of the half-doped nd R cations are the titanates, and d Mott insulating An exception has of very small Aa rocksalt charget insulating phase r hand, in layered ATiO -RTiO superlattice sation, P (µC/cm2 ), band gap, ∆ (eV), and gain of energy - Ferromagnetic for FM vs AFM solution (see Methods) per 20-atom formula unit, ∆E (meV). Symmetryadaptedmodeanalysis R, A Sm, Sr Y, Sr Tm, Sr Sm, Ba Y, Ba Tm, Ba Φ+ z Φ− xy 0.96 1.10 1.18 0.75 0.95 1.05 1.19 1.30 1.36 0.96 1.08 1.16 (a0a0c+)(a-a-c0) Q Pxy 0.56 0.66 0.72 0.48 0.59 0.65 BJT 0.10 0.11 0.11 0.13 0.14 0.16 MJT 0.04 0.04 0.03 0.07 0.07 0.07 P ∆ ∆E 14.9 16.7 18.2 18.6 21.2 23.4 0.46 0.57 0.63 0.50 0.60 0.66 20.1 18.0 16.4 18.5 13.9 10.5 Pnma-like(a-a-c+) groundstate E = λφ xy− φ z+ Pxy Ferroelectric: AmplificationofP throughdissimilarZ* can display ferromagnetic (FM) or A-type AFM metallic behaviour [5–7] or more commonly a CE-type AFM Mott insulating phase [8, 9] associated with two different charge orderings (Rocksalt [10] and Columnar [11]), and two different orbital orderings (“ferro” and “antiferro” Mn d eg orderings [12]). The preferred electronic phase appears to be strongly dependent on the A and R cation sizes and whether they appear disordered (such as with Ca and La/Pr) or layered (such as for Ba and La/Tb/Y [5, 10, 12]) in the crystal. observed ferromagnetism. A symmetry lowering structural distortion enabling this particular orbital ordering System remains insulating In this regard, it is interesting to compare the physics of the half-doped manganites, with that of the half-doped titanates. At the bulk level, the A and R cations are found to naturally disorder [13, 14] in the titanates, and typically no charge and orbital ordered Mott insulating phase is observed at half-doping [15]. An exception has been recently discovered for the case of very small Acations, such as Ca0.5 Lu0.5 TiO3 , where a rocksalt chargeordered and dxy t2g orbital-ordered Mott insulating phase was recently proposed [16]. On the other hand, in layered TABLE I: Key quantities for a selection of ATiO3 -RTiO3 suz distortions perlattices including amplitude Q (Å) of lattice y + − (in-phase Φz and anti-phase Φxy AFD motions, polar mode Pxy , Jahn-Teller mode appearing at the M -point of the cux bic Brillouin zone MJT , breathing Jahn-Teller BJT ), polarisation, P (µC/cm2 ), band gap, ∆ (eV), and gain of energy for FM vs AFM solution (see Methods) per 20-atom formula unit, ∆E (meV). R, A Sm, Sr Y, Sr Tm, Sr Sm, Ba Y, Ba Tm, Ba Φ+ z Φ− xy 0.96 1.10 1.18 0.75 0.95 1.05 1.19 1.30 1.36 0.96 1.08 1.16 Q Pxy 0.56 0.66 0.72 0.48 0.59 0.65 BJT 0.10 0.11 0.11 0.13 0.14 0.16 MJT 0.04 0.04 0.03 0.07 0.07 0.07 P ∆ ∆E 14.9 16.7 18.2 18.6 21.2 23.4 0.46 0.57 0.63 0.50 0.60 0.66 20.1 18.0 16.4 18.5 13.9 10.5 System remains insulating z y x d0 d1 d1 d0 d1 d0 d0 d1 Charge ordered (d1- d0) state associated with a Breathing distortion LiftsthedegeneracybetweenneighboringTisites Chargeorderreportedinsimilarsystems: R. Pentcheva and W.E. Pickett, Phys. Rev. Lett. 99, 016802 (2007) A.C. Komarek et al., arXiv:1109.0234 (2012) Electronic structure – charge+ orbital ordering Projected DOS z Total Density of States O 2p y ‘d1’ x Ti t2g -0.5 dxz 0.0 Total up Total down Ti1 dxz + Ti3 dyz Ti2+4 dxz+yz -4 -3 -2 -1 0 Energy (eV) 1 mixed ‘d0’ - Spin-polarizedsplit-offd1 band - Nottheideald1–d0 occupancy - d1 site:orbitalorderingdxz – dyz - d0 site:orbitalmixing ‘d1’d yz nly a CE-type AFM ated with two different d Columnar [11]), and ferro” and “antiferro” erred electronic phase nt on the A and R pear disordered (such d (such as for Ba and l. o compare the physics that of the half-doped A and R cations are ] in the titanates, and € dered Mott insulating 15]. An exception has case of very small Ahere a rocksalt chargeMott insulating phase other hand, in layered tural distortion enabling this particular orbital ordering Origin of orbital ordering TABLE I:M Keydistortionallowedbysymmetry quantities for a selection of ATiO3 -RTiO3 suJT perlattices including amplitude Q (Å) of lattice distortions − (in-phase (equivalenttothecouplinginPnma) Φ+ z and anti-phase Φxy AFD motions, polar mode Pxy , Jahn-Teller mode appearing at the M -point of the cu− Jahn-Teller− BJT ), polaribic Brillouin zone MJT , +breathing z gap, xy ∆ (eV), xy JT and xy gain of energy sation, P (µC/cm2 ),xyband for FM vs AFM solution (see Methods) per 20-atom formula unit, ∆E (meV). F ∝P φ φ +P M φ R, A Sm, Sr Y, Sr Tm, Sr Sm, Ba Y, Ba Tm, Ba Φ+ z 0.96 1.10 1.18 0.75 0.95 1.05 Φ− xy 1.19 1.30 1.36 0.96 1.08 1.16 Q Pxy 0.56 0.66 0.72 0.48 0.59 0.65 BJT 0.10 0.11 0.11 0.13 0.14 0.16 MJT 0.04 0.04 0.03 0.07 0.07 0.07 P ∆ ∆E 14.9 16.7 18.2 18.6 21.2 23.4 0.46 0.57 0.63 0.50 0.60 0.66 20.1 18.0 16.4 18.5 13.9 10.5 Origin of orbital ordering MJT distortionsproducestheC-typeorbitalordering F ∝ Pxyφ φ + Pxy M JT φ + z MJT distortion € − xy − xy FM due to intrasite Hund’s FM Hund’s dxz! dxz! dyz! pz! dyz! py! AFM Pauli’s dxy! dxy! px! Ti1 “d1” dxy! py! O1 Ti2 “d0” O2 Ti3 “d1” MJT crucial for FM IfweartificiallysuppressAFDmotionsandhenceMJT − xy xy E ∝ λ M JT φ P - Noorbitalordering:dxy occupancyeverywhere - AFMGS - Pauli’sexclusionprinciple FM Hund’s WithMJT motions: dxz! dxz! dyz! pz! dyz! py! AFM Pauli’s WithoutMJT motions: dxy! dxy! px! Ti1 “d1” dxy! py! O1 Ti2 “d0” O2 Ti3 “d1” Highlight three P-JT couplings Symmetryanalysissupportedbyfirstprinciplescalculations(PBEsol+U and/orB1WC) 1)Superlattices (d1-d0) Titanates:ATiO3-RTiO3 2)Superlattices (d2-d2) Vanadates:RVO3-R’VO3 3)Epitaxialbulk(alldfillings) ferrites,titanates,manganites … − xy xy E ∝ λ M JT φ P Bristowe, Varignon, Fontaine, Bousquet & Ghosez, Nat. Commun. 