Transcript Giant Kohn Anomaly in Charge Density Wave ZrTe3

Electron-Phonon Coupling in
Charge Density Wave ZrTe3
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
ECRYS 2008 – Cargèse
25. 8. 2008
Slide: 1
ZrTe3 crystal structure and resistivity
0
1
2 mm
resistivity anomaly
along a and c
TCDW = 63 K
prismatic (ZrTe3)∞ chains along b
TCDW = 63 K,
Te – Te chains along a
anisotropy
ra / rb ~ 1
rc / ra ~10
QCDW = (1/14 0 1/3 )
S. Takahashi et al. Journal de Physique 6 (1983) C3-1733
D.J. Eaglesham et al. J.Phys. C 17 (1984) L697
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 2
anomalous feature in the diffuse scattering
diffuse scattering at SNBL BM01A reconstructed a*-c* plane MAR345 image plate detector
T = 295 K
(4.7 TCDW)
T = 80 K
(1.3 TCDW)
c*
a*
(300)
(301)
(h0l)-plane
(400)
(401)
(h0l)-plane
qCDW = (0.07 0 0.3333)
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 3
dispersion across qCDW
6
energy (meV)
5
dispersion at T = 100 K
sinusoidal model
4
3
qCDW
2
qCDW
1
to
(4 0 1)
0
-3.88
-3.92
-3.96
-4.00
along qCDW (a* component)
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 4
temperature evolution of the Kohn anomaly
3.0
energy (meV)
4
T = 292 K
T = 158 K
T = 100 K
T = 83 K
T = 78 K
T = 73 K
T = 68 K
model
3
phonon frequency (meV)
5
ni
2.5
2.0
1.5
phonon frequency at qCDW
1.0
0.5
((T - Tc ) / Tc )
(1/8)
((T - Tc ) / Tc )
(1/2)
0.0
2
0
1
1
2
(T - T c) / Tc
3
4
mean field theory
CDW
0
-3.88
-3.92
-3.96
along qCDW (a* component)



 T  TCDW
 
 TCDW



-4.00
giant Kohn anomaly leads to the lattice instability.
1/ 2
 T  TCDW
 1.14 0 
  b  
= ni  a  ln
 k BT 
 TCDW
observation close to CDW
ECRYS 2008 – Cargèse 25. 8. 2008
1/ 8
Slide: 5
origin of the diffuse scattering intensity
at T = 68 K
0.8
0.3
0.10
0.2
0.05
0.1
0.0
0.00
-3.84
-3.88
-3.92
-3.96
along qCDW (a* component)
-4.00
IXS central
IXS phonon
diffuse scatt.
0.6
0.15
0.10
0.4
0.05
0.2
0.0
scattering intensity
0.4
0.15
scattering intensity
IXS central
IXS phonon
diffuse scatt.
0.5
intensity from fit
0.20
at T = 73 K
intensity from fit
0.6
0.00
-3.84
-3.88
-3.92
-3.96
along qCDW (a* component)
-4.00
IXS intensities from fit vs diffuse scattering intensity
diffuse scattering is dominated by non-phonon scattering
--> onset of order contributes strongly to diffuse scattering
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 6
diffuse scattering around qCDW
5000
sharpening up
of diffuse
scattering
intensity (cps)
T > TCDW
4000
T = 73 K
T = 83 K
T = 292 K
q
CDW
3000
2000
0
15
10
0.2
-4.00
12 K
19 K
28 K
38 K
43 K
48 K
53 K
60 K
66 K
-0.3 -0.2 -0.1 0.0 0.1 0.2
b* across qCDW (r.l.u.)
2.5
lorentzian
fit
2.0
intensity
scattering intensity (normalized)
growth of
intensity
of superstructure
reflection
20
0.3
0.0
-3.88
-3.92
-3.96
along qCDW (a* component)
T < TCDW
0.4
66 K
68 K
70 K
80 K
93 K
155 K
175 K
293 K
0.1
1000
25
lorentzian
fit
0.5
normalized intensity
6000
1.5
1.0
5
0.3
12 K
28 K
38 K
43 K
48 K
53 K
56 K
60 K
62 K
64 K
0.5
0
0.0
-3.88
-3.92
-3.96
along qCDW (a* component)
-4.00
-0.04
-0.02 0.00
0.02
b* across qCDW (r.l.u.)
0.04
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 7
power law exponents
intensity at qCDW
T < TCDW
growth of
intensity
of superstructure
reflection
0.15
0.12
TCDW = 63 K
0.10
0.08
0.05
0.04
0.00
50
100 150 200
temperature (K)
intensity
intensity at qCDW
power law fit
intensity
2
0.1
9
8
7
-> β = 0.13 ± 0.03
sharpening up
of diffuse
scattering
250
300
width
6
2
width (lattice units)
order parameter
T > TCDW
0.00
0
 T  T  

