Sliding charge density wave in manganites
Susan Cox, J. Singleton, R.D. McDonald, A. Migliori, P.B. Littlewood
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Sliding charge density wave in manganites
Susan Cox, ∗ J. Singleton, R.D. McDonald, A. Migliori, P.B. Littlewood National High Magnetic Field Laboratory, Ms-E536, Los Alamos National Laboratory,New Mexico, 87545, USA Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK ∗ e-mail:[email protected] so-called stripe phase of the manganites is an important example of the complex be-haviour of metal oxides, and has long been interpreted as the localisation of charge at atomicsites . Here, we demonstrate via resistance measurements on La . Ca . MnO that thisstate is in fact a prototypical charge density wave (CDW) which undergoes collective trans-port. Dramatic resistance hysteresis effects and broadband noise properties are observed, bothof which are typical of sliding CDW systems. Moreover, the high levels of disorder typical ofmanganites result in behaviour similar to that of well-known disordered CDW materials. Ourdiscovery that the manganite superstructure is a CDW shows that unusual transport and struc-tural properties do not require exotic physics, but can emerge when a well-understood phase(the CDW) coexists with disorder.The stripe phase in manganites of the form La − x Ca x MnO appears as the temperature islowered through T ≃ K, and the superstructure wavevector settles on a final value of q ≃ (1 − x ) a ∗ (where a ∗ is the reciprocal lattice vector) for . ≤ x < . , at T ≃ K . Basedon the insulating nature of the manganites up to room temperature, and the observation of stripesof charge order in transmission electron microscopy (TEM) images, early studies concluded thatthe superstructure arose from localisation of charge at atomic sites . However, neutron and x-ray studies found the degree of charge localisation at Mn sites to be small, and subsequenttheoretical work suggested that a CDW model may be more applicable . This suggestion issupported by the observation that q/a ∗ is strongly temperature dependent , indicating that amodel in which the superstructure periodicity is derived from the sample stoichiometry cannotbe valid. In addition, heat capacity peaks at the transition to the stripe phase can be modelledas “dirty Peierls transitions”, expected in a disordered CDW system . However, the possibilityof the stripe phase exhibiting sliding behaviour, as seen in many other CDW systems , couldnot be probed without the ability to make orientation-dependent resistivity measurements. Herewe describe the first such measurements on the manganite stripe phase, which reveal dramatic2rientation-dependent resistivity and broadband noise effects which are characteristic of CDWsliding.Orientation-dependent resistivity measurements require thin films, because untwinned sin-gle crystals of the insulating manganites cannot be grown . The 80 nm thick La . Ca . MnO thin film was grown on an NdGaO substrate as described in . The film was prepared for TEMby conventional grinding of the substrate to 50 µ m and then milling a small window using afocused ion beam microscope to a thickness of around 200 nm. The sample was examined ina Philips CM30 microscope and was cooled to 90 K using a Gatan liquid nitrogen stage. Theuniaxial stripe phase was identified via superlattice reflections in a selected area TEM diffrac-tion pattern (illustrated below in Figure 2a); these reflections are detectable at 190 K, reaching astable form at 90 K. (Note that previous resistivity measurements of thin film La . Ca . MnO have failed to produce consistent results , because of the difficulty of producing high qual-ity films and a failure to check for the superstructure using a microscopic technique.)For the resistance measurements, gold wires were attatched to the thin film sample usinggraphite paint. The differential resistivity of the sample studied here was measured by using alock-in amplifier to detect the AC voltage produced in response to a 17 Hz AC current plus a DCbias; contacts were placed around the edges of the film to enable the current and bias to be ap-plied along different directions, chiefly parallel and perpendicular to the superlattice direction.Both four-point and two-point configurations were employed for the resistivity experiments toeliminate possible contact resistance effects; the noise measurements reported below employedtwo contacts.Analogies between La . Ca . MnO and other CDW systems are clearly apparent in Fig-ure 1, which shows the differential resistivity under zero DC bias versus temperature. Themeasurements appear similar to the resistivities of prototypical CDW systems doped with im-purities , in that there is no clear feature at the expected CDW ordering temperature, with3nsulating behaviour (i.e. decreasing resistivity with increasing temperature) persisting wellabove it. This has been interpreted as the “smearing” of the transition caused by the large im-purity density . Analogous behaviour is also seen in cuprate ladder compounds exhibitingsliding density waves below T ≃
