Physica B 460 (2015) 96–99

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Sliding state of the quasi-two dimensional CDW system TbTe3 probedby coherent x-ray diffraction

D. Le Bolloc'h a,n, A.A. Sinchenko b,c, V.L.R. Jacques a, L. Ortega a, E. Lorenzo d, P. Lejay d,T. Schülli e, G. Chahine e, P. Monceau d

a Laboratoire de Physique des Solides (CNRS-UMR 8502), Bât. 510, Université Paris-Sud, 91405 Orsay, Franceb Kotelnikov Institute of Radioengineering and Electronics of RAS, Moscow, Russiac National Research Nuclear University (MEPhI), 115409 Moscow, Russiad Institute Néel CNRS and Université Joseph Fourier, BP166, 38042 Grenoble, Francee ESRF-The European Synchrotron, 71 Avenue des Martyrs, Grenoble, France

a r t i c l e i n f o

Available online 11 December 2014

Keywords:Sliding charge density wavesCoherent x-ray diffraction

x.doi.org/10.1016/j.physb.2014.11.04826/& 2014 Elsevier B.V. All rights reserved.

esponding author.ail address: lebolloch@lps.u-psud.fr (D. Le Bol

a b s t r a c t

Coherent x-ray diffraction experiments have been performed to probe the sliding state of a quasi-twodimensional charge density wave (CDW) in TbTe3. The 2kF satellite reflection associated with the CDWhas been observed with respect to external dc currents, on both sides of the threshold current. Thesemeasurements illustrate how the periodic lattice distortion associated to the CDW supports the collectivemotion of a sliding CDW in a quasi-two dimensional system. A comparison with the quasi-one dimen-sional NbSe3 system is done.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

A charge density wave (CDW) is a modulation of the electronicdensity which relies upon a nesting property of the Fermi surfaceand a periodic distortion of the lattice. When incommensurate, theelectronic modulation has the remarkable property to carry cor-related charges when the system is submitted to an external cur-rent. This phenomenon is commonly interpreted as based on asliding effect of the incommensurate electronic modulation overthe atomic lattice.

The transport of correlated charges is well measured bytransport measurements. Above a threshold current, the differ-ential resistivity suddenly drops and a periodic time-dependentvoltage is observed in the non-linear state [1].

What is the behavior of the lattice? How the periodic latticedistortion supports the collective motion of charges? This dyna-mical effect is difficult to measure with classical techniques. Weshow here that coherent scattering is particularly well suited forsuch experiment because this technique is sensitive to the phaseof any modulation in condensed matter. Coherent scattering ex-periments provide an original picture of the sliding state of acharge density wave via the observation of the phase of the per-iodic lattice distortion.

loc'h).

2. Coherent x-ray diffraction

2.1. Obtaining coherent x-ray beams from poorly coherent synchro-tron sources

Coherent x-ray beams can now be obtained from synchrotronsources by playing with the optical path of the x-ray beam. Indeed,the transverse coherence length ξT of a beam can be written as [2]

dTξ λ

σ∝

where λ is the wavelength, d the distance from the source and sthe source size. In the x-ray regime, the length ξT is intrinsicallysmall because of the prefactor λ. However, the use of small sourcesizes s and large distances d provide micrometer coherent x-raybeams. The experimental proof of this is to perform diffractionexperiment of a rectangular aperture. Diffraction patterns ob-tained in the x-ray regime are now very similar to what we used tosee with visible light, from the Fraunhofer to the Fresnel regime[3]. From the visibility of fringes, the degree of coherence of thex-ray beam can be calculated and is greater than 90% [3].

2.2. Coherent diffraction and phase shifts

In contrast to classical diffraction, the use of a coherent beamallows us to observe the fluctuations of matter. In that case indeed,the x-ray beam can be considered as a plane wave and the dif-fraction pattern results of a Fourier transform of the electronic

D. Le Bolloc'h et al. / Physica B 460 (2015) 96–99 97

density, without the usual procedure of space averaging in-trinsically linked to classical diffraction. As a consequence, dif-fraction patterns result of a sum of amplitudes which give rise todestructive or constructive interferences between domains. Thesmooth diffraction profiles obtained with classical x-ray beamsgive way to speckles when using a coherent beam.

The interpretation of speckle patterns is never easy because thediffraction pattern results of interferences between domainswhose distribution in real space is inherently difficult or im-possible to predict. However, dynamics of fluctuations [4] orcomparisons between spatial fluctuations of coexisting phases [5]can be done.

A coherent x-ray beam has another specific virtue: it is ex-tremely sensitive to any phase shift in condensed matter. As anillustration, the coherent diffraction pattern of a silicon wafercontaining a single dislocation embedded at few micrometers inthe bulk leads to a destructive interference at the exact Bragg re-flection position [6].

In CDW systems, the phase of periodic lattice distortion playsan important role. The disorder of the CDW appears through thisphase and can take many topologies such as isolated solitons,soliton lattice or dislocation. Those three topologies have beenobserved either by coherent diffraction in the bulk [7,8] or at thesurface by STM [9].

Fig. 1. Transport measurements in NbSe3 (quasi 1D) and TbTe3 (quasi 2D). (a) Ex-cess of current versus the external current. (b) Differential resistance showingthreshold currents of IS¼11 mA in TbTe3 and IS¼0.8 mA in NbSe3.

