Electron-Phonon Coupling in Charge Density Wave ZrTe 3

Slide: 1ECRYS 2008 – Cargèse 25. 8. 2008

Electron-Phonon Coupling in Charge Density Wave ZrTe

3

Moritz Hoesch,

Alexey Bosak, Alessandro Mirone, Michael KrischEuropean Synchrotron Radiation Facility ESRF

Helmuth Berger École Polytechnique Fédérale de Lausanne, SuisseDmitry Chernyshov Swiss-Norwegian Beamlines at ESRF


ZrTe3 crystal structure and resistivity

prismatic (ZrTe3)∞ chains along b

Te – Te chains along aS. Takahashi et al. Journal de Physique 6 (1983) C3-1733

D.J. Eaglesham et al. J.Phys. C 17 (1984) L697

resistivity anomaly along a and c

anisotropy

a b

c a

CDW

0 1 2 mm

TCDW = 63 K, QCDW = (1/14 0 1/3 )


anomalous feature in the diffuse scatteringdiffuse scattering at SNBL BM01A reconstructed a*-c* plane MAR345 image plate detector

(h0l)-plane (h0l)-plane

T = 295 K(4.7 TCDW)

T = 80 K(1.3 TCDW)

qCDW = (0.07 0 0.3333)

a*c*

(300) (400)

(301) (401)


dispersion across qCDW

qCDW

to(4 0 1)

6

5

4

3

2

1

0

energy (meV)

-4.00-3.96-3.92-3.88along qCDW (a* component)

dispersion at T = 100 K sinusoidal model

qCDW


temperature evolution of the Kohn anomaly

giant Kohn anomaly leads to the lattice instability.

2/1

014.1ln ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⋅≅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅−=

CDW

CDW

BniCDW T

TTb

Tka

εωω

mean field theory

observation close to

8/1

⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝

CDW

CDWCDW T

TTω

5

4

3

2

1

0

energy (meV)


T = 292 K T = 158 K T = 100 K T = 83 K T = 78 K T = 73 K T = 68 K model

3.0

2.5

2.0

1.5

1.0

0.5

0.0

phonon frequency (meV)

43210(T - Tc) / Tc

ωni

phonon frequency atqCDW

(( -T Tc)/Tc)(/8)

(( -T Tc)/Tc)(/2)


origin of the diffuse scattering intensity

IXS intensities from fit vs diffuse scattering intensity

diffuse scattering is dominated by non-phonon scattering--> onset of order contributes strongly to diffuse scattering

0.8

0.6

0.4

0.2

0.0

intensity from fit

-4.00-3.96-3.92-3.88-3.84along qCDW (a* component)

0.15

0.10

0.05

0.00

scattering intensity

at T = 68 K

IXS central IXS phonon diffuse scatt.

0.6

0.5

0.4

0.3

0.2

0.1

0.0

intensity from fit

-4.00-3.96-3.92-3.88-3.84along qCDW (a* component)

0.20

0.15

0.10

0.05

0.00

scattering intensity

at T = 73 K

IXS central IXS phonon diffuse scatt.


diffuse scattering around qCDW

2.5

2.0

1.5

1.0

0.5

0.0

intensity

-0.04 -0.02 0.00 0.02 0.04b* across qCDW (r.l.u.)

12 K 28 K 38 K 43 K 48 K 53 K 56 K 60 K 62 K 64 K

lorentzian fit

0.5

0.4

0.3

0.2

0.1

0.0

normalized intensity

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3b* across qCDW (r.l.u.)

66 K 68 K 70 K 80 K 93 K 155 K 175 K 293 K

lorentzianfit

T < TCDW

growth ofintensityof superstructurereflection

T > TCDW

sharpening upof diffusescattering

6000

5000

4000

3000

2000

1000

0

intensity (cps)


qCDW

T = 73 K T = 83 K T = 292 K

25

20

15

10

5

0

scattering intensity (normalized)


12 K 19 K 28 K 38 K 43 K 48 K 53 K 60 K 66 K


power law exponents

width

TDS-regimeorder parameter

-> β = 0.13 ± 0.03

( ) β2

)( ⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝

c

c

T

TTTI

ν

ξ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝−

c

c

T

TT1

inverse correlation length

-> ν = 0.85 ± 0.2

intensity

0.16

0.12

0.08

0.04

0.00

intensity at

qCDW

300250200150100500

temperature (K)

