Egami Research Group

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Egami Research Group

 Structure and Dynamics of Complex Materials by Neutron Scattering.

– Mechanism of high temperature superconductivity in the FeAs compounds and the cuprates.

– Complex functional oxides: CMR and Ferroelectrics

 Liquid-State-Physics.

– Elementary excitation and statistical mechanics – Nature of the glass transition

– Molecular dynamics simulation and experiments

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Approach

 Experiment

– Neutron scattering (SNS, HFIR, LANSCE, ISIS, ILL ….)

 Inelastic scattering

 Spin-polarized scattering

 Pulsed neutron PDF and DPDF

– Synchrotron radiation (APS)

 Inelastic x-ray scattering

 Diffuse scattering, PDF, DDF

 Theory

– Theory of HTSC

 Strong electron correlation and electron-phonon coupling

 Intermediate state between Mott-Hubbard insulator and Fermi- liquid

– Theory and simulation of liquids and glasses

 Topological fluctuation theory

 Molecular dynamics

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Members

 T. Egami (DS): Theory of glasses and HTSC

 W. Dmowski (RP): PDF and DPDF measurement

 V. Levashov (PD): Simulation and analysis of liquids

 T. Ieashita (PD): Simulation and analysis of liquids

 K. Lokshin (PD): Oxide synthesis, diffraction

 O. Lipscombe (PD): Superconductivity of Fe pnictides

 Z. Marton (GS): Field effects in manganites

 D. Parshall (GS): Superconductivity of Fe pnictides

 Chad Mitchell (GS): Ferroelectric materials, scattering

 Jennifer Niezdiela (GS): Superconductivity of Fe pnictides

 Collaborators

– UT (Dagotto, Dai, Liaw)

– ORNL (Morris, Stocks, Liu, Mook, Mandrus, Wang, Mamontov) – Heidelberg (B. Fine: Theory of HTSC)

– UVa (Poon, Shiflet, Louca) – J-PARC (Arai, Shamoto) – LANL (Bishop, Proffen)

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SNS, officially the most powerful neutron source in the world

 Just recorded 1 MW.

 Inelastic Scattering:

– ARCS

– SEQUOIA – BASIS

 Elastic Scattering:

– NOMAD – POWGEN

Joint Institute for Neutron Sciences

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JINS

 We move into the JINS building, to be completed

by March, 2010, next to the SNS.

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High Temperature Superconductivity

 Discovered by K. A. Müller and J. G. Bednorz in 1986 (Nobel Prize 1987).

 Very high T_C (up to 138 K) for low charge density. It cannot be explained by the

conventional BCS theory.

 The first of the remarkable properties found in transition metal oxides.

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FeAs Superconductors

T_C up to 55 K.

Metallic magnetism.

Magnetism strongly affected by the lattice.

Unconventional electron-phonon coupling.

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Data from ARCS, SNS

Spin excitation intensity measured by the ARCS spectrometer of the SNS, energy integrated from 5 to 25 meV, for a single crystal of

Ba(Fe_0.92Co_0.08)₂As₂ at T = 16 K [1]. The intensity is centered at (0.5, 0.5, L), where scattering due to anti-

ferromagnetic order is seen in the parent (undopd) compound.

M. D. Lumsden, A. D. Christianson, D. Parshall, M. B. Stone, S. E. Nagler, H. A. Mook, K.

Lokshin, T. Egami, D. L. Abernathy, E. A. Goremychkin, R. Osborn, M. A. McGuire, A. S.

Sefat, R. Jin, B. C. Sales, and D. Mandrus, “Two-Dimensional Resonant Magnetic Excitation in BaFe_1.84Co_0.16As₂”, Phys. Rev. Lett., 102, 107005 (2009).

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Spin excitation intensity measured by the ARCS spectrometer of the SNS for single crystals of

Ba(Fe_0.92Co_0.08)₂As₂ at T = 16 K [2].

The vertical axis is excitation

energy in meV, and the horizontal axis is Q = (0.5+h, 0.5+h, L).

Intensities away from h = 0 are noise due to the detector edges.

A column of excitation spectrum is seen at Q = (0.5, 0.5, L),

corresponding to Fig. 1.

D. Parshall, K. Lokshin, Jennifer Niedziela, A. D. Christianson, M. D. Lumsden, H. A. Mook, S. E. Nagler, M. A. McGuire, M. B. Stone, D. L. Abernathy, A. S.