6, 6677 (2015) E ∝ λ M JT Pz RJT Varignon, Bristowe, Bousquet & Ghosez, Sci Reports 5, 15364 (2015) E ∝ λ M JT Pxy Axy Varignon, Bristowe & Ghosez, Phys. Rev. Lett 116, 057602 (2016) RVO3 Pnma P21/c G-o.o Pnma Pnma P21/c G-o.o P21/c G-o.o G-type AFM Pnma C-o.o P21/c C-o.o + G-o.o C-type AFM Rare-earthvanadates Pnma atroomT,andwithdecreasingT appearanceof: - CandGtypeorbitalorderings - GandCtypeAFMorderings - StructuralphasetransitiontoP21/cforC-AFM Sage et al, PRB 76 195102 (2007) P properties, including ferroelectricity, (anti)ferromagnetism Φ+z (AFM), superconductivity and magnetoresistance. This 3 diverse behaviour is appealing for both3 fundamental and applied P4/mmm investigations, and has resulted in an intense global research structure P4/mmmref effort over the past few decades. Many of these functional AFMG Pb2and AFMCPb • Ground state: 1m subtle properties manifest due to the complex interplay between spin, charge, orbital and lattice degrees of +7.76meV freedom in YVO/LaVO 0meV perovskites1–4. Of the perovskites, the doped manganites have PrVO/YVO 0meV -0.87meV Breathing oxygen become a prototypical playground for the study of this interplay. BOC 0meV Just considering thePrVO/LaVO case of half-doping, that is, A20:5þ -3.72meV R30:5þ MnO3 , 3 þ is a metal ion and R where A2 þ is a divalent alkaline earth (“Pnma”) (“P21/c”) _ trivalent rare earth ion, manganites exhibit a rich variety (“Pm3m”) of electronic phases. For example, half-doped manganites can display ferromagnetic (FM) or A-type AFM metallic behaviour • Symmetry mode analysis of ground states (Å) 5–7 8,9 or more commonly a CE-type- AFM +Mott insulating phase Φxycharge Φzorderings Φz- (rocksalt RJT 10 and MJT Pz Pxy associated with two different and two different columnar11)Pb2 YVO/LaVO 1.58 orbital 1.14 orderings (‘ferro’ and 0.12 0.77 1m AFMG 12). The preferred electronic phase Figure 1 | Superlattice geometry, ma ‘antiferro’ Mn d e orderings g PrVO/YVO Pb AFMC 1.61 1.16 0.01 0.10 0.04 0.01 0.81 appears to be strongly dependent on the A2 þ and R3 þ cation resulting ferroelectric, charge and o 3 þ TiO digital PrVO/LaVO Pb AFMC 1.36disordered 0.94 (such 0.01 as with 0.10 Ca and 0.01 R0.00(4) 0.59 superlattice 10-atom sizes and whether they appear 3 -c0) (a-afor reference structure undergoes two m a0c+) La/Tb/Y5,10,12) in the La/Pr) or layered (such as Ba(a0and motions and a breathing oxygen cage crystal. “Pnma”-liketiltpattern In this regard, it is interesting to compare the physics of the of large (blue) and small (grey) octahe half-doped manganites, with that of the half-doped titanates. At are shown in the 20-atom cell. The A 3 þ cations are found to naturally Pb component,andcombinationofbothJahn-Tellers through a unique anharmonic couplin thephaseshaveadditionalP bulk level, the A2 þ andz R disorder13,14 in the titanates, and typically no charge and orbital- combination of the AFD motions and RVO -R’VO Superlattices R’VO3-RVO3 couplings (RVO3)1/(R’VO3)1 superlattice expansion [2] • Pb21m (Pnma in bulk) • Pb (P21/c in bulk) [1] New trilinear coupling identified Out-of-plane polarization coupled to Jahn-Teller ! [1] Bousquet et al, Nature 452 (2008) [2] Fukushima et al, Phys. Chem. Chem. Phys 13 (2011); Rondinelli et al, Adv. Materials 24 (2012) Magnetoelectric application? Electric field