Anomalous Noise in the Pseudogap Regime of YBa 2 Cu 3 O 7−δ
D. S. Caplan, V. Orlyanchik, M. B. Weissman, D. J. Van Harlingen, E. H. Fradkin, M. J. Hinton, T. R. Lemberger
aa r X i v : . [ c ond - m a t . s up r- c on ] A p r Anomalous Noise in the Pseudogap Regime of YBa Cu O − δ D. S. Caplan, V. Orlyanchik, ∗ M. B. Weissman, D. J. VanHarlingen, E. H. Fradkin, M. J. Hinton, and T. R. Lemberger Department of Physics and Materials Research Laboratory,University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Department of Physics, Ohio state University, Columbus, Ohio 43210, USA (Dated: November 6, 2018)An unusual noise component is found near and below about 250 K in the normal state of un-derdoped YBCO and Ca-YBCO films. This noise regime, unlike the more typical noise above 250K, has features expected for a symmetry-breaking collective electronic state. These include largeindividual fluctuators, a magnetic sensitivity, and aging effects. A possible interpretation in termsof fluctuating charge nematic order is presented.
PACS numbers: 74.40.+k, 74.72.Bk, 74.78.Bz
Key questions about pseudogap phenomena [1, 2] inhigh- T c superconductors remain unsettled. Some de-scriptions of pseudogap physics involve at least localbreaking of various symmetries, including translationalinvariance, point group symmetries and time-reversal [3–8]. Recently experimental evidence for such orderedstates has been found in many cuprates, including thecleanest YBa Cu O − δ (YBCO) materials. STM im-ages in BSCCO[9, 10] show local electronic nematic or-der. Static stripes are shown by neutron scattering[11]in LBCO near x = 1 / Cu O − δ (YBCO),attributed to stripes [19], are related to the peculiar mag-netic memory effects [17]. If the transport anisotropycomes from stripes, then any slow fluctuations in thislocal symmetry breaking should give rise to transportnoise [25] as found in diverse other systems including an-tiferromagnets [26], spin glasses [27], and ferromagnets[28]. Discrete resistance steps seen in small samples ofYBCO [24], and an unusual increase in normalized noisepower found in larger samples [29, 30] also suggest largecollective fluctuators, as expected from stripes. So farproperties such as distinctive temperature dependence ormagnetic sensitivity needed to clearly connect such noisewith stripe-like physics have not been reported.In this Letter we report that low-frequency trans-port noise in underdoped YBCO and Ca-dopedY − x Ca x Ba Cu O − δ (Ca-YBCO) films shows a well de-fined temperature, around 250 K, dependent on measure-
70 140 210 2800.00.10.20.3 (a) ( S V x V o l ) / V ( - m ) (b) T E T (K) f ~10 Hz D E=43±2meV -1 ) l n ( f M ) T (K) R ( k W ) FIG. 1: (color online) (a) Noise power, S V , in four consecutiveoctaves vs. T smoothed over the range of 0.3 K for the samplewith T c =58 K. Note the significant deviation of the noisepower from what would be expected by extrapolating fromhigh T part (solid line). Inset: Dependence of the resistanceon temperature; (b) Excess noise after subtraction of high-Tpart (see text) shown by a straight line in (a) for octave 6.The arrow marks T E ( f ) (see text). Inset: Dependence of T E on measurement frequency. Solid line is Arrhenius fit to thedata. ment frequency but very little on doping, below whichan extra noise component, exhibiting magnetic sensitiv-ity, aging effects and some large discrete fluctuators, setsin. Such effects are characteristic of noise from collec-tive states in disordered systems [26–28, 31]. Magneticmemory effects in the transport noise implies its connec-tion with magnetic hysteresis [17], suggesting coupling tosome other magnetic order. The large fluctuators allowfor mesoscopic thermodynamic characterization of thestates involved. [28, 31]. Noise symmetry measurements[31] further characterize the collective order.Thin YBCO and Ca-YBCO films (30-35 nm) weregrown by pulsed laser deposition. Except for one filmgrown on a vicinal SrTiO (001) (STO) substrate to re-duce twinning [32], LaAlO (LAO) substrates were cho-sen for their lower low-frequency noise [33]. The filmswere first nearly optimally doped, then annealed in lowO pressure to obtain 30K < T c <
85K corresponding to0.65 > δ > µ m wideand 15 µ m long. The contact area was ion milled beforedepositing the gold contacts to minimize their noise. Re-sistance (R) vs. temperature (T) showed typical behav-ior for underdoped material, as in the inset to Fig. 1(a).The partially untwinned sample showed a typical resis-tive anisotropy ratio between the two inequivalent crystaldirections [19].To measure noise a DC current was passed throughthe sample and the resulting voltage drop was fed intoan AC coupled SR552 low noise preamplifier followed byan anti-alias filter SR640. We compute the voltage spec-tral density, S( f, T ), for 0.3 Hz < f <
112 Hz from thefiltered AC voltage digitized at 300 Hz. A zero-currentbackground spectrum is subtracted to obtain S V ( f, T ),the portion of S( f, T ) due to fluctuations in R. (S V ( f, T )is quadratic in applied current up to the largest currentsused.) We compact and average S V ( f, T ) by integratingover f into octave sums, convenient for spectra of the formS( f ) ∝ /f α , since for α = 1 each octave has the samepower [31]. During T-dependence measurements, T wasswept continuously with typical rate of 0.1-0.3 K/min.No difference between data taken on cooling and heatingwas found.Figure 1(a) shows the T-dependent octave sums (nor-malized by V ) for the sample with a T c of 58 K. Anextra low-temperature noise source appears to be presentbelow about 250 K. We define T E ( f ) as T at which theexcess of S V (f) above its high-T extrapolation reacheshalf its maximal value. The f-dependence of T E ( f )(see inset Fig. 1(b)) follows thermally activated kinetics f M = f exp [ − ∆ E/k B T E ] ( f M measurement frequency),with a typical attempt rate of f ∼ − Hz and anactivation energy of ∆ E ∼ . E ( f ) gives noindication of a genuine phase or glass transition in thisvicinity, just a rather sharp change in a distribution ofactivation energies.This feature appeared in the noise power for all 13samples measured, patterned from 7 separate thin films.Except for one sample from a film which showed severalsigns of significant inhomogeneity, T E ( f ) and the derived∆ E were nearly the same in samples with T c ’s rangingfrom 35 K to 85 K, regardless of substrate or Ca con-tent. We shall later discuss the sharp difference between -0.14-0.070.000.070.14 (b) B (c) T/T E l n ( S C hanged V / S V ) A T=160K (a)
H=0 H=63kG H=0 ( S V x V o l ) / V ( - m ) t (min) l n ( S V / S V ) First Second Third
FIG. 2: (color online) (a) Noise power before, during and afterapplication of 6.3 T (H || c ). (b) Log of ratio of noise power topre-field value immediately after removal of H (dT/dt >
0) andduring 2 consecutive thermal cycles (dT/dt < C =62 K. (c) Per-sistent changes in S V that occurred in two samples (sample Aand B) from the same film with T C =85 K. Significant changesin (b) and (c) are found only below T E . such behavior and measures of the onset of pseudogapcorrelations. As we now discuss, aging effects, large dis-crete fluctuators, and magnetic sensitivity found exclu-sively below ∼
250 K indicate that the extra noise is dueto large-scale collective effects associated with electronicsymmetry breaking.Fig. 2(a) shows an example of the magnetic sensitivityof the noise at low T, in this case an increase in magni-tude of about 6% upon application of 6.3 T with H k c.Removing H gave no significant immediate change, butupon subsequent T-cycling the spectrum relaxed towarda different value, as shown in Fig. 2(b). Importantly, thechanges in the spectrum, both in response to the fieldand over time, are negligible above ∼
250 K. Changes inspectra of other samples induced by magnetic fields differin detail but also are negligible above ∼
250 K.As in the Kerr effect [17], the noise memory of the mag-netic perturbations persists even after cycling to roomtemperature. Unless YBCO has two different types ofhigh-T magnetic memory, (the origin of even one suchmemory is currently unknown) the transport noise is con-nected with the same time-reversal symmetry-breakingseen via the Kerr effect. Both the noise and Kerr memo-ries may involve special magnetic regions with high melt-ing temperature, e.g. surface antiferromagnetism. How-ever, neither method shows symptoms of these magneticeffects until T is lowered enough for more pervasive mag-netic correlations to show up.In another pair of samples, T c =85 K, a persistentchange in the T-dependent spectra occurred, only be-low ∼
250 K, in between T-cycles (see Fig. 2(c)). Themagnetic sensitivity of the noise (found below 250 K)also changed significantly. We found no accompanyingchange in R.The sensitivity of the noise to magnetic field changes,found only in the low-T regime, strongly suggests thatthis noise mechanism is associated with some sort ofmagnetic order. However, the results on the magneticsensitivity of different samples to different magnitudes,histories, and orientations of fields are too complex forus to characterize without further study.Below 200 K we often find large, T-dependent indi-vidual fluctuators (see Fig. 3), mostly of the two-levelform, showing activated kinetics with attempt rates ofabout 10 Hz, for which our frequency window