1. Neutron scattering investigation of (TMTTF) 2 PF 6 P. Foury-Leylekian a, S. Petit b, B. Hennion b, A. Moradpour a and J.-P. Pouget a 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 ECRYS Cargèse, Corse (F) August 25-29 2008

2. Phase diagram of (TMTCF)2X Loc SP ground state 4k F charge ordering at T CO =90K O PF 6 (D12)

3. Spin susceptibility measurements: (TMTTF) 2 X T SP Thermal behavior of a S=1/2 Heisenberg chain J~410-420K (Dumm et al PRB 62, 6510 (2000)) T CO no effect at T CO : spin – charge decoupling

4. Ground states of the 1D Heisenberg chain  =1 (1 electron per site) Mott-Hubbard localization case of CuGeO 3 AF SP  =1/2 (1 electron per dimer) Case of (TMTTF) 2 X 2k F SDW 2k F bond « CDW » (BOW) Spin-Peierls

5. Spin-Peierls transition  S → 0 at T=0: S=0 ground state

6. ( TMTTF) 2 PF 6 : superlattice reflexions below T SP 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))

7. T SP =13K Thermal dependence of the (TMTTF) 2 PF 6 (D 12 ) (1/2,1/2,1/2) superlattice peak intensity max d  /dT: T SP =12.9K

8. Magnetic excitations in the SP ground state: T=0K q/q SP Δσ spin-peierls gap Triplet excitations of the SP dimer: S=1 magnon mode gapped at Δ σ Continuum of excitations gapped (Uhrig et Schulz PRB 54, R9624 (1996)) at 2 Δ σ S=0 S=1

9. Magnetic excitations in the SP ground state 1 - magnon mode: propagation of the triplet excitations (S=1) of the SP dimer dispersion: ħω M (q)= E(q) with E(q)=[Δ 2 (q)+ε 2 (q)] 1/2 Δ(q)= Δcos2πq, ε(q)=J eff sin2πq J eff =J (πJ/2) for the XY(Heisenberg) chain (Bonner & Blote PRB 25, 6959 (1982)) 2 - continuum of double magnon excitations located in between: ħω l (q)= Δ +E(q) and ħω s (q)= 2E(q/2) (Uhrig & Schulz PRB 54, R9624 (1996))

10. Inelastic neutron scattering study performed with ~1cm 3 of 98% deuterated (TMTTF) 2 PF 6 powder (A. Moradpour LPS) 2T triple axis study at Orphée reactor (LLB Saclay)

11. 1D magnon collective mode Min of E(q): Δ σ Max of E(q): J eff 1D continuum Simulation of powder average* Energy scan in Q SP = (3/2,-1/2,1/2)= 1.66 Å -1 S. Petit Min of ħω l (q): ≥ 2Δ σ Max of ħω l (q): Δ σ +J eff * Simulation ignoring factor structure effects

12. neutron count variation inside the SP phase of (TMTTF) 2 PF 6 (d 12 ): I(4K)-I(11K) broad excitation Δ U narrow excitation Δ L Double gap structure previously observed in CuGeO 3 single crystals (Ain et al PRL 78, 1560, 1997) evidence of two excitation energies ΔσΔσ 2Δσ2Δσ Δ max The continuum of excitations is more peaked in (TMTTF) 2 PF 6 than in CuGeO 3 (magnetism more 1D in (TMTTF) 2 X than in CuGeO 3 ?)

13. Low T excitation gaps Powder Δ L ~67K Δ U ~150K Single crystal Δ L =68K 0 Δ L ~ Δ U /2 I (4K) – I(18K) reference of intensity 18-20K well above T SP =13K negative intensity because of the formation of a gap in the excitations of the Heisenberg chain (reference of intensity above T SP ) ΔLΔL ΔUΔU

14. Spin-Peierls ground state: Singlet-Triplet splitting gap  exp-    /T PF 6 (D 12 ):   = 75K =  U /2 ~  L (C. Coulon)

15. 1D magnon collective mode Min of E(q): Δ σ Max of E(q): J eff 1D continuum Simulation of powder average* High energy scan S. Petit Min of ħω l (q): ≥ 2Δ σ Max of ħω l (q): Δ σ +J eff * Simulation ignoring factor structure effects

16. High energy scan at Q = 3.4 Å -1 response at 55meV ~ J eff (if Δ neglected) J eff = πJ/2 leads to J~400K OK with J=410-420K obtained for the « Bonner et Fisher » fit of χ spin (T)

17. Thermal dependence of the magnetic excitations in the SP phase scan difference: I(T)-I(18K) Reference scan

18. Only the « Δ U » continuum of excitations is detected at 7K (~T SP /2)! divergence of the density of state of the continuum of 1D magnetic excitations gapped excitations

19. Reasons for the non–observation of the Δ L 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 approachingT SP XX S=1 S=1/2 Binding due to unfavorable (out of phase) interchain coupling S=1/2

20. Decay of magnon into two bound spinons Possible near T SP when the cost of interchain coupling is not large Creation of bound spinons inside the SP phase of (TMTTF) 2 PF 6 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 2 nd order transition) when Δ→0 from the excitations of the SP chain to those (only a continuum of free spinons) of the Heisenberg chain

21. In the vicinity of T SP the intensity of the Δ U peak drops and a larger gap in the excitations of the Heisenberg chain is revealed!

22. A broad max of intensity at « Δ U » and a large gap in the excitations of the Heisenberg chain are still observed above T SP ! I<0 below 20meV: pseudo-gap formation? difference with thermal correction

23. Thermal evolution of the upper gap: Δ U T SP Δ u does not vanishes at T SP ! (linear extrapolation to zero at ~35K) 2Δχspin

24. χ RPE du (TMTTF) 2 PF 6 (D 12 ) C. Coulon drops below ~ 40K vanishing of  U in the  pseudo-gap region?

25. 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 T SP in (TMTTF) 2 PF 6 and AsF 6 1D structural SP fluctuations above T SP

26. mean-field energy scale 1D structural fluctuations detected until: ~60-80K PF 6 (H 12 )- 40K AsF 6 If one takes T SP MF ~60K for the PF 6 (D 12 ), the BCS relationship gives: 2Δ 1D MF ~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)

27. 2Δ MF Scan difference:

28. Summary This is the first time that magnetic excitations have been measured by neutron scattering in an organic conductor The SP transition of (TMTTF) 2 PF 6 and of CuGeO 3 differs: in (TMTTF) 2 PF 6 : - the magnon mode decay inside the SP phase - above T SP : there are pretransitional SP fluctuations and a pseudo gap formation (adiabatic limit) in CuGeO 3 : - a sharp and intense magnon mode is followed until T SP where Δ vanishes abruptly - no pseudo gap effects are observed above T SP (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