driven magnetic transition ? YVO/LaVO: ΔE(AFMG-AFMC) = -7.76 meV Ground-state: Pb21m (‘’Pnma’’) – AFMG phase: Change of orbital and AFM orderings ! Electric field driven magnetic transition Finite electric field method (transition at 0.55 V / bilayer) Pb21m Pb E-field directly controls RJT distortion amplitude! In turn, this induces M transition Highlight three P-JT couplings Symmetryanalysissupportedbyfirstprinciplescalculations(PBEsol+U and/orB1WC) 1)Superlattices (d1-d0) Titanates:ATiO3-RTiO3 2)Superlattices (d2-d2) Vanadates:RVO3-R’VO3 3)Epitaxialbulk(alldfillings) ferrites,titanates,manganites … − xy xy E ∝ λ M JT φ P Bristowe, Varignon, Fontaine, Bousquet & Ghosez, Nat. Commun. 6, 6677 (2015) E ∝ λ M JT Pz RJT Varignon, Bristowe, Bousquet & Ghosez, Sci Reports 5, 15364 (2015) E ∝ λ M JT Pxy Axy Varignon, Bristowe & Ghosez, Phys. Rev. Lett 116, 057602 (2016) Can couplings appear in general bulk ABO3? Strainengineering? TERS Can couplings appear in general bulk ABO3? Strainengineering? PHYSICAL UnusualPmc21phase(equivalentlyPb21m)undertensilestrain: GroundstateforBiFeO3,PbTiO3,BaMnO3,EuTiO3,CaTiO3 (+?)atabout5%[1] week ending “Orbitalordering”observedforBiFeO 3 AUGUST 2012 3 [1] (thoughnoJahn-Tellerdistortionmentioned) Tri-linearcouplingfound[2]: (butnotinvolvingJahn-Teller?) E ∝ λ Axyφ z+ Pxy Axy (M5+) [1]Yangetal.,Phys.Rev.Lett.109 057602(2012) F1:1 [2]Yangetal.,Phys.Rev.Lett.112 057202(2014) FIG. 1. Schematic view of the main four lattice distort Reinvestigate Pmc21 phase PHYSICAL REVIEW LETTERS Trulygeneral?Testonarangeofd-fillings TABLE I. Epitaxial strain (%), magnetic ground state, amplitudes of distortions (Å), and electronic band gap value (eV) for each material. The spontaneous polarization is also reported in μC cm−2 . Only the relevant distortions are d0 d3 d4 d5 summarized in the present table [59]. Strain Magnetism P (Γ−5 ) þ M Qþ 2JT (M 3 ) A (M þ 5) þ ϕz (M þ 2) Gap (%) (Å) (μC cm−2 ) (Å) (Å) (Å) (eV) SrTiO3 BaMnO3 BiFeO3* þ7.35 [61] NM 0.615 76 0.232 0.558 0.640 3.02 þ6.1 [61] FM 0.421 45 0.190 0.217 P H Y0.059 SICAL 0.28 þ5.8 [61] AFMG 0.346 29 0.644 1.072 R E1.668 VIEW 1.88 YMnO3* þ4.0 [61] AFMG 0.753 7 [62] 0.737 0.940 L E T1.733 TERS 1.88 the authors reported the existence of *AlsodevelopΦ xy 169 170 171 172 173 174 175 direction is along the [001] axis of the Pbnm structure). Beyond around 5% tensile strain, the four compounds, th modefound:M 4 indeed, develop the desired Pb21 m ground state.JTStrained BaMnO3 [ferromagnetic (FM)] and YMnO3 [G-type antiVerylarge! ferromagnetic (AFMG)] exhibit a different magnetic ground state compared to the bulk (AFMG and E-type antiferromagnetic, ↑↑↓↓ zigzag chains coupled antiferro- 3þ the Fe 3d orbitals,active explained from expected since YMnO3 is known to be Jahn-Teller in 210 polar and yield the bulk. We emphasize, at this stage, thatthe theantipolar polar modemotion in 211 [33]. This 212 orbita BiFeO3 (and YMnO3 ) is not distortion unstable, andpattern therefore, highly in this