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Electron-Phonon Coupling in Charge Density Wave ZrTe 3. Moritz Hoesch , Alexey Bosak, Alessandro Mirone, Michael Krisch European Synchrotron Radiation Facility ESRF Helmuth Berger École Polytechnique Fédérale de Lausanne, Suisse Dmitry Chernyshov Swiss-Norwegian Beamlines at ESRF. - PowerPoint PPT Presentation
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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
Slide: 2ECRYS 2008 – Cargèse 25. 8. 2008
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 )
Slide: 3ECRYS 2008 – Cargèse 25. 8. 2008
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)
Slide: 4ECRYS 2008 – Cargèse 25. 8. 2008
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
Slide: 5ECRYS 2008 – Cargèse 25. 8. 2008
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)
-4.00-3.96-3.92-3.88along qCDW (a* component)
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)
Slide: 6ECRYS 2008 – Cargèse 25. 8. 2008
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.
Slide: 7ECRYS 2008 – Cargèse 25. 8. 2008
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)
-4.00-3.96-3.92-3.88along qCDW (a* component)
qCDW
T = 73 K T = 83 K T = 292 K
25
20
15
10
5
0
scattering intensity (normalized)
-4.00-3.96-3.92-3.88along qCDW (a* component)
12 K 19 K 28 K 38 K 43 K 48 K 53 K 60 K 66 K
Slide: 8ECRYS 2008 – Cargèse 25. 8. 2008
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
Slide: 9ECRYS 2008 – Cargèse 25. 8. 2008
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.
Slide: 10ECRYS 2008 – Cargèse 25. 8. 2008
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`*
Slide: 11ECRYS 2008 – Cargèse 25. 8. 2008
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.
Slide: 12ECRYS 2008 – Cargèse 25. 8. 2008
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.
Slide: 13ECRYS 2008 – Cargèse 25. 8. 2008
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
Slide: 14ECRYS 2008 – Cargèse 25. 8. 2008
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?
Slide: 15ECRYS 2008 – Cargèse 25. 8. 2008
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