Sefat, B. C. Sales, D. G. Mandrus, and T. Egami, “Spin Excitations in

BaFe_1.84Co_0.16As₂ Superconductor Observed by Inelastic Neutron Scattering”, Phys. Rev. B, 80, 012502 (2009).

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Inelastic X-Ray Scatering

 Incident energy: 20 keV

 Energy resolution 2 meV

 ∆E/E = 10^-7

 Backscattering Si monochromator.

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-10 0 10 20 30 40 50 1E-7

1E-6 1E-5 1E-4

Acoustic

Q=(0.07, 0.07, 6.87)

Fe-As (IR) As-As (Raman) Ba

Elastic line

Scattering Intensity (arb. units)

Energy (meV)

-10 0 10 20 30 40 50

1E-7 1E-6 1E-5

1E-4 Q=(0.04, 0.04, 6.2)

Acoustic Elastic line

Energy (meV)

-10 0 10 20 30 40 50

1E-7 1E-6 1E-5

1E-4 Q=(0.04 0.04 4.87)

Energy (meV)

-10 0 10 20 30 40 50

1E-7 1E-6 1E-5

1E-4 Q=(0 0 5.53)

Energy (meV)

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 Phonon dispersions calculated for the non-magnetic state do not agree with experiment.

0 5 10 15 20 25 30 35

40

^(a)

Z M

Γ D Γ Z

E ner gy ( m eV )

Ba(Fe_0.92Co_0.08)₂As₂

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 Magnetic ground state does much better, but complex splitting is not observed.

0 5 10 15 20 25 30 35

40

^(b)

Z M

Γ D Γ Z

E ner gy ( m eV )

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Spin-Lattice Interaction

 Landau theory for the dependence of the magnetization on the atomic displacement of As, u (z atomic position of As):

Calculated dependence of the Fe moment on As

displacement for BaFe₂As₂

( )

²

2 4

1

F = AM + BM + Fs p₋ +C z − z

z_c: Quantum critical point for the spin-lattice interaction.

Fluctuation around it must be large.

( ) ( )

² ²

s p c c

F ₋ = ^

α

z − z +

β

z − z ^ M

( ) ( )

²

2

^c ^c

M z z z z

B

α β

α

 

=   − − −  

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Experimental Data on CeFe(As

_1-x

P

_x

)O

 Stoner QCP: z

_c

= 1.28 Å.

C. de la Cruz, W. Z. Hu, S. Li, Q. Huang, J. W. Lynn, M. A. Green, G. F. Chen, N. L. Wang, H. A. Mook, Q. Si and P. Dai, submitted

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Phonon Measurement with INS at ISIS, HFIR

 YBa₂Cu₃O_6.95, cut along the x-axis, T = 110 K

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Quasi-elastic Scattering

 BASIS-SNS

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Spin-polarized Neutron Scattering

 BT-7 at NIST, with

3

He spin polarizer and analyzer.

 Decay of

polarization was a

challenge.

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High-resolution pulsed neutron scattering with NPDF, LANSCE, LANL

 High Q resolution ∆Q/Q = 0.0015, high real space resolution for PDF.

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Local Jahn-Teller (JT) Distortion

 The first peak of the PDF (Ni-O peak) is

consistent with the z²-type JT orbital state with 4 short, 2 long bonds.

 But there is no long-range JT distortion.

PDF Obtained with the NPDF, LANSCE

J.-H. Chung, et al., PRB 71, 064410 (2005).

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PDF and Local Structure

 PDF from NPDF (above), and from HIPD (below),

show non-trivial variation with temp.

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HIPD PDF Fitting – Freedom for As

Rietveld Values Only

With Free Arsenic z positions

With Free Arsenic and Iron z

positions T=12.5 K

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Distribution of As-As bond lengths in the two samples near the superconducting transition temperature. There is a distinct separation of the bond lengths. All data

were refined using PDFGui, over the fitting range of 2-6 Angstroms. Arsenic and Iron z positions allowed to

vary. Short bond is shown in blue,

Long bond is shown in red.

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Dynamic PDF by Inelastic Neutron Scattering

 Fourier-transform of S(Q,ω) is the dynamic PDF.

 S(Q,ω) has to be determined over large ranges of Q and ω.

 Measurement with PHAROS

(inelastic chopper spectrometer) of LANSCE, Los Alamos NL.

 Powder sample 100 grams.

 Incident energy 250 meV, covering up to 20 Å^-1.