200 K. As in the case of the cuprates, the resistivity of La . Ca . MnO shows an activated temperature dependence with an activation energy whichvaries from ≃ − K (Figure 1b and c).Figure 2 shows the differential resistivity as a function of DC bias applied parallel (alongthe lattice vector a ) and perpendicular to (along the lattice vector c ) the superlattice direction.At 157 K (Figure 2(f)), the differential resistivity drops in a similar fashion when the DC biasis applied in either direction. However, at temperatures < ∼ K, the differential resistivityundergoes a sharp drop when the bias is applied in the a direction; the effect is very much lessmarked with the bias in the c direction (Figure 2(b)-(e)). In addition, there is a large hysteresisbetween the differential resistance recorded when the bias is first applied in the a direction aftercooling from 300 K, and that measured on subsequent bias sweeps (in Figure 2 b-e the upperline in each direction shows the data from the first sweep after cooling and the lower line showsthe data from subsequent sweeps); the area enclosed by the hysteresis loop increases rapidly asthe temperature falls.The hysteretic resistivity features shown in Figure 2 are typical of CDWs . As the sampleis cooled, the CDW settles into a minimum-free-energy pinned configuration, correspondingto maximum electrical resistivity . On the application of electric field, the CDW initially un-dergoes local distortions that occur over longer and longer lengthscales as the field increases;eventually, the threshold field is reached and the CDW starts to slide. As the field is reducedagain, the CDW freezes into a distorted state, characterized by a lower resistivity; the initial,minimum energy state cannot be regained without thermally cycling the sample , explainingthe hysteresis in our data. 4ther mechanisms such as avalanche breakdown or sample heating cannot account for thedata in Figure 2. Whilst these effects might produce a falling differential resistivity as the fieldincreases, they would not produce a history-dependent result; on removing the field, the samplewould return to its initial state. Moreover, whilst the DC resistivity for currents in the c directionis 2 times higher than that for currents parallel to a , the drop in resistivity as the field increasesis five times larger in the latter direction (Figure 2); this anisotropy both fits naturally into theCDW picture and excludes heating and breakdown as possible mechanisms. The anisotropy inthe observed effects also excludes ferromagnetic domains (sample inhomogeneity) as a possiblemechanism; in this case the effects would be the same in the two orientations.Having explained the hysteresis when the bias is along a , we attribute the small amount ofhysteresis seen when the bias is along c (Figure 2) to imperfect contact geometry; i.e. misalign-ment results in a small amount of bias being applied in the perpendicular direction.Another distinguishing feature of CDWs is that they exhibit a broadband noise spectrumwith an amplitude proportional to f − α , where f is the frequency . Noise measure-ments were performed using a low-noise current source. The noise signal was amplified witha high input impedence, low noise preamplifier and was recorded via a digitizing oscilloscope.Lead capacitance, and the typical Ω sample resistance, limited noise measurements to below10 kHz. Other techniques commonly used on CDW systems such as NbSe were considered orattempted but typical properties of manganite films rendered them impossible; manganite filmresistivities and geometries lead to RC time constants that are too high to perform experimentsthat measure effective pulse line or duration memory effects.Figure 3 shows that significant broadband noise is observed in La . Ca . MnO when theDC bias is applied in the superstructure direction. By contrast, the noise amplitude is muchsmaller with the bias in the non-superstructure direction. The exponent α in La . Ca . MnO runs from 0.8 (156 K) to 2.0 (100 K), a similar range to values seen in the prototypical CDW5ystem NbSe (0.8-1.8) . However, the magnitude of the broadband noise in La . Ca . MnO is much larger than that observed in clean CDW systems; for La . Ca . MnO the effectivenoise temperature at 300 Hz is ∼ K for a sample temperature of 100 K, while in pureNbSe the effective noise temperature