Large response of charge stripes to uniaxial stress in La 1.475 Nd 0.4 Sr 0.125 Cu O 4
T. J. Boyle, M. Walker, A. Ruiz, E. Schierle, Z. Zhao, F. Boschini, R. Sutarto, T. D. Boyko, W. Moore, N. Tamura, F. He, E. Weschke, A. Gozar, W. Peng, A. C. Komarek, A. Damascelli, C. Schüßler-Langeheine, A. Frano, E. H. da Silva Neto, S. Blanco-Canosa
LLarge response of charge stripes to uniaxial stress in La . Nd . Sr . CuO T. J. Boyle,
1, 2, ∗ M. Walker, ∗ A. Ruiz,
3, 4, ∗ E. Schierle, Z. Zhao, F. Boschini,
6, 7, 8
R. Sutarto, T. D. Boyko, W. Moore, N. Tamura, F. He, E. Weschke, A. Gozar,
2, 11
W. Peng, A. C. Komarek, A. Damascelli,
6, 7
C. Sch¨ußler-Langeheine, A. Frano, † E. H. da Silva Neto,
1, 2, 11, ‡ and S. Blanco-Canosa
13, 14, § Department of Physics, University of California, Davis, California 95616, USA Department of Physics, Yale University, New Haven, Connecticut 06520, USA Department of Physics, University of California, San Diego, California 92093, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, Albert-Einstein-Straße 15, 12489 Berlin, Germany Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada Department of Physics & Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Centre ´Energie Mat´eriaux T´el´ecommunications, Institut National de la Recherche Scientifique, Varennes, Qu´ebec J3X 1S2, Canada Canadian Light Source, University of Saskatchewan, Saskatoon, Saskatchewan S7N 2V3, Canada Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA Energy Sciences Institute, Yale University, West Haven, Connecticut 06516, USA Max Planck Institute for Chemical Physics of Solids, N¨othnitzerstrasse 40, 01187 Dresden, Germany Donostia International Physics Center, DIPC, 20018 Donostia-San Sebastian, Basque Country, Spain IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
The La-based ‘214’ cuprates host several symmetry breaking phases including superconductivity, charge and spin order in the form of stripes, and a structural othorhombic-to-tetragonal phase transi-tion. Therefore, these materials are an ideal system to study the effects of uniaxial stress onto the variouscorrelations that pervade the cuprate phase diagram. We report resonant x-ray scattering experimentson La . Nd . Sr . CuO (LNSCO-125) that reveal a significant response of charge stripes to uni-axial tensile-stress of ∼ . GPa. These effects include a reduction of the onset temperature of stripesby ∼ K, a K reduction of the low-temperature orthorhombic-to-tetragonal transition, competitionbetween charge order and superconductivity, and a preference for stripes to form along the direction ofapplied stress. Altogether, we observe a dramatic response of the electronic properties of LNSCO-125 toa modest amount of uniaxial stress.
Cuprate high-temperature superconductors may be thequintessential example of a strongly correlated quantumsystem, featuring a complex interplay between brokensymmetry states, often referred to as intertwined orders[1, 2]. This rich interplay is evident in the charge or-der (CO) state: a periodic modulation of charge that isintertwined with superconductivity, magnetism, the crys-tal structure, and nematicity (four-fold C to two-fold C symmetry breaking [3]). These various links between or-dered states and CO are perhaps most clearly observed inthe ‘214’ family of La-based cuprates. (i) CO and mag-netism emerge intertwined in the form of stripes. (ii)
Thestripes are C symmetric, with their orientation alternatingby ◦ between adjacent CuO planes [4]. (iii) The stripesare strongly pinned to the low temperature tetragonal (LTT)crystal structure, which stabilizes the alternating pattern[5, 6]. (iv)
Finally, the stabilization of stripes occurs in con-cert with the suppression of three-dimensional (3D) super-conductivity, which results from a frustration of the Joseph-son coupling between adjacent CuO layers [7, 8]. Deter-mining how all these ordered states are interconnected is amajor challenge in the field of high-temperature supercon-ductivity.There are different methods to tune the intertwined or-ders in the cuprates. Typically, a magnetic field [9, 10],chemical doping [11], or pressure [12] are used to ad- just the relative strengths of the ordered states. For in-stance, the application of . GPa of hydrostatic pres-sure to La . Ba . CuO decouples the LTT and COphases, suppressing the former while allowing the latterto survive with an onset temperature of K [13]. How-ever, controlling the rotational symmetry of the correla-tions in the CuO planes requires a tuning parameter thatcouples directionally to the electronic degrees of freedom.This can be achieved with the uniaxial application of pres-sure, or stress, which has recently become the focus ofseveral cuprate studies. For example, recent experimentson YBa Cu O y indicate that attaining uniaxial strainaround 1% can modify the inter-layer interaction of the COand its coupling to acoustic phonons [14, 15]. In the ‘214’family, uniaxial stress has repeatedly been shown to in-crease the onset temperature of superconductivity [16–19].A small value of uniaxial stress, approximately . GPa,dramatically increases the onset of 3D superconductivity inLa . Ba . CuO (LBCO-115) from K to K [19].Remarkably, the same application of uniaxial stress alsoreduces the onset of spin stripe order from K to K.These opposing effects between superconductivity and spinstripes highlight the importance of uniaxial stress experi-ments to the study of intertwined orders. Still, diffractionexperiments that directly measure the effects of uniaxialstress on charge stripe order and the LTT structure in the a r X i v : . [ c ond - m a t . s t r- e l ] D ec [110][100] [010] LTO LTT - Cu - O q || (r.l.u.) I n t e n s i t y ( a . u . )
10 K30 K50 K65 K80 K150 K200 K (a) (b) (c) (d) q || (r.l.u.) q || (r.l.u.)
80 K150 K200 K
FIG. 1. (a) A diagram depicting the CuO octahedral tilts in both the LTO and LTT phases. In the LTO phase, neighboring oc-tahedra tilt in opposite directions (clockwise and counter-clockwise) along the [110] direction. In the LTT phase, adjacent CuO layers have orthogonal tilts along the [100] and [010] directions. (b) Temperature dependence of the CO peak in LNSCO-125. Sharppeaks corresponding to charge stripes are observed below 65 K in the LTT phase. The gray dashed line is a polynomial fit of thehigh-temperature background curve measured at 300 K. (c) RXS scans in the LTO phase showing broad peaks corresponding to COcorrelations. (d) Lorentzian fits of the background-subtracted curves shown in (c). La-based cuprates have not been reported.Here we report a Cu-L and O-K edge resonant x-rayscattering (RXS) study of CO and the LTT structure inLa . Nd . Sr . CuO (LNSCO-125) under the influ-ence of modest uniaxial stress, approximately . GPa, ap-plied along the a axis of the LTT structure ( i.e. along theCu-O bond direction). We first performed a detailed zero-stress control experiment on LNSCO-125, where we ob-served CO correlations above the onset of stripes near Kand detectable up to at least
K. Upon introducing uni-axial tensile-stress, the onset of the LTT phase ( T LTT ) isreduced by K, from K to K. Additionally, the on-set of stripe order decreases by approximately K, from ≈ T LT T + 12
K in the absence of strain to ≈ T LT T − Kin the presence of strain. This overall shift is larger thanthe one observed for T LTT , which likely reflects the com-petition between CO and superconductivity. An additionaloffset of approximately K is observed between the on-set of charge stripes along the a and b directions. De-spite the effects of stress on the LTT and the charge stripephases, we find no appreciable modification of the high-temperature CO correlations. Altogether, our experimentsnot only show that a small amount of uniaxial stress trig-gers responses from the various intertwined orders, theyalso establish uniaxial stress as a powerful tool to controlthe electronic properties of LNSCO-125.The single crystals were synthesized by floating zoneand previously characterized by means of resonant x-rayscattering and magnetometry [20]. LNSCO-125 hosts sev-eral classic features of La-based cuprates near / holedoping. In the low temperature orthorhombic (LTO) phase,the CuO octahedra tilt about an axis parallel to the [110] direction, which is ◦ from the Cu-O bond direction. Atlower temperatures, in the LTT phase, the CuO octahedratilt about axes parallel the Cu-O bond directions [21, 22].Importantly, in the LTT phase the tilt axis alternates be-tween [100] and [010] through consecutive CuO planes,Fig. 1(a). Thus, while the LTT is a globally tetragonalphase, it is actually two-fold C symmetric within eachCuO plane, which provides a natural motif to stabilize thestripe order.Previous RXS experiments on LNSCO-125 indicate theappearance of stripe order at approximately T LTT [24]. Ourdetailed RXS experiments show that the peak at q || = q CO = 0 . rlu (reciprocal lattice units) survives at hightemperatures, above T LTT , albeit with much lower intensitywhen compared to the low-temperature signal. Figure 1(b)shows the temperature evolution of the CO peak at q CO inLNSCO-125, showing a clear and rapid enhancement be-low T LT T = 63
K. However, the data also show that cor-relations at q CO persist even for T > T
LT T and continueto decrease with increasing temperature. It is difficult todetermine the onset temperature for these correlations, butwe still observe a clear evolution of the peak at q CO be-tween K and
K, Fig. 1(c), which is better visualizedby subtracting the
