Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3

1. Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3 Tomislav Ivek, Tomislav Vuletić, Silvia Tomić Institut za fiziku, Zagreb, Croatia Ana Akrap, Helmuth Berger, László Forró Ecole Polytechnique Fédérale, Lausanne, Switzerland T. Ivek et al., Phys. Rev. B 78, 035110 (2008).

2. BaVS3 • Consists of VS3 chains separated by Ba atoms • Neighboring VS6 octahedra share a face, stack along c-axis • Room Temperature: primitive hexagonal unit • 2 formula units per primitive cell • At ~240 K: transition to orthorhombic structure • At ~70 K: monoclinic structure • Internal distortion of VS6 octahedra • Tetramerization of V4+ chains S Ba V Lechermann et al., PRB 76, 085101 (2007) T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

3. S1 S2 S2 S1 S2 S2 BaVS3 • 2 electrons in: • a wide A1g band (dz2) • narrow Eg1, Eg2 bands (et2g) • Filling of bands governed by Coulomb repulsion, local Hund’s rule coupling • A1g, Eg1 close to half-filling • Metal-to-insulator phase transition at TMI≈70 K • Diffuse x-ray scattering: Fagot et al., PRL 90, 196401 (2003) • pretransition fluctuations up to 170 K • qc ≈ 2kF (A1g) superstructure • characteristic for a Peierls transition and Charge Density Wave ground state • No charge disproportionation in anomalous x-ray scattering! - Fagot et al., PRB 73, 033102 (2006) • Magnetic transition at Tχ≈30 K:incommensurate magnetic ordering (Nakamura et al., J. Phys. Soc. Jpn. 69, 2763 (2000), Mihály et al., PRB 61, R7831 (2000)) Lechermann et al., PRB 76, 085101 (2007) LDA + DMFT • Nature of MI transition? • Ground state? T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

4. Samples • Needle-like single crystals grown along c-axis, hexagonal cross-section • 3 x 0.25 x 0.25 mm3 • Important quality check: suppression of insulating phase at 20 kbar • Contacts: • evaporated 50 nm chrome • evaporated 50 nm gold • DuPont silver paint 6838 cured at 350°C for 10 min in vacuum T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

5. Low-Frequency Dielectric Spectroscopy Ivek et al., PRB 78, 035110 (2008) • 0.01 Hz – 10 MHz • Complex conductivity -> Complex dielectric function • Insulating phase • single symmetrically widened overdamped loss peak • reminiscent of a Charge Density Wave phason response (Littlewood, PRB 36, 3108 (1987)) • What is the connection of this relaxation with the MI transition? T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

6. Metal-InsulatorPhase Transition • TMI ≈ 67K: peak in dc resistivity derivation • dc gap 2Δ≈500 K corresponds to the optical gap (Kézsmárkiet al., PRL 96, 186402 (2006)) • Peak in Δε at the same T! • Screening by free charge carriers T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

7. CDW Phasons? • Do we have a long-wavelength, phason response? • Screening by free charge carriers: Littlewood • Unexpected Δε behavior • CDW: Δε(T)~const.≈107 • Lack of a significant non-linear dc conductivity – no sliding • Another DW phason fingerprint: a narrow microwave pinned mode • no experimental results T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

8. Energy (eV) 0.01 0.02 300K 85K 60K 10K • . Kézsmárkiet al., PRL 96, 186402 (2006) Hopping conduction? • Cross-over frequency far above the observed dielectric response • Optical conductivity not enhanced compared to dc values • Not a candidate T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

9. Ferroelectric nature of the MI transition? • Below TMI: noncentrosymmetric structure with a polar axis in the reflection plane of VS3 chains • High polarizability of electron system coupled to V4+ displacements could induce high Δε • BVS (Fagot et al., Solid State Sci. 7, 718 (2005)): some charge disproportionation at low T • But, overestimated due to a nonsymmetric V4+ environment, thermal contraction, imprecise atomic coordinates (Foury-Leylekian (2007)) • Charge redistribution not larger than 0.01e (Fagot et al., PRB 73, 033102 (2006)) • FE cannot explain our dielectric results T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

10. Orbital ordering? • No charge modulation in the insulating phase • Fagot et al., Lechermann et al.: modulation of orbital occupancy • 51V NMR and NQR measurements suggest an orbital ordering below TMI that is fully developedonly atTx(Nakamura et al., PRL 79, 3779 (1997)) • Magnetic susceptibility (Mihály et al., PRB 61, R7831 (2000)): lack of magnetic long-range order between TMI and Tχ • Magnetic anisotropy (M. Miljak, unpublished): AF domain structure below Tχ Fagot et al., PRB 73, 033102 (2006) T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

11. Interpretation in the context ofOrbital Order • Δε ~ collective excitation density, i.e. number of domain walls • Domains consolidate: number of domain walls diminishes with cooling • Δε decreases only down to Tχ • Below that a long-range spin ordering is established and Δε stays constant • Primary order parameter for the MI phase transition: 1D Charge Density Wave instability • Orbital ordering transition happens at TMI, driven via structural changes, tetramerization • Domains of OO gradually develop in size with lowering temperature • OO coupled with spin degrees of freedom, drives the spin-ordering into an AF-like ground state below 30K; domains persist! • Short-wavelength excitations of domain walls T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

12. Conclusion • BaVS3 – system with orbital degeneracy • Metal-Insulator transition at TMI~67 K • Magnetic transition at Tχ=30 K • Low-Frequency Dielectric Spectroscopy: the observed mode cannot be assigned to phason excitations • Density of excitations decreases from TMI with decreasing T, becomes constant under Tχ • Short-wavelength excitations <-> Orbital Ordering T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

13. Hopping Dyre and Schroeder, Rev.Modern Physics 72, 873 (2000) b) frequency marking the onset of ac conduction ncrossis roughly proportional to the dc conductivity: Barton-Nakajima-Namikawa relation connects sdc and dielectric loss peak frequency t0-1: sdc  t0-1 - BaVS at low T: sdc 10-5 – 10-6W-1cm-1 →ncrossexpected at > 1 MHz - For BaVS simple calculation yields: ncross (25 K) = 360 MHz and ncross (50 K) = 3.8 GHz T.Vuletic et al., Physics Reports 428, 169 (2006). c) t00  1ns is too long to be attributed to quasi-particles T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

14. T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

15. T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

16. Contacts T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

17. Low-Frequency Dielectric Spectroscopy • Complex conductivity as a function of frequency T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

18. Low frequencies, high impedances • Lock-in + current preamplifier • Voltage output • Measuring the current • 10 mHz – 3 kHz • Resistances up to 1 TΩ sample T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

19. Autobalancing bridge • ~10 Hz up to ~100 MHz • Resistances up to ~1 GΩ • Virtual ground avoids capacitive coupling to ground • Lc is kept at 0 potential by a feedback loop T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

20. Dana analysis • We measure complex admittance Y=G+iB as a function of frequency • After subtracting the background, complex dielectric function is given by T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

21. B G Havriliak-Negami model dielectric function •  = (0)-(): dielectric strength • 0: mean relaxation time • (1-): relaxation time distribution width T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

22. T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3

23. T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS3