neutron scattering investigation of (tmttf) 2 pf 6 p. foury-leylekian a, s. petit b, b. hennion b,...
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Neutron scattering investigation of (TMTTF)2PF6
P. Foury-Leylekiana, S. Petitb, B. Hennionb, A. Moradpoura and J.-P. Pougeta
a. Laboratoire de Physique des Solides, CNRS-UMR 8502, Université Paris-sud, 91405 Orsay, France
b. Laboratoire Léon Brillouin,CEA-CNRS, UMR 12, 91191 Gif-sur-Yvette, France
ECRYSCargèse, Corse (F) August 25-29 2008
Spin susceptibility measurements: (TMTTF)2X
TSP
Thermal behavior of a S=1/2 Heisenberg chain
J~410-420K(Dumm et al PRB 62,
6510 (2000))
TCO
no effect at TCO: spin – charge decoupling
Ground states of the 1D Heisenberg chain
=1 (1 electron per site) Mott-Hubbard localization
case of CuGeO3
AF
SP
=1/2 (1 electron per dimer)Case of (TMTTF)2X
2kF SDW
2kF bond « CDW » (BOW)Spin-
Peierls
(TMTTF)2PF6: superlattice reflexions below TSP
h= ½ a* : 2a periodicity
chain dimerization (pairing of S=1/2 units into
S=0 singlet)
Elastic neutron scattering
(P. Foury-Leylekian et al PRB 7 R180405 (2004))
TSP=13K
Thermal dependence of the (TMTTF)2PF6 (D12) (1/2,1/2,1/2) superlattice peak intensity
max d/dT: TSP=12.9K
Magnetic excitations in the SP ground state: T=0K
q/qSP
Δσ spin-peierls gap
Triplet excitations of the SP dimer: S=1 magnon mode gapped at Δσ
Continuum of excitations gapped
(Uhrig et Schulz PRB 54, R9624 (1996))
at2 Δσ
S=0 S=1
Magnetic excitations in the SP ground state 1 - magnon mode:propagation of the triplet excitations (S=1) of the SP dimer
dispersion: ħωM(q)= E(q) with E(q)=[Δ2(q)+ε2(q)]1/2
Δ(q)= Δcos2πq , ε(q)=Jeff sin2πq
Jeff=J (πJ/2) for the XY(Heisenberg) chain
(Bonner & Blote PRB 25, 6959 (1982))
2 - continuum of double magnon excitations located in between:
ħωl(q)= Δ +E(q) and ħωs(q)= 2E(q/2)
(Uhrig & Schulz PRB 54, R9624 (1996))
Inelastic neutron scattering study
• performed with ~1cm3 of 98% deuterated (TMTTF)2 PF6 powder(A. Moradpour LPS)
• 2T triple axis study at Orphée reactor
(LLB Saclay)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Q
Ene
rgy
(meV
)
0 0.5 1 1.5 2 2.5 3 0
20
40
60
80
100
120
1D magnon collective mode
Min of E(q): Δσ
Max of E(q): Jeff
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
QE
nerg
y (m
eV)
0 0.5 1 1.5 2 2.5 3 0
20
40
60
80
100
120
1D continuum
Simulation of powder average*
Energy scan in QSP = (3/2,-1/2,1/2)= 1.66Å-1
S. Petit
Min of ħωl(q): ≥ 2Δσ
Max of ħωl(q): Δσ+Jeff
* Simulation ignoring factor structure effects
neutron count variation inside the SP phase of (TMTTF)2 PF6 (d12): I(4K)-I(11K)
-100
-50
0
50
100
150
0 5 10 15 20
Cou
nts
Energy (meV)
Difference 4K-11K avec correctionDifference 4K-11K
Fit1(x)
broad excitation ΔU
narrow excitation ΔL
Double gap structure previously observed in CuGeO3 single crystals(Ain et al PRL 78, 1560, 1997)
evidence of two excitation energies
Δσ 2Δσ
Δmax
The continuum of excitations is more peaked in (TMTTF)2PF6 than in CuGeO3
(magnetism more 1D in (TMTTF)2X than in CuGeO3?)