K curve, Fig. 1(d).It is important to note that since our RXS experimentsare done in energy-integrated mode, the high-temperaturepeak at q CO may originate from both elastic (static) andinelastic (dynamic) correlations. In fact, high-temperaturedynamic CO signals have recently been observed in manycuprates, including other La-based systems [25, 26]. Whileit may be tempting to assign the same rotational symme-try of the charge stripes to the high-temperature correla-
10 20 30 40 50 60 70 80
Temperature (K) I n t e n s i t y ( a . u . )
34 K 63 K σ > 0 σ = 0 (a)(b) Stresssample Controlsample2 mm
FIG. 2. (a) An image of the titanium strain device and LNSCO-125 crystals. The stress sample is mounted in the center across agap using a stiff epoxy and the control sample is mounted on thetitanium using silver paint [23]. (b) Temperature dependence ofthe (001) Bragg peak on the apical O-K edge in both the stressand control samples corresponding to the LTT phase transition.The transition temperature is suppressed by 29 K with the appliedstress. tions, such correspondence has not been experimentallyverified. Here we refer to the low temperature signal ascharge stripes and cautiously refer to the high-temperaturesignal simply as CO correlations. As we will discuss later,we do not detect modifications to the CO correlations dueto uniaxial stress in our experiments despite observing sig-nificant effects to the LTT phase and charge stripes.To investigate what happens to the CO and the LTTphase when we perturb the LNSCO-125 sample with ex-trinsic uniaxial stress, σ (cid:54) = 0 , we embed the crystal inan apparatus whose geometry explicitly breaks C sym-metry, Fig. 2(a). The sample is constrained on two-edgesacross a gap using expoy in a device constructed of ma- chined high-purity titanium [23]. Differential thermal con-traction occurs upon cooling due to the different coeffi-cients of the thermal expansion of the sample, epoxy and ti-tanium, which causes the LNSCO-125 crystal to be uniaxi-ally stretched relative to an unconstrained crystal [23]. Ourexperimental setup also includes a second sample mounteddirectly on one of the faces of the device using silver paint,which allows us to perform control measurements on a σ = 0 sample in the same experiment, Fig. 2(a). (Notethat σ refers to externally applied stress and does not in-clude the intrinsic stress due to the thermal contraction ofthe crystals themselves.) Unlike many strain experimentsthat cannot directly probe the lattice parameters, we canaccess the lattice constants by measuring the Bragg peaksof the LNSCO-125 crystal. We find those measurementsto yield strain values of ≈ . ± .
026 % [23]. Us-ing C = 232 GPa for the elastic modulus [27], we esti-mate σ = 0 . ± . GPa. Additionally, we perform amultiphysics simulation that incorporates all key elementsof the assembly, including the thermal and elastic proper-ties of the materials, as well as the geometry of the assem-bly [23, 28]. The simulation produces an approximatelyuniform tensile strain pattern of the same order of magni-tude as measured by the Bragg peaks when the apparatusis cooled to K. Although the amount of stress is rela-tively small, it is comparable in magnitude to the compres-sive stress used in the LBCO-115 experiments mentionedabove, which were shown to have significant effects on thesuperconductivity and spin-stripe order [19].A striking consequence of σ (cid:54) = 0 in our experimentson LNSCO-125 is the dramatic reduction of T LTT from K to K, Fig. 2(b). This is directly seen in our ex-periments via apical O-K edge RXS measurements of the(001) Bragg peak (in Miller index notation), whose reso-nant cross-section is an increasing function of the octahe-dral tilts in the LTT phase [24]. We can understand the re-duction of T LTT as a consequence of uniaxial stress, whichspoils the global tetragonality of the LTT phase. Althoughit still emerges at low temperatures, our experiments unveila remarkable response of the LTT structure in LNSCO-125to the application of uniaxial stress.In principle, uniaxial stress could result in the transitionof the macroscopic crystal into a mixed LTO/LTT phaseor a decrease in the LTT octahedral tilt angle, as hypoth-esized from measurements of the magnetic properties ofLBCO-115 [19]; neither effect is resolved in our experi-ments. First note that the intensity of the (001) Bragg peak,whose cross-section is an increasing function of the octahe-dral tilt angle, appears unchanged by σ at 10 K. This indi-cates that, within the LTT phase, the structure is unaffectedby stress. Second, the LTO-LTT transition remains sharpwith non-zero σ , which suggests that the stressed sampleenters the LTT phase in a rather uniform fashion. Whilethe uniformity of the strain field on the sample may varybetween different uniaxial strain setups, our experimentsdo not provide evidence of a mixed phase or reduced octa- Temperature (K) P e a k I n t e n s i t y ( a . u . ) q || (r.l.u.)