 Intensity corrected for absorption, background, multiple scattering

and multi-phonon intensity. MERLIN, ISIS

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Dynamic PDF

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Average (Static) Structure

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Dynamic PDF

W. Dmowski, et al., PRL 100, 137602 (2008).

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Glass and the Glass Transition

 DFT calculation can now predict many properties of crystalline solids and molecules; they can now be designed.

 But the science of glass lags well behind.

 Unlike in gasses atoms are strongly correlated in liquids and glasses.

 This many-body nature makes perturbational approach (from free gas) fail, and deeply

frustrates the theorists.

P. W. Anderson, Science 267, 1615 (1995).

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Atomic Level Stresses

 Atomic level stresses relate the local

topology to the local energy landscape.

(

i^zz

)

yy i xx

i

pi = σ +σ +σ 3

1

∑

^⋅

=

j

ij ij

i

i 1 f r

σ ^αβ ^α ^β

Ω

T. Egami, K. Maeda and V.

Vitek, Phil. Mag. A41, 883 (1980).

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 Glass transition temperature is equal to the energy of local density fluctuation with the long-range stress field at a critical strain level. ε_v,T = 0.0917 0.003 (4%). T. Egami, et al., Phys. Rev. B 76, 024203 (2007).

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Viscosity

 Glass transition defined by η = 10¹³ poise.

 Change in η by 15 orders of magnitude.

 Atomic structure changes little.

 How does η depends on

the structure? R. Bush, et al. (W. L. Johnson) Mater. Sci.

Forum, 269-272, 547 (1998).

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Viscosity

 Green-Kubo equation (fluctuation-dissipation theorem);

 In terms of the atomic level stresses,

( ) ( )

⁰

xy xy

kT t dt

η = V

∫

σ σ

( ) ( )

,

xy 0 xy

i j i j

i j

kT t dt

η = V

∫ ∑

Ω Ω σ σ

( ) ^{r t} ^, ^σ

^xy

( ^{, 0} ) ( ^σ

^xy

^, ^t ) ^δ ( ^r ) ^{d d}

Σ = ∫∫ ^r' ^r" − r' - r" r' r"

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 Liquid iron.

 T = 5000 K

 T

_g

= 800 K, T

_CO

= 2300 K

 L and T waves are seen.

( )

^{r t}^, ^σ ^xy

(

^{, 0}

) (

^σ ^xy ^,^t

)

^δ

(

^r

)

^{d d}

Σ =

∫∫

^r' ^r" − r' - r" r' r"

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Shear Deformation at a Constant Rate

 Shear deformation at a constant rate, and flow stress is determined.

 4000 atom model of Zr₅₀Cu₄₀Al₁₀ (EAM potential).

10¹ 10² 10³

10^-1 10⁰

shear strain rate

0.001 0.005 0.0001

shear stress

σ (GPa)

t (ps)

χ(γ)^. _100K

10^-4 10^-3 10^-2 10^-1 10⁰ 10^-3

10^-2 10^-1 10⁰

100K 300K 600K 700K 800K 840K 860K 900K 940K 1000K 1040K 1100K 1200K

Shear stress σ (GPa)

Shear strain rate(1/ps)

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10¹ 10² 10³

10¹ 10² 10³ 10⁴ 10⁵ 10⁶

100K 300K 500K 600K 700K 800K 840K

900K 940K 1000K 1100K 1200K

α/β

η−1 /|(Τ−Τ g)/Τ g|α

∆ = σ/|[(Τ−Τ

_g

)/Τ

_g

|

^β

α = 1.23 β = 0.6

∆

^α/β

T_g = 860K

T > T_g

T < T_g

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Viscosity vs. Temperature and Stress

 A cut of the jamming phase diagram at a constant density.

 Lines for constant viscosity are self- similar:

( ) ( )

2

0 0

T 1 T

σ

η σ η

 

+  =

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0

0.2 0.4 0.6 0.8 1.0 1.2

σ/σ

₀

T/ T

0 ¹

2 4 5

log₁₀η₀=5

log₁₀η

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New Scaling Law

 Temperature scaling (α

= 1.23)

 Stress scaling (γ = 1.08)

( )

1

0 0 1 ,

T

T T

η α

η η

  − 

 

=  +    

( )

1

0 0 1 ,

γ σ

σ η σ η

η

  − 

 

=  +   

( ) ( )

2

0 0

T 1 T

σ

η σ η

 

+  =

0.0 0.2 0.4 0.6 0.8 1.0 1.2

T/ T

0

(η )

50K 100K 300K 500K 600K 700K 800K 840K 940K 1000K 1100K

Egami Research Group