limitsobservable δE to about 20k B T. In all 13 samples, manyon multiple T-sweeps, we found no discrete fluctuatorsabove 200 K. These detectable discrete fluctuators havemagnitudes δR/R > − , at least 3 orders of magni-tude larger than would be expected due to changes inscattering from the motion of small defects if the con-ductivity were approximately uniform [31]. Thus eitherthe conductivity is highly non-uniform or there are largecollective fluctuations, or both [28]. Both non-uniformityand large fluctuators are expected in stripe-like pictures[25].For two-level fluctuators we calculate the free energydifference between the levels, ∆ F , from the ratio r ( T )of time spent in each level from the Boltzmann expres-sion r ( T ) = exp (∆ F/k B T ). The temperature derivativeof ∆ F then yields the change in entropy ∆ σ and thechange in energy ∆ U , using standard thermodynamicrelations. Pure switching between different versions ofa broken-symmetry phase should give zero for ∆ σ and∆ U . We find typical values of | ∆ σ | <
10, but someoutside the error bars from zero. We measured a fluctu-ation isotropy parameter [31] S ≡ h Det ( δρ ) ih T r [( δρ ) ] i , where ρ isthe two-dimensional resistivity [31], in one YBCO sam-ple with T c =65 K. We found S ∼
0, indicating that δρ isnot a scalar ( S = 1), but also is not a rotation of an easyaxis in an otherwise symmetrical environment ( S = − ∼ -2-100 2 4 6 8 10-2-10 Ds =3±0.6 D U=37±6 meV l n (r) -1 ) T=100K t (sec.)
T=108K d V ( a r b . un i t s ) FIG. 3: (color online) Boltzmann factor for the fluctuatorfrom the inset vs. inverse temperature. Solid line is a fit to aBoltzmann expression. Inset: Discrete two-level fluctuator attwo temperatures. Sample: YBCO, T C =85 K. Nernst effect evidence [20] for nematic order in the pseu-dogap temperature range over a broad doping range inYBCO samples also supports interpreting the fluctuatorsas local nematic patches.
30 40 50 60 70 80 9010 -28 -27 -26 ( S V x V o l ) / V ( m ) T C (K) d FIG. 4: (color online) Amplitude of the excess noise at T E ( p )vs. T c and δ (oxygen deficiency) for each distinct sample.Circles and triangles are YBCO on LAO substrate 4 and 8 -terminal geometry, respectively. Stars and hexagon are Ca-YBCO on LAO substrate with 4 and 8 terminal geometry,respectively. Squares are YBCO on STO substrate with 4terminal geometry. The solid line is guide to the eyes. In the simplest picture of nematic order [25], twinningprovides a random field breaking up the simple orderedstate, allowing noise from rotations of the easy axis ofstripe domains. To the extent that nematic order iscoherent over distances large compared to the twinningscale, the rotations would occur in symmetrical environ-ments and hence not change scalar quantities. We findsome fluctuations in scalar quantities: energy, entropy,and resistivity tensor trace. Thus the collective stateis likely not to show rigid nematic order over distancesmuch larger than the typical twinning scale of severaltens of nanometers, consistent with neutron scatteringresults. [35]Although noise from disordered collective states iscommon, the onset of the low-T noise in these YBCOfilms is peculiar in showing simple thermally activatedkinetics, rather than any sort of sharp transition orcrossover [26, 28, 31]. Another low-frequency phe-nomenon in YBCO, internal friction, shows thermally ac-tivated features in this approximate temperature range[34, 36], but none of the features provide an obviousmatch to our noise results, and the origins of the frictionpeaks are themselves unclear. T E ( f ) lacks the dopingdependence of signatures of the onset of electronic cor-relations (e.g. by neutron scattering and the Kerr effect[15–17]).We are then left with a puzzle. Below T E ( f ) noiseappears with the qualitative features expected from dis-ordered correlated electronic states involving magnetism.The Arrhenius dynamical crossover into this regime is notitself the onset of dynamical cooperativity, which wouldshow sharper T-dependence. The most important sur-prising feature of the noise is that it ’remembers’ theeffects of magnetic fields even after warming to roomtemperature, just as does the Kerr effect in similar films[17]. There must be some magnetic order, e.g. antiferro-magnetic surface layers, which remains even at such tem-peratures. That suggests a tentative explanation for thecrossover into the low-temperature noise regime. Mag-netic exchange interactions in these materials lack strongdoping dependence [5]. The 0.4 eV activation energycould then represent the strength of pinning of stripe-likeorder to antiferromagnetic layers. 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