I (T )   c
 Tc 
width along b* (r.l.u)
0.16
inverse correlation length
TDSregime
0.1

 T T c 

 Tc 
8
6
 1  
4
2
0.01
width FWHM
power law fit
8
6
-> ν = 0.85 ± 0.2
4
4
2
8 6
4
0.1
( Tc - T ) / Tc
2
0.01
2
0.01
4
2
4
0.1
1
(T - Tc) / Tc
2
4
10
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 8
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.
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 9
the CDW superstructure
LDA calculation of the Fermi surface
C. Felser et al. J. Mater Chem 8, 1787
b*
a*
c`*
colors:
Fermi
velocity
convergent beam electron diffraction at 50 K
D.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
CDW
nesting
vector
1/ )
3
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 10
Fermi – surface map (ARPES)
hv = 45.2 eV
lin. polarized
T = 160 K
two
Two quasi 1-dim.
Fermi-surfaces:
(a) hybridized Zr 4d
along b*
(b) Te 5px along a*
LMTO
K. Stöwe,
F.R. Wagner,
J. Solid St.data,
Chem
160
M. Hoesch,
X. theory
Cui, K. Shimada
(Hiroshima
Univ.) unpublished
see138
also (1998)
T. Yokoya
et al., PRB 71 (2005) 140504R.
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 11
lattice dynamics at room temperature
Inelastic x-ray scattering, resolution DE = 3.2 meV
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
Raman data: A. Zwick, M.A. Renucci, A. Kjekhus, J. Phys. C: Solid State Phys. 13 (1980) 5603.
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 12
comparison TDS vs IXS
5
T = 292 K
T = 83 K
T = 73 K
intensity (cps)
4
250
q
4000
q
CDW
CDW
= (-3.93
0
1.333)
200
3000
150
2000
100
1000
50
x 10-4
0
0
-4.15
-4.10 -4.05 -4.00 -3.95 -3.90 -3.85
momentum along CDW (a* component)
thermal diffuse scattering (TDS)
measures S(Q)
Bragg intensity (cps with filter)
5000
300x10
3
energy (meV)
6000
T = 292 K
T = 83 K
T = 73 K
3
2
1
0
-4.00
-3.96
-3.92
-3.88
momentum along CDW (a* component)
inelastic x-ray scattering (IXS)
measures S(Q, ) and gives 
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 13
survey of momentum space
diffuse scattering at SNBL BM01A T = 295 K
tomographic single crystal diffractometer
MAR345 image plate detector
reconstructed (hk0)-plane
(0kl)-plane
(h0l)-plane
qCDW = (0.07 0 0.3333)
where’s the soft mode?
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 14
IXS spectrometer schematic
undulator source
and Si(111)
pre-monochromator
li tuned
by thermal
expansion
sample
detector
Ei
Monochromator:
Si(n,n,n), qB = 89.98º
Spot size:
250 x 60 mm2
(H x V)
n = 8 - 13
reflection
DE (meV)
DQ (nm-1)
(8 8 8)
5.5
0.05
(9 9 9)
3.0
(11 11 11)
1.7
(13 13 13)
0.9
Analyser:
Si(n,n,n), q B = 89.98º
n = 8 - 13
Ef
l f constant
0.15
ECRYS 2008 – Cargèse 25. 8. 2008
Slide: 15