Probing Phase Separation and Local Lattice Distortions in Cuprates by Raman Spectroscopy

Review Probing Phase Separation and Local Lattice Distortions in Cuprates by Raman Spectroscopy

Efthymios Liarokapis

Department of Physics, National Technical University of Athens, 15780 Athens, Greece; [email protected]; Tel.: +30-210-7722930 Received: 25 September 2019; Accepted: 27 October 2019; Published: 1 November 2019

Abstract: It is generally accepted that high temperature superconductors emerge when extra carriers are introduced in the parent state, which looks like a Mott insulator. Competition of the order parameters drives the system into a poorly defined pseudogap state before acquiring the normal Fermi liquid behavior with further doping. Within the low doping level, the system has the tendency for mesoscopic phase separation, which seems to be a general characteristic in all high Tc compounds, but also in the materials of colossal magnetoresistance or the relaxor ferroelectrics. In all these systems, metastable phases can be created by tuning physical variables, such as doping or pressure, and the competing order parameters can drive the compound to various states. Structural instabilities are expected at critical points and Raman spectroscopy is ideal for detecting them, since it is a very sensitive technique for detecting small lattice modifications and instabilities. In this article, phase separation and lattice distortions are examined on the most characteristic family of high temperature superconductors, the cuprates. The effect of doping or atomic substitutions on cuprates is examined concerning the induced phase separation and hydrostatic pressure for activating small local lattice distortions at the edge of lattice instability.

Keywords: phase separation; lattice distortions; high temperature superconductors; cuprates; Raman spectroscopy

1. Introduction Among the most fascinating discoveries over the years is the identification of mesoscopic phase separation (MePhS) in a number of materials, ferroelectrics [1,2], magnetoresistive manganites [3–11], nikelates [12,13], A15 alloys [14], and cuprates [15–52] in which case a spectacular diverse range of exotic magnetic, electronic, and crystal structures can coexist at different locations in the same crystal. In an apparently homogeneous material, it turns out to be surprisingly easy to achieve phase coexistence using a wide range of parameters by playing with the chemical composition or microstructure, increasing an electric or magnetic field, tuning the elastic strain field [53], or by photoinduced phase separation [54,55]. The coexisting phases may form robust magnetic, electronic and crystallographic textures of “mesoscopic” length scales, that is, over tens or hundreds of nanometers. By controlling an array of textured phases, analogous to those in liquid crystals, it is possible to modify locally the electronic structure and properties without atomic-scale fabrication. In manganites for example, a simple domain wall in the ferromagnetic metallic phase could spontaneously develop an insulating barrier of the charge order phase creating the ultimate spin-tunnel junction. Alternatively, in the cuprates, the superconducting domains are separated from an insulating matrix where the thread and the matrix are made of identical material. With these and numerous other ideas for potential applications, one can enter a realm of inorganic material science that is reminiscent of the complex self-organized structures seen in soft condensed matter physics or polymer science.

Condens. Matter 2019, 4, 87; doi:10.3390/condmat4040087 www.mdpi.com/journal/condensedmatter Condens. Matter 2019, 4, 87 2 of 23

Structural instability appears in several systems of condensed matter and can play a key role in the characteristic properties of several other compounds (e.g., ferroelectrics), manganites, and high temperature superconductors (HTSC). The role played in the case of HTSC was revealed soon after their discovery [15] by J.C. Philips who correctly pointed out the structural instabilities that accompany either intermetallic or oxide superconductors [56]. For the old superconductors, it had already been found that, in A-15 compounds, structural instability and superconductivity are related [14]. The structural instability actually creates a softening of the lattice and is reflected in several physical properties including the associated phonon modes. In superconductors, the underlying idea of MePhS is that, in the insulator-superconductor transition, the holes introduced in the insulator matrix by the dopant are rejected, forming mesoscopic clusters of the superconducting phase (physical phase separation). The magnetic fluctuations are suppressed in the small dimensions of the randomly oriented clusters and superconductivity is stabilized. The whole process is self-organized, but the metastable phases of the system can be reached by tuning physical variables such as pressure or charge density. Although the mechanism that produces high transition temperature is still unknown, there is general agreement that understanding the normal state where several degrees of freedom (spin, charge, orbital, and lattice) compete, could clarify the situation. It is now well established that, between the Mott insulator and heavy doping charge, ordered states (stripes) are created [12,18] from the competition of the kinetic energy and Coulomb repulsion, but the exact connection