Electronic soft matter Incommensurate and textured phases in manganites Peter Littlewood Theory of Condensed Matter Group Cavendish Laboratory University of Cambridge pbl21@cam.ac.uk Theory: Luis Brey (Madrid) Maria Calderon (Madrid), Valeria Ferrari, Simon Kos, Geoff Milward, Mike Towler (TCM) Experiment: Paul Attfield (Edinburgh), Tony Williams (Chemistry, Cambridge) Casey Israel, James Loudon, Neil Mathur, Paul Midgley (Mat Sci, Cambridge) Alex de Lozanne (Texas) Susan Cox, John Singleton (LANL) Ferrari, Towler, PBL, Phys. Rev. Lett. 91 , 227202 (2003) Milward, Calderon, PBL, Nature 433 , 607 (2005) Loudon et al., Phys. Rev. Lett. 94 097202 (2005) Cox et al. Physical Review B 73 132401 (2006) Cox et al Nature Materials 7, pp25-30 (2008)
An aside .... Exciton Polariton Condensation A new kind of BEC of a bosonic quasiparticle http://www.tcm.phy.cam.ac.uk/icsce4/schedule.html Has a set of talks at a recent meeting held in Cambridge
Polaritons: Matter- Polaritons: Matter -Light Composite Bosons Light Composite Bosons photon [C. Weisbuch et al., PRL 69 3314 (1992)] in-plane ph momentum energy UP photon QW mirror mirror QW exciton LP Effective Mass m * ~ 10 -4 m e T BEC ~ 1/m * momentum
Occupancy as a function of power Polariton BEC in CdTe microcavities: Kasprzak et al, Nature, 443 , 409 (2006)
What has been observed • Condensation in momentum space (open system) • Spatial first order coherence demonstrated • Vortices • Bogoliubov modes (?) • Driven dynamics • Several kinds of traps • Crossover to conventional laser • Non-equilibrium operation near room T in GaN Issues of principle • Decoherence – open system • Composite particles – strongly interacting system • 2D • Non-equilibrium and quantum dynamics
“Soft” matter is not confined to soft materials Defects in nematic liquid crystal Soft condensed matter physics is the study of materials with mesoscale structures often entropically dominated; e.g. liquid crystals, complex fluids, membranes. “Softness” implies pliable rearrangement to external forces “Stripes” of charge-density wave in TaSe 2 100 nm 30 nm patches of charge-order in LaCaMnO 3 C.H.Chen Loudon & Midgley
“Colossal” magnetoresistance (CMR) in manganites Phase transition between metallic G.H. Jonker and J.H. Van Santen, Physica 16 337 ferromagnet and insulating or poorly (1950), J.H. Van Santen and G.H. Jonker, Physica 16 599 (1950). metallic paramagnet Urushibara et al 1995
Perovskite manganites • A “doped” oxide - e.g. La 1-x Ca x MnO 3 where Mn the formal valence of Mn varies between O Mn 3+ and Mn 4+ Re/Ae • A “strongly correlated” electron system close to a (Mott) metal-insulator transition Hopping - aligns core moments and Jahn-Teller distortion leads to ferromagnetic metal suppresses hopping Mn 4+ Mn 3+ Mn 3+ Mn d-levels e g e g Leads to insulating state with t 2g t 2g orbital and/or charge order Distorted Cubic Cubic
Generic phase diagram • Ferromagnetic metal Cross over degenerate electron plasma 1 st order suppressed lattice distortions PM T CO liquid /PM • Charge/orbital ordered solid ordered insulating array of 3+/4+ * • Polaronic liquid CO dynamic lattice distortions FM 2 nd order local charge/orbital order electronically insulating Effective electron-phonon coupling Resistance Coexistence? Tuned by doping, rare earth size, Hysteresis? magnetic field, elastic strain, …. Phase separation? Temperature Urushibara et al 1995
Manganite phase diagrams • Many complicated phases showing competition of electronic structure, lattice distortions and magnetism • Can be difficult to separate phenomena due to disorder from “true” phase coexistence • Puzzling asymmetry near x=1/2
“Striped” phases of La 0.33 Ca 0.67 MnO 3 TEM image shows periodic ordered lattice Interpreted as periodic array of 3+/4+ ions ??? S Mori, CH Chen and S-W Cheong, Nature 392 (1998) 473
How should we think about the short length- scale charge order that is most evident in the “striped” phases of the manganites?