0.15

0.10

0.05

0.00

width along

b*

(r.l.u)

TCDW = 63 K

4

68

0.01

2

4

68

0.1

2

width (lattice units)

0.012 4

0.12 4

12 4

10(T - Tc) / Tc

width FWHM power law fit

T > TCDW

sharpening upof diffusescattering

T < TCDW

growth ofintensityof superstructurereflection

6

7

8

9

0.1intensity

0.012468

0.124

( Tc - T ) / Tc

intensity at qCDW

power law fit


conclusions

ZrTe3 shows a soft-mode driven Peierls transition.

Electron-phonon coupling leads to a Kohn Anomaly (KA) at high temperatures.

The coupling occurs in the mostly transverse acoustic phonon along qCDW.

The KA becomes giant and leads to the lattice instability as TCDW is approached.

Fluctuating CDW-order leads to enhanced diffuse scattering around qCDW.

The CDW order is three-dimensional with finite correlation along c* (out-of-plane).

The order parameter increases rapidly away from TCDW with a small power law:

ωCDW with power law 1/8 and intensity with β = 0.13 ± 0.03.

Transition is close to (blurred) first order transition, like (TaSe4)2I or blue bronze.


the CDW superstructure

convergent beam electron diffraction at 50 KD.J. Eaglesham et al. J.Phys. C 17 (1984) L697

chemical modulation “A” vanishes with time(no observed with x-rays)

CDW-modulation “B”: qCDW ~ (1/14 0 1/3)

LDA calculation of the Fermi surfaceC. Felser et al. J. Mater Chem 8, 1787

CDW nesting vector

colors: Fermi velocity

a*

b*

c`*


two

Fermi – surface map (ARPES)

Two quasi 1-dim.Fermi-surfaces:

(a) hybridized Zr 4d along b*

(b) Te 5px along a*

LMTO theory K. Stöwe, F.R. Wagner, J. Solid St. Chem 138 (1998) 160

hv = 45.2 eVlin. polarizedT = 160 K

M. Hoesch, X. Cui, K. Shimada (Hiroshima Univ.) unpublished data, see also T. Yokoya et al., PRB 71 (2005) 140504R.


lattice dynamics at room temperature

ZrTe3 phonon dispersions along a* and b*

three kinds of modes are observed: - collective acoustic phonons- bending and torsion modes of the chains- optical modes of Te - atoms

Inelastic x-ray scattering, resolution E = 3.2 meV

Raman data: A. Zwick, M.A. Renucci, A. Kjekhus, J. Phys. C: Solid State Phys. 13 (1980) 5603.


comparison TDS vs IXS

thermal diffuse scattering (TDS)measures S(Q)

inelastic x-ray scattering (IXS)measures S(Q, ω) and gives ω

x 10-4

6000

5000

4000

3000

2000

1000

0

intensity (cps)

-4.15 -4.10 -4.05 -4.00 -3.95 -3.90 -3.85

momentum along CDW (a* component)

300x103

250

200

150

100

50

0

Bragg intensity (cps with filter)

qCDW

qCDW

= (-3.93

01.333)

T = 292 K T = 83 K T = 73 K

5

4

3

2

1

0

energy (meV)

-4.00 -3.96 -3.92 -3.88

momentum along CDW (a* component)

T = 292 K T = 83 K T = 73 K


survey of momentum spacediffuse scattering at SNBL BM01A T = 295 K

tomographic single crystal diffractometer

MAR345 image plate detector

reconstructed (hk0)-plane (0kl)-plane (h0l)-planeqCDW = (0.07 0 0.3333)

where’s the soft mode?


IXS spectrometer schematicundulator sourceand Si(111)pre-monochromator

0.150.9(13 13 13)

1.7(11 11 11)

3.0(9 9 9)

0.055.5(8 8 8)

Q (nm-1)E (meV)reflection

Monochromator:Si(n,n,n), B = 89.98º

n = 8 - 13

ituned by thermal expansion

f constant

sample

Ei

Ef

detector

Spot size:

250 x 60 m2 (H x V)

Analyser:Si(n,n,n), B = 89.98º

n = 8 - 13

Electron-Phonon Coupling in Charge Density Wave ZrTe 3

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