is ∼ K. This is attributable to the large amountof disorder present in La . Ca . MnO (see above), so that there are many more pinning-depinning events compared to e.g. pure NbSe . Although broadband noise has previously beenobserved in impurity-pinned CDWs , narrowband noise has not been observed in an impurity-doped or radiation-damaged sample, probably because the width of the narrowband noise peakis proportional to the magnitude of the broadband noise . Therefore a high level of disorderor impurity pinning will lead to a large amount of broadband noise and unobservably smallnarrowband noise, as seen here in La . Ca . MnO .As seen in other CDW systems , the amount of broadband noise decreases with increasingtemperature (Figures 3a,c,e). For a bias above E T ( ≃ V/m) in the superstructure directionthis decrease is approximately linear with temperature (Figure 4c), as observed in the CDWsystem TaS . With the bias in the non-superstructure direction, the noise increases muchmore slowly; at 100 K it is more than an order of magnitude smaller than that with the biasalong a (Figure 4c).Figures 4a and b show the variation of the broadband noise amplitude with applied biasbetween the first bias sweep after cooling from 300 K and on a subsequent sweep. On firstbiasing, the noise ampitude shows a large peak at the same point as the large fall in differentialresistance (Figure 4a). On subsequent bias sweeps, the noise increases more slowly with bias(Figure 4b). The large peak during the first bias sweep is caused by a high level of randomtelegraph signal (RTS) noise, which occurs in CDW systems as they switch from pinned todepinned states and back again close to the threshold field. The distinctive shape of theRTS noise is shown in Figure 4d, another factor adding weight to our identification of a CDW6n La . Ca . MnO .In conclusion, we have demonstrated via resistivity and noise measurements that the super-structure in the stripe phase of manganites is a CDW which slides in the presence of an electricfield. The manganite CDW is a fully gapped system with no screening electrons, which haspreviously only been observed in extremely clean organic materials . However, the manganiteCDW exists with a high level of impurities, leading to dramatic hysteresis effects in the resis-tance. Our findings call for a reanalysis of the large region of the manganite phase diagram, . ≤ x < . , which is occupied by the CDW. This is the first observation of sliding in amaterial which undergoes 3D charge ordering . In a wider context, this result is important be-cause of the prevalence of stripe and checkerboard phases in oxide materials, including chelates,cobaltites, nickelates and cuprates; in particular, evidence is mounting that a glass of the stripephase in cuprates is linked to high temperature superconductivity , making an understandingof the stripe phase a matter of urgency.We thank N. Harrison, N.D. Mathur, P.A. Midgley, G. Kotliar and E. Rosten for helpfulcomments. S. Cox acknowledges support from the Seaborg institute. The sample was grownat Cambridge where research was funded by the UK EPSRC. This research was funded bythe U. S. Department of Energy (DoE) under Grant ldrd-dr 20070013. Work at NHMFL isperformed under the auspices of the NSF, the State of Florida, and the US DoE.The authors declare no competing financial interests. References [1] Chen, C. H., Mori, S. & Cheong, S.-W. Anomalous melting transition of the charge-ordered state in manganites.
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Science , 315 , 1380–1385, 2007.10igure 1: (a) Differential resistance of La . Ca . MnO with the current in the a (red) and c (blue) directions versus temperature (zero DC bias). The resistivity is similar to that of theladder compound Sr Cu O , shown in yellow . (b) and (c) demonstrate that the resistivityis activated over all temperatures, being fitted to two exponentials.Figure 2: (a) Linescan of TEM image in a (red) and c (blue) directions showing the superstruc-ture reflections present in only the a direction. (b)-(f) Differential resistivity of La . Ca . MnO versus DC bias with bias applied in the a (red) and c (blue) directions at various temperatures.In each case the upper curve is the differential resistivity obtained after cycling the temperatureto 300 K, and the lower curve is the path followed by subsequent bias sweeps.Figure 3: Frequency and current depedence of the broadband noise. 97 K data with the currentparallel (a) and perpendicular (b) to q . 123 K data with the current parallel (c) and perpendicular(d) to q . 156 K data with the current parallel (e) and perpendicular (f) to q . The color scale is inunits of V /Hz.Figure 4: (a) Resistivity displayed as R ( E ) /R (0)(0)