ferroelectric system, noinJahn-Telle strained BiFeO3 appears assince, an improper 213 3þ contradiction to Refs. [18]form anda [64]. the (Fe 214 Mott Computing insulating state a 2 phonons in the intermediatespin strained phase of both 215 t32g ePbnm g configuration). A Jahn-Te BiFeO3 and YMnO3 compounds only one in hybrid is yetreveals to be reported the Pb2216 1m p form a M spin configuration). A Jahn-Tell spin t32g e2g is yet to be reported in the Pb2 phb 1 m to is yet best of our knowledge. Frombest ourofsyo clearly demonstrate that, as this Pb2de clearly 1 aforementioned distortions (P,aforemen A, and + Axy Φz of Eq. (1) is automatically lowered of Eq. thr (1) (M5+) (M2+) four of a fourth lattice distortion:of aa Jahn Therefore Therefore, while it may not Teller be unst mo Teller motion is forced into the system mechanis mechanism arising from theresult trilinea cla F1:1 FIG.+ 1. Schematic view of the main four lattice distortions result clarifies the origin of displayed the unu in the Pb2 m phase of perovskites under tensile FIG. 1. Schematic view of theF1:2 mainxyinvolved four lattice distortions P Hby Y STI C A L REV I EitW z xy xy 1 JT xydisplayed achieve a ; moreover, pr þ 3R − EBiFeO P H Y S I C A L R E V I E W L T E S epitaxial strain. Polar distortion (irreps Γ5 ), (b) Q2 Jahninvolved in the Pb21 m phase F1:3 of perovskites under(a) tensile þ bulkofpero achieve an electric field control th þ − F1:4 Teller distortion (irreps M 3 ), (c) antipolar A distortion (irreps epitaxial strain. (a) Polar distortion (irreps Γ ), (b) Q Jahn2 5 þ þ the pr a The F1:5 M 5 ), (d) a0 a0 cþ ϕþ antiferrodistortive motion (irreps M 2 ). the existence þ bulk perovskites. z the authors reported Teller distortion (irreps M 3 ), (c) antipolar A distortion (irreps perovskit thePb F 3þ þ 0 0 þ þ The predicted highly strained the Fe 3d orbitals, explained fro Mþ ), (d) a a c ϕ antiferrodistortive motion (irreps M ). z 2 5 to occur a polar perovskites is the notperovskite restricted motion toinBiFeO Starting from the reference Pm3̄mand cubic 86 polar antipolar yi 3 BaMn Pxy M − disto phase, the condensation JT of the mode Ppattern (irreps Γ 87 to polar occur also in some titanates (CaTiO distortion [33]. This orb 5) pound Tb + (GM ) þ (M3 ) þ 5 3̄m cubic perovskite Starting from the reference88Pm since and the JT mode Q2 (irreps Min3 ) BaMnO lowers the a no in [33],system, andtoeven athen Jaha since, in3 symmetry this Jahn-Te are − phase, the condensation of the 89polarPb2 mode P (irreps Γ5 ) subgroup form a polar ofTbMnO Pbnm. We, then, 3þ 1 m phase, pound [36]. The highly strai between form a Mott insulating state (Fe 3 þ þ perform free energytoexpansion the reference and the JT mode Q2 (irreps M3 90 ) lowers the asymmetry a spin 3 2ideal order to c are[25] then(around an playground to demo spin t e configuration). A Jahng 2g structure) termsthen, of the lattice distortions allowed by 91 Pb21 m phase, a polar subgroup of Pbnm.in We, yet between the polarization