Low T excitation gaps
Powder ΔL~67K ΔU~150K
Single crystalΔL=68K
0
-100
-50
0
50
100
150
0 5 10 15 20
Cou
nts
Energy (meV)
Difference 4K-18K avec correctionDifference 4K-18K
Fit1(x)
ΔL~ ΔU/2
I (4K) – I(18K) reference of intensity 18-20K well above TSP=13K
negative intensity because of the formation of a gap in the excitations of the Heisenberg chain (reference of intensity above TSP)
ΔL ΔU
Spin-Peierls ground state: Singlet-Triplet splitting gapexp-/T
PF6(D12): = 75K = U/2 ~ L
(C. Coulon)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Q
Ene
rgy
(meV
)
0 0.5 1 1.5 2 2.5 3 0
20
40
60
80
100
120
1D magnon collective mode
Min of E(q): Δσ
Max of E(q): Jeff
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
QE
nerg
y (m
eV)
0 0.5 1 1.5 2 2.5 3 0
20
40
60
80
100
120
1D continuum
Simulation of powder average*
High energy scan
S. Petit
Min of ħωl(q): ≥ 2Δσ
Max of ħωl(q): Δσ+Jeff
* Simulation ignoring factor structure effects
High energy scan at Q = 3.4 Å-1
-100
-50
0
50
100
150
40 45 50 55 60 65 70 75
Cou
nts
Energy (meV)
Fit1(x)Difference 4K-18K
response at 55meV ~ Jeff (if Δ neglected)
Jeff= πJ/2 leads to J~400KOK with J=410-420K obtained for the « Bonner et Fisher » fit of χspin(T)
Thermal dependence of the magnetic excitations in the SP phase
scan difference: I(T)-I(18K)
Reference scan
Only the « ΔU » continuum of excitations is
detected at 7K (~TSP/2)!
divergence of the density of state of the continuum of
1D magnetic excitations
gapped excitations
Reasons for the non–observation of the ΔL magnon peak
• Peak merges in the continuum?• Peak intensity vanishes?• Peak broadens?
life time effect: efficient decay mode• Possible explanation: magnon mode decays into two
bounded spinons on approachingTSP
X X
S=1
S=1/2
Binding due to unfavorable (out of phase) interchain coupling
S=1/2
Decay of magnon into two bound spinons
• Possible near TSP when the cost of interchain coupling is not large
• Creation of bound spinons inside the SP phase of (TMTTF)2PF6 is possible because the 3D spin-Peierls distortion (i.e. SP satellite intensity) is very weak(P. Foury-Leylekian et al PRB 70, R180405 (2004))
• By this scenario one passes continuously (through a 2nd order transition) when Δ→0 from the excitations of the SP chain to those (only a continuum of free spinons) of the Heisenberg chain
In the vicinity of TSP the intensity of the ΔU peak drops and a larger gap in the excitations of the
Heisenberg chain is revealed!
A broad max of intensity at « ΔU » and a large gap in the excitations of the Heisenberg chain are still observed
above TSP!I<0 below 20meV: pseudo-gap formation?
difference with thermal correction
Thermal evolution of the upper gap: ΔU
TSP
Δu does not vanishes at TSP! (linear extrapolation to zero at ~35K)
2Δχspin
Pouget et al Mol. Cryst.Liq. Cryst. 79, 129 (1982)
Pseudo-gap built by SP 1D structural fluctuations:1D X-ray diffuse scattering observed above TSP in
(TMTTF)2PF6and AsF6
1D structural SP fluctuationsabove TSP
mean-field energy scale
• 1D structural fluctuations detected until:
~60-80K PF6 (H12)- 40K AsF6
If one takes TSPMF~60K for the PF6 (D12), the BCS relationship
gives:
2Δ1DMF~215K=18.5meV
In this energy range inelastic neutron scattering reveals a drop of the magnetic excitation spectrum of the Heisenberg chain
negative intensity in the scan difference I(T) - I(18K)
Summary• This is the first time that magnetic excitations have been measured by
neutron scattering in an organic conductor
• The SP transition of (TMTTF)2PF6 and of CuGeO3 differs:
in (TMTTF)2PF6: - the magnon mode decay inside the SP phase- above TSP: there are pretransitional SP fluctuations and a pseudo gap formation (adiabatic limit)
in CuGeO3 :
- a sharp and intense magnon mode is followed until TSP where Δ vanishes abruptly- no pseudo gap effects are observed above TSP (non adiabatic limit)
Crossover of S(q,ω) from the SP ground state (with magnon excitations) to the uniform Heisenberg chain (with spinon excitations) need to be calculated
Chain fluctuations needed to be included in the treatment of excitations