3. Results

3.1. TbTe3 structure and sliding properties

The new family of rare-earth tritellurides RTe3 compounds hasraised intense research during the last five years. Those structuresare weakly orthorhombic and are made of double layers with al-most square Te sheets perpendicular to the b direction and sepa-rated with RTe slabs. Classical diffraction experiments [10] haveshown the appearance of an incommensurate charge density wavefor the whole R series associated with a periodic lattice distortionlocated at the incommensurate wave vector k2 (0 0 )F

27

= ∼ inTbTe3. ARPES measurements [11] reveal an almost square Fermisurface in the (an,cn) plane compatible with a nesting effect re-sponsible for the CDW instability. Finally, transport measurementshave recently shown non-linear transport properties in DyTe3 [12]and in TbTe3 [13] along the cn axis.

3.2. Experimental setup

The coherent x-ray diffraction experiment was performed atthe ID01 beamline at the ESRF synchrotron. A channel-cut Si(111)monochromator has been used which leads to a longitudinal co-herence length /2 0.6 mL

2ξ λ λ= Δ = μ at E¼7.4 keV. The coherenceset up was made of two sets of slits [14]. The second one wasopened at S H V20( ) 60( ) m0

2= × μ at 40 cm from the sample, fol-lowed by a Fresnel zone plate at 17 cm and focusing the coherentx-ray beam on a 0.5 m 0.5 mμ × μ spot located 23 cm further on thesample surface. The 2D diffraction patterns have been recordedwith a pixel detector (Maxipix camera made of 512�512 pixels of55 m 55 mμ × μ each) and located at 1.2 m from the sample.

A TbTe3 single-crystal has been selected and prepared from1 mm2 square surface, with a thickness of 1.6 μm. The sample usedhad an elongated shape (1 mm length and 120 mμ width) and wasoriented along the c-axis.

We used a 4-probe method and the distance between the po-tential probes was 0.6 mm. The current–voltage characteristicswere measured during the experiment at room temperature.Transport measurements were used to determine the threshold

current value: IS¼11 mA (see Fig. 1). The current–voltage char-acteristics have been continuously measured to check the stabilityof this value during the experiment.

3.3. Coherent diffraction and transport measurements performedsimultaneously in TbTe3

The rocking curve of the 2kF satellite displayed in Fig. 2corresponds to the sum over the 2D camera. When increasingcurrent, the corresponding profile remains stable up to IS with nodecrease of the intensity. Just above the threshold current(I 11 mAS = ), a sudden shift of the maximum is observed towardslarger angles. This shift cannot be attributed to a heating effectunder current.

The complete current cycle (from I¼0 mA up to I¼þ60 mAand down to I¼�60 mA to I¼0 mA) displays a strong hysteresis.At the end of the current cycle, the 2kF profile does not completelyrecover the original profile of the pristine state. This memory ef-fect is also observed in NbSe3 and it K0.3MoO3.

The main difference between TbTe3 and NbSe3 concerns thespatial fluctuations below the threshold (see Fig. 3). Indeed, in theNbSe3 system, the width of the 2kF satellite increases, the max-imum of intensity is reduced by a factor of three and specklesappear along the transverse direction only, perpendicular to thesliding direction, i.e. perpendicular to the chains axis [15]. Thetransverse coherent length of the CDW modulation decreasesthrough CDW dislocation nucleation. This decrease of the trans-verse coherence can be attributed to a moving glass behavior of

Fig. 2. (a) Rocking curve of the Q k(1 15 2 )cdw F= satellite reflection associated tothe CDW in TbTe3 versus external current at T¼300 K. A shift of diffraction profilestowards larger angles is observed for currents greater than the threshold current(at IS¼12 mA). (b) Same data displayed as a 2D map.

Fig. 3. Coherent diffraction patterns of the 2kF satellite reflection associated to the CDWcorresponding profiles (from [15]) and (c) in the quasi-two dimensional TbTe3 system,

Fig. 4. Diffraction profile of the speckle patterns displayed in Fig 3c, along thewhite line, below and above the threshold current. Speckles remain almost stablebelow the threshold current. A clear change is observed above the threshold.

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the CDW [16]. Above the threshold current, speckles disappear andthe intensity profile becomes smooth: the CDW recovers a longrange order thanks to the motion (Fig. 3a, right panel).

There is nothing of that kind in TbTe3. Speckles spread in thethree directions of space and remain almost identical below thethreshold current. No decrease of the intensity is observed (seeFig. 3c and the corresponding profile in Fig. 4). The distribution ofCDW domains seems very stable below the threshold.

Above the threshold current, a modification of the CDW wavevector is observed (see Fig. 2) as well as a complete reorganizationof the CDW domains.

versus external current in (a) the quasi-one dimensional NbSe3 system with (b) theon both sides of the threshold current.

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4. Discussion

As for quasi-one dimensional systems such as NbSe3, the slid-ing state of TbTe3 measured by transport measurement is directlyrelated to a modification of the periodic lattice distortion.

A contraction of the CDW period has been already observed inNbSe3. In that case however, this effect is observed when themeasurement is performed close to electrical contacts. It is not soin the present case where the measurement has been done farfrom any contacts. The origin of this CDW period modification atthe threshold in TbTe3 seems to be different and remains to beexplained.

Contrary to NbSe3, no decay of the transverse coherence lengthbelow the threshold is observed in TbTe3. The competition be-tween elasticity and disorder is strongly dependent on the di-mensionality. This could explain why this phenomenon is notobserved in TbTe3.

In the flow regime, above IS, TbTe3 does not display narrowingeffect by motion like in NbSe3. This phenomenon, even if it oc-curred, might be not seen because the sample quality is not goodenough. However, we clearly see an important reorganization ofCDW domains in the sliding regime.

References

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