and this theisLette Jahn Invariants analysis F1:1 F1:2 F1:3 F1:4 F1:5 86 87 88 89 E ∝ λA φ P + λA M P t32g e2g E-field control of gap via JT YMnO3 largesteffectsinceitisJTactive HYSICAL REVIEW LETTERS + 4,5 0,4 0,2 1,5 -1 -0,5 0 0 0,05 0 -0,05 -0,1 0 -0,5 dz2 1 1,5 EFermi (eV) 2 0,5 0 -0,5 -1 2,5 0,3 0,2 SrTiO3 BaMnO3 YMnO3 BiFeO3 0,1 0 0,6 ∆Gap (eV) 4 0,4 ΔQ∆Q MJT (Å) 2 5 4 3 2 1 0 dxz 0,4 0,2 0 -0,2 0 10 5 15 -1 Electric field (MV.cm ) 20 On-going/Future research in my group Emergentphenomenaatperovskite interfaces: DFT and DFPT Phonon Calculations Khang Le Negativethermalexpansion Innaturallylayeredperovskites Fvib = c X ~!sq sq 2 ✓ +kB T ln 1 e Strainengineeringstructuralphases ◆ ~!sq kB T 200 150 100 JordanCowell -1 ω (cm ) ChrisAblitt 50 Grüneisen Analysis 0 AndrewWarwick -50 γ i 12 10 8 6 4 2 0 -2 -4 = ✓ @ ln (!i ) @ ln(V ) ◆ P5 M5+ Γ5X3+ Λ5 -100 -150 Emergentferroic ordersatdomainwalls Γ Photoferroicity inlayeredhybridperovskites 7 Methodology “Effectivepotential”forlatticedynamics Wojdel etal.,JPCM25 305401(2013) Energy changes around reference structure due to distortions: (1) Energy change from atomic displacements (p: phonons), with: (2) Energy change due to strain only FiniteE:PbTiO3-SrTiO3 0.4 Polarization along z (C/m2) Strain (from DFT cubic SRO) 0.014 0.012 KENNEDY, HUNTER, AND HESTER 0.008 0.3 Pz Px 0.04 0.2 0.02 0.1 PHYSICAL REVIEW B 65 224103 0 0 -0.1 0.006 0.06 -0.02 -0.2 0.004 0.002 -0.04 -0.3 0 FIG. 1. Temperature dependence of the lattice parameters for SrRuO3 . The open and closed symbols give the results of duplicate measurements. The vertical dashed lines show the transitions between the three phases. 100 200 300 400 500 600 700 800 900 Temperature (K) reflections indicating the presence of in-phase !!" and outof-phase !"" tilts, respectively.17 The data were well fitted to 9,10,12 FIG. 2. Portions of the synchrotron diffraction patterns recorded at 363, 678, 883, and 948 K, showing the splitting indicative Pnma, Imma, I4/mcm and Pm3 m phases, respectively. The indices of the reflections in the cubic structure are indicated. -0.4 -0.15 -0.1 -0.05 0 0.05 0.1 Electric field along z (GV/m) lost while the peaks clearly show a tetragonal splitting and the assignment of cubic symmetry is the point at which no asymmetry of the diagnostic reflections remains. The diffraction data clearly reveal the presence of two -0.06 0.15 Polarization along x (C/m2) FiniteT:SrRuO3 0.01 (3) Strain-phonon coupling term Collaborators Theoretical Materials Physics, University of Liege, BELGIUM Philippe Ghosez, Julien Varignon (now at CNRS/Thales), Eric Bousquet CSIC, UAB, Spain Massimiliano Stengel, Miguel Pruneda Department of Materials, Imperial College London, UK Arash Mostofi, Chris Ablitt Department of Chemistry, University of Warwick, UK Mark Senn LIST, Luxembourg Jorge Iniguez Collaborators Theoretical Materials Physics, University of Liege, BELGIUM Philippe Ghosez Eric Bousquet Julien Varignon NowatCNRS,Thales,France Denis Fontaine