Electronic soft matter Incommensurate and textured phases in - - PowerPoint PPT Presentation

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

LP UP

momentum energy photon QW exciton

[C. Weisbuch et al., PRL 69 3314 (1992)]

mirror QW mirror ph

photon

in-plane momentum Effective Mass m* ~ 10-4 me TBEC ~ 1/m*

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

100 nm

30 nm patches of charge-order in LaCaMnO3

Loudon & Midgley

“Stripes” of charge-density wave in TaSe2

C.H.Chen

“Colossal” magnetoresistance (CMR) in manganites

Urushibara et al 1995

Phase transition between metallic ferromagnet and insulating or poorly metallic paramagnet

G.H. Jonker and J.H. Van Santen, Physica 16 337 (1950), J.H. Van Santen and G.H. Jonker, Physica 16 599 (1950).

Perovskite manganites

• A “doped” oxide - e.g. La1-xCaxMnO3 where

the formal valence of Mn varies between Mn3+ and Mn4+

• A “strongly correlated” electron system close

to a (Mott) metal-insulator transition

Mn O Re/Ae

Mn d-levels

Distorted Mn3+ t2g eg Cubic Mn4+ t2g eg Cubic Mn3+ Hopping - aligns core moments and leads to ferromagnetic metal Jahn-Teller distortion suppresses hopping Leads to insulating state with

• rbital and/or charge order

Generic phase diagram

Temperature

Resistance

T

Effective electron-phonon coupling

FM CO PM CO liquid /PM

*

1st order 2nd order Cross over

Coexistence? Hysteresis? Phase separation?

• Ferromagnetic metal

degenerate electron plasma suppressed lattice distortions

• Charge/orbital ordered solid
• rdered insulating array of 3+/4+
• Polaronic liquid

dynamic lattice distortions local charge/orbital order electronically insulating Tuned by doping, rare earth size, magnetic field, elastic strain, ….

Urushibara et al 1995

• 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

Manganite phase diagrams

“Striped” phases of La0.33Ca0.67MnO3

S Mori, CH Chen and S-W Cheong, Nature 392 (1998) 473

TEM image shows periodic

• rdered lattice

Interpreted as periodic array of 3+/4+ ions ???

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

• Pure LaMnO3 – herringbone pattern of
• rbital order of Mn3+
• La1-xCaxMnO3 - “stripes” composition of

Mn3+:Mn4+ in ratio (1-x):x Mn(III) Mn(IV) x=1/2 Antiferromagnetic CE phase

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 La0.5Ca0.5MnO3

– 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 La0.5Ca0.5MnO3

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

• Pure LaMnO3 – herringbone pattern of
• rbital order of Mn3+
• La1-xCaxMnO3 - “stripes” composition of

Mn3+:Mn4+ in ratio (1-x):x Mn(III) Mn(IV) x=1/2 x>1/2 periodic array of discommensurations S p a c i n g 1 / ( x

• 1

/ 2 )

“Striped” phases of La0.33Ca0.67MnO3

S Mori, CH Chen and S-W Cheong, Nature 392 (1998) 473

TEM image shows periodic

• rdered lattice

Interpreted as periodic array of 3+/4+ ions ???

TEM images of charge ordering in La0.5Ca0.5MnO3

Chen & Cheong, PRL 76, 4042 (1996)

Substantially incommensurate at high T Ferromagnetic in incommensurate phase

Zoom in on La0.48Ca0.52MnO3

• 500 nm region gives q/a*=0.468±0.003
• Alternating Mn3+/Mn4+ planes when x=0.5
• Expect extra Mn4+ 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
• Modulation has uniform periodicity

3.6 nm 500 nm

200 100 000 100 200

Loudon et al. Phys. Rev. Lett. 94, 097202 (2005).

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 TCO
• 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)

• 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)

ρM 2Q · ∇ρ

) ; ( ) ( ) ( ρ ρ M F F M F F

CO mag

Δ + + =

2 2ρ

M F + ∝ Δ

φ ρ ∇ ∝ Δ

2 2

M F

• Write Free energy as function of

variables M, ρ , etc.

• Can generate terms in Free energy that favour

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 incommensurability (relative to 1/2) For x=1/2, possibly incommensurate if also magnetic

Coupled order parameters

For x < 1/2, natural incommensurability cancelled by coexisting magnetism

(magnetic structure is canted AF), (Jirak 1985)

x q 0.5

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

0.465 q/a* 0.476

0.465 q/a* 0.476 Superlattice control through strain release La0.5Ca0.5MnO3

Cox et al. cond-mat/0504476

Sliding CDW in La0.5Ca0.5MnO3 epitaxial films?

Linear resistivity shows small gap ~ 100 meV

Cox et al. arXiv:0705.4310

Non-linear resistivity with “threshold” electric field

qCDW

Aligned thin film Diffraction intensity Resistance as function of field

Broad band noise

97K 123 K 156 K

I ⊥ q

I/ /q

Cox et al. arXiv:0705.4310

“Stripes” or CDW ?

• Strong local lattice coupling is evident in “CMR” – at

compositions which are bad metals

• Apparently weaker local lattice coupling in insulating charge-
• rdered compounds – these look like classic charge-density

wave materials

• Role of screening? – substantial local charge fluctuations can
• ccur in the d-band only if screened by other orbitals.

Effective “U” for Ni

13.5 eV 1.8 eV

Hierarchy of inhomogeneous structures Hierarchy of inhomogeneous structures

• Periodic Jahn

Periodic Jahn-

• Teller order (e.g. LaMnO

Teller order (e.g. LaMnO3

3, La

, La1/2

1/2Ca

Ca1/2

1/2MnO

MnO3

3)

)

• thermodynamic phase

thermodynamic phase

• Periodic incommensurate superstructures, periodic

Periodic incommensurate superstructures, periodic mixture of ferromagnetic metal / charge ordered insulator mixture of ferromagnetic metal / charge ordered insulator

• first order phase transition pre

first order phase transition pre-

• empted by long

empted by long-

• period phase which is

period phase which is effectively a periodic effectively a periodic “ “mixture mixture” ”

• also a thermodynamic phase

also a thermodynamic phase

• microscopics

microscopics? ? – – driven by entropy or driven by entropy or energetics energetics? ?

• Disordered textured phases

Disordered textured phases

• phase separation/phase coexistence

phase separation/phase coexistence

• are these real thermodynamic phases (e.g. if

are these real thermodynamic phases (e.g. if entropically entropically driven), or driven), or due to kinetics/disorder ? due to kinetics/disorder ?

• Strain compatibility favours

Strain compatibility favours “ “herringbone herringbone” ” and and “ “tweed tweed” ” patterns with patterns with length scales fixed by kinetics, film thickness, disorder, .... length scales fixed by kinetics, film thickness, disorder, ....

Conclusions

• View of commensurate/incommensurate charge-ordered phases

as ordered arrays of 3+/4+ ions is oversimplified

– Charge inhomogeneity is small

• First order transition between two competing phases can be

preempted by incommensurate coexistence.

– General arguments suggest that this is not an uncommon phenomenon

• Charge/orbital ordering is a CDW-like state rather than a striped

state

– i.e. CDW is stiff, incommensurate, and slides – Relationship to fermi surface instability ?.

• We can use strain modulation to control electronic phase

structure Just as in conventional “soft” matter the competition between two fundamental phases (“oil” and “water”) does not necessarily lead to complete phase segregation – but also to new mesoscopic phases based on coexistence.