15 K 0.1 0.2 0.3 q || (r.l.u.)
23 K 0.1 0.2 0.3 q || (r.l.u.)
35 K01020304050 I n t e n s i t y ( a . u . ) (a)(b) σ = 0 σ > 0 a b T LTT T LTT
FIG. 3. (a) Temperature dependence of the CO peaks in the stressand control samples. The solid lines serve as guides to the eye.The dashed lines correspond to the LTT transition temperaturesdetermined from Fig. 2(b). The inset shows a diagram of thestress sample, where we label a (blue) and b (orange) as the direc-tions parallel to and perpendicular to the direction applied stressrespectively. Measurements of the stress sample along the a di-rection were performed at two different synchrotrons: measure-ments from the Canadian Light Source are triangles and mea-surements from BESSY-II are circles [23]. (b) Comparison ofstress sample RXS scans along the a and b directions near theLTT transition. The gray dashed line is a polynomial fit of thehigh-temperature background curve measured at 150 K. The on-set of the charge stripes along the direction of applied stress pre-cedes that of the perpendicular direction by approximately K. hedral tilt angle.Within the same experiment we can also track the tem-perature dependence of the charge order in the stressedLNSCO-125 crystal, which is summarized in Fig. 3(a). Aconsequence of uniaxial stress is the reduction of the onsettemperature of charge stripes by K, which is larger thanthe change of K observed for T LTT . If the only effectof uniaxial stress was the suppression of T LTT , one might have expected the same change to occur for the onset ofcharge stripes. However, the additional shift of K sug-gests that one should also consider interactions with addi-tional intertwined orders, such as superconductivity. Uni-axial stress on the order of . GPa has been shown toincrease T c by K in LNSCO-120 and by K in LBCO-115 [16, 19], showing that superconductivity is enhanced intandem with the suppression of the LTT phase. Addition-ally, cuprates that lack a similar structural transition, suchas Bi Sr CaCu O δ and YBa Cu O y , exhibit compe-tition between superconductivity and CO [9, 29, 30]. To-gether, the suppression of the LTT phase and the enhance-ment of superconductivity would account for the largersuppression of the onset of stripes, relative to the suppres-sion of T LTT .In addition to the effects on stripe order due to its inter-twining with the LTT phase and superconductivity, uniax-ial stress may also directly influence the pinning of stripesalong a and b . For example, given the C symmetry ofstripe order, one may expect that a finite σ in the absence ofan LTT phase would cause the onset temperatures of stripesalong a and b to split. Indeed, this split is resolved byour detailed temperature dependent RXS measurements,Fig. 3(a). This is seen more clearly by directly comparingthe RXS data along the two directions, Figure 3(b), whichshows that at K the peak along a (parallel to the appliedstress) has already entered the charge stripe phase, whilethe peak along b is still very similar to the peak in the high-temperature phase – compare to the K data. Eventually,at K the two signals approach the same saturation value,which may indicate that the LTT structure has suppressedthe effects of σ ≈ . GPa at this temperature. Neverthe-less, our observations show that uniaxial stress can be usedto pin the direction of stripes in the CuO plane.While our measurements show a delicate balance be-tween charge stripes, superconductivity and structural dis-tortions, a direct effect of uniaxial stress on the high-temperature CO correlations is not clearly observed in ourdata. Just above the onset of charge stripe order, the intensi-ties of the RXS peaks at q CO are indistinguishable betweenthe stressed and control samples. We also do not resolve aclear difference between the CO correlations along a and b in the stressed sample – for example see the K data inFig. 3(b). Figure 3(a) suggests that the onset of CO corre-lations at high-temperatures may be impacted by the appli-cation of stress along a . However, there are several com-plications that prevent us from reaching that conclusionwith any reasonable confidence. First, as mentioned above,the CO correlations evolve very slowly with temperature,which makes the assignment of an onset temperature diffi-cult. Second, the stress produced by our apparatus is tem-perature dependent and we estimate a 3 to 5 fold decreasein the applied stress from K to
K. Third, the com-parison of small RXS peaks between the stress and controlsamples can be influenced by variations in the fluorescencebackground, which is sensitive to sample surface condi-tions. The effects of uniaxial stress to the high-temperaturecorrelations will likely require experiments that tune thestress at a fixed temperature. Altogether, we cannot con-clude the observation of any direct coupling between uni-axial stress and high-temperature CO correlations.Our experiments demonstrate the complex relation-ship between uniaxial stress, charge stripes and the low-temperature tetragonal structure in LNSCO-125. Increas-ing σ from zero to . GPa causes a simultaneous reductionin the onset temperatures of both the LTT phase and chargestripes, as well as a temperature splitting in the formationof charge stripes along the a and b directions. Addition-ally, the effects of superconductivity need to be includedto describe our observations, with the competition betweensuperconductivity and charge order together with the en-hancement of T c under uniaxial stress serving as a naturalexplanation for the additional suppression of the onset ofstripe order with respect to T LTT . Furthermore, we find thatlarger stress may be necessary to cause significant changesto the high-temperature CO correlations. Nevertheless, therelatively small amount of stress necessary to tune the elec-tronic properties of the La-based cuprates near / hole-doping is quite remarkable. For example, strain on the or-der of . % is necessary to modify the properties of chargeorder in YBa Cu O y [15] or to shift the superconduct-ing transition by K in Sr RuO [31, 32]. While achieving . % strain may be quite challenging and difficult to re-produce, . % or even smaller is clearly sufficient to al-ter the electronic properties of LNSCO-125, which opensnew opportunities for switchable devices and precision de-tectors at the current frontier of technology.The research described in this paper was carried out atUE-46-PGM1 and UE-56/2-PGM2 beamlines of BESSYII, a member of the Helmholtz Association (HGF), andat the Canadian Light Source, a national research facil-ity of the University of Saskatchewan, which is supportedby the Canada Foundation for Innovation (CFI), the Natu-ral Sciences and Engineering Research Council (NSERC),the National Research Council (NRC), the Canadian In-stitutes of Health Research (CIHR), the Government ofSaskatchewan, and the University of Saskatchewan. Thismaterial is based upon work supported by the National Sci-ence Foundation under Grant No. 1845994 and 2034345.Part of the research leading to these results has been sup-ported by the project CALIPSO and under the Grant Agree-ment 730872 from the EU Framework Programme for Re-search and Innovation HORIZON 2020. S.B.-C. acknowl-edges the MINECO of Spain for financial support throughthe project PGC2018-101334-A-C22. A. R. acknowledgessupport from the University of California President’s Post-doctoral Fellowship Program. This work was supportedby the Alfred P. Sloan Fellowship (E.H.d.S.N. and A.F.).The research in Dresden is supported by the DeutscheForschungsgemeinschaft through Grant No. 320571839.This research was undertaken thanks in part to fundingfrom the Max Planck-UBC-UTokyo Centre for Quantum Materials and the Canada First Research Excellence Fund,Quantum Materials and Future Technologies Program. ∗ These authors contributed equally to this work. † [email protected] ‡ [email protected] § [email protected][1] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, andJ. Zaanen, Nature , 179 (2015).[2] E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Rev. Mod.Phys. , 457 (2015).[3] E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein,and A. P. Mackenzie, Annual Review of Condensed MatterPhysics , 153 (2010).[4] J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Nakamura,and S. Uchida, Nature , 561 (1995).[5] J. Fink, E. Schierle, E. Weschke, J. Geck, D. Hawthorn, V. Soltwisch, H. Wadati, H.-H. Wu, H. A. D¨urr, N. Wizent,B. 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