1. Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 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. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Outline Chain sulfide BaVS 3 Low-frequency dielectric spectroscopy: complex dielectric function in the insulating phase of BaVS 3 Nature of the insulating phase ground state? Collective excitations of the orbital ordering

3. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 BaVS 3  Consists of VS 3 chains separated by Ba atoms  Neighboring VS 6 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 VS 6 octahedra  Tetramerization of V 4+ chains Ba V S Lechermann et al., PRB 76, 085101 (2007)

4. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 BaVS 3  2 electrons in:  a wide A 1g band (d z2 )  narrow E g1, E g2 bands (e t2g ) S2 S1  Filling of bands governed by Coulomb repulsion, local Hund’s rule coupling  A 1g, E g1 close to half-filling  Metal-to-insulator phase transition at T MI ≈70 K  Diffuse x-ray scattering: Fagot et al., PRL 90, 196401 (2003)  pretransition fluctuations up to 170 K  q c ≈ 2k F (A 1g ) 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 T χ ≈30 K: incommensurate magnetic ordering (Nakamura et al., J. Phys. Soc. Jpn. 69, 2763 (2000), Mihály et al., PRB 61, R7831 (2000)) Nature of MI transition? Ground state? Lechermann et al., PRB 76, 085101 (2007) LDA + DMFT

5. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Samples Needle-like single crystals grown along c-axis, hexagonal cross-section 3 x 0.25 x 0.25 mm 3 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

6. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 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)) Low-Frequency Dielectric Spectroscopy What is the connection of this relaxation with the MI transition? Ivek et al., PRB 78, 035110 (2008)

7. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Metal-Insulator Phase Transition T MI ≈ 67K: peak in dc resistivity derivation dc gap 2Δ≈500 K corresponds to the optical gap (Kézsmárki et al., PRL 96, 186402 (2006)) Peak in Δε at the same T! Screening by free charge carriers

8. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 CDW Phasons? Do we have a long- wavelength, phason response? Screening by free charge carriers: Littlewood Unexpected Δε behavior  CDW: Δε(T)~const.≈10 7 Lack of a significant non-linear dc conductivity – no sliding Another DW phason fingerprint: a narrow microwave pinned mode  no experimental results

9. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Hopping conduction? Cross-over frequency far above the observed dielectric response Optical conductivity not enhanced compared to dc values Not a candidate 300K 85K 60K 10K 0.010.02 Energy (eV). Kézsmárki et al., PRL 96, 186402 (2006)

10. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Ferroelectric nature of the MI transition? Below T MI : noncentrosymmetric structure with a polar axis in the reflection plane of VS 3 chains High polarizability of electron system coupled to V 4+ 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 V 4+ 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

11. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Orbital ordering? No charge modulation in the insulating phase Fagot et al., Lechermann et al.: modulation of orbital occupancy 51 V NMR and NQR measurements suggest an orbital ordering below T MI that is fully developed only at T x (Nakamura et al., PRL 79, 3779 (1997)) Magnetic susceptibility (Mihály et al., PRB 61, R7831 (2000)): lack of magnetic long-range order between T MI and T χ Magnetic anisotropy (M. Miljak, unpublished): AF domain structure below T χ Fagot et al., PRB 73, 033102 (2006)

12. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Interpretation in the context of Orbital 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 T χ 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 T MI, 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

13. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Conclusion BaVS 3 – system with orbital degeneracy Metal-Insulator transition at T MI ~67 K Magnetic transition at T χ =30 K Low-Frequency Dielectric Spectroscopy: the observed mode cannot be assigned to phason excitations Density of excitations decreases from T MI with decreasing T, becomes constant under T χ Short-wavelength excitations Orbital Ordering

14. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Hopping b) frequency marking the onset of ac conduction cross is roughly proportional to the dc conductivity: Barton-Nakajima-Namikawa relation connects  dc and dielectric loss peak frequency   -1 :  dc    -1 Dyre and Schroeder, Rev.Modern Physics 72, 873 (2000) - BaVS at low T:  dc  10 -5 – 10 -6  -1 cm -1 → cross expected at > 1 MHz - For BaVS simple calculation yields : cross (25 K) = 360 MHz and cross (50 K) = 3.8 GHz T.Vuletic et al., Physics Reports 428, 169 (2006). c)  00  1ns is too long to be attributed to quasi-particles

15. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3

16. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3

17. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Contacts

18. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Low-Frequency Dielectric Spectroscopy Complex conductivity as a function of frequency

19. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Low frequencies, high impedances Lock-in + current preamplifier Voltage output Measuring the current 10 mHz – 3 kHz Resistances up to 1 TΩ sample

20. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 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

21. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3 Dana analysis We measure complex admittance Y=G+iB as a function of frequency After subtracting the background, complex dielectric function is given by

22. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3  =  (0)-  (  ) : dielectric strength  0 : mean relaxation time (1-  ): relaxation time distribution width Havriliak-Negami model dielectric function G B

23. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3

24. 29 August 2008 T. Ivek: Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS 3