Cartoon of ordered structure near ½ hole concentration Mn(III) • Pure LaMnO 3 – herringbone pattern of orbital order of Mn 3+ • La 1-x Ca x MnO 3 - “stripes” composition of Mn 3+ :Mn 4+ in ratio (1-x):x Mn(IV) Antiferromagnetic CE phase x=1/2
Aside: Realistic electronic structure versus cartoon • Conventional story relies on 3+/4+ ordering – Large Coulomb cost of charge disproportionation? – Considerable evidence for “holes on Oxygen”, esp. optics and photoemission – Disputed picture of structural ordering • “stripes” [Chen et al PRL 76, 4042 (1996)] • “crystal” [Radaelli et al PRB 55, 3015 (1997)] • “molecular polarons” [Daoud-Aladine et al. PRL 89, 97205 (2002)] • ferroelectricity [Efremov et al condmat/0306651] • Ab initio Hartree-Fock for La 0.5 Ca 0.5 MnO 3 – Input is atomic positions (Radaelli et al) – CRYSTAL98 code V Ferrari, MD Towler and PBL, Phys. Rev. Lett. 91 , 227202 (2003) – See also (esp for discussion of Zener polaron) Zheng and Patterson, Phys. Rev. B 67 , 220404 (2003) (including structural minimisation) C H Patterson, cond-mat/0405299
UHF spin density in La 0.5 Ca 0.5 MnO 3 V Ferrari et al, Phys. Rev. Lett. 91 , 227202 (2003)
Real phase diagrams • Many complicated phases showing competition of electronic structure, lattice distortions and magnetism • Can be difficult to separate phenomena due to disorder from “true” phase coexistence • Puzzling asymmetry near x=1/2
Cartoon structure of phases near doping 1/2 Mn(III) • Pure LaMnO 3 – herringbone pattern of orbital order of Mn 3+ • La 1-x Ca x MnO 3 - “stripes” composition of Mn 3+ :Mn 4+ in ratio (1-x):x Mn(IV) x=1/2 S p a c i x>1/2 n g 1 periodic array of discommensurations / ( x - 1 / 2 )
“Striped” phases of La 0.33 Ca 0.67 MnO 3 TEM image shows periodic ordered lattice Interpreted as periodic array of 3+/4+ ions ??? S Mori, CH Chen and S-W Cheong, Nature 392 (1998) 473
TEM images of charge ordering in La 0.5 Ca 0.5 MnO 3 Substantially incommensurate at high T Ferromagnetic in incommensurate phase Chen & Cheong, PRL 76, 4042 (1996)
Zoom in on La 0.48 Ca 0.52 MnO 3 • 500 nm region gives q/a*= 0.468±0.003 500 nm 3.6 nm 200 100 000 100 200 Alternating Mn 3+ /Mn 4+ planes when x=0.5 • Expect extra Mn 4+ planes every 9.6 nm when x=0.52 • • Expect doubled period between stacking faults (q/a*=0.5) • 3.6 nm region never shows q/a*=0.5 • 3.6 nm region gives q =0.473±0.005 Loudon et al. Phys. Rev. Lett. 94, 097202 (2005). • Modulation has uniform periodicity
Puzzles about the charge-ordered phases • Unexpected incommensurability – Even at x=1/2, onset q ~ 0.4 Chen & Cheong, Phys. Rev. Lett. 76 , 4042 (1996) • Weak ferromagnetism just below T CO • Onset of AF at lower T, when q saturates • Asymmetry near 1/2 – Low T value of incommensurability as expected from doping for x>0.5 – where CO is seen for x<0.5, q =0.5 • Canted magnetism in CO phase, x<1/2 • Uniformly incommensurate phase – no domain walls Loudon et al, Phys. Rev. Lett. 94 097202 (2005)
Phenomenology • Phenomenological explanation can be found in Ginzburg- Landau theory – coupling between gradients of order parameters M (magnetism) and ρ (density wave) ρ M 2 Q · ∇ ρ • Homogeneous coexistence dis-favored • Inhomogeneous coexistence favored – negative free energy for a domain wall • Destabilises first order transition in favor of continuous transition via inhomogeneous phases. • Distortion is weakly coupled to lattice Milward, Calderon and PBL Nature 433 , 607 (2005)
Coupled order parameters • Write Free energy as function of = + ρ + Δ ρ variables M, ρ , etc. F F ( M ) F ( ) F ( M ; ) mag CO q • Can generate terms in Free energy that favour Δ ∝ + 2 ρ 2 F M coexistence or not of phases (presumably CO and FM do NOT like homogeneous coexistence). • Generically there are also couplings between “gradients” favouring either positive or negative Δ ∝ ρ ∇ φ 2 2 F M 0.5 incommensurability (relative to 1/2) x For x=1/2, possibly incommensurate if also magnetic For x < 1/2, natural incommensurability cancelled by coexisting magnetism (magnetic structure is canted AF), (Jirak 1985)
Coexisting FM and CO Magnetisation Incommensurability
Internal structure of domain walls Charge order appears at magnetic domain wall Also: Rzchowski and Joynt, Europhys.Lett. 67 287 (2004) Magnetism enhanced near discommensuration Current experiments show magnetism to be uniform and commensurability effects weak
Superlattice control through strain release La 0.5 Ca 0.5 MnO 3 0.465 0.476 0.465 0.476 q/a* q/a* Cox et al. cond-mat/0504476
Sliding CDW in La 0.5 Ca 0.5 MnO 3 epitaxial films? Linear resistivity shows small gap ~ 100 meV Cox et al. arXiv:0705.4310
Non-linear resistivity with “threshold” electric field Aligned thin film q CDW Resistance as function of field Diffraction intensity
Broad band noise I/ /q I ⊥ q 97K 123 K 156 K Cox et al. arXiv:0705.4310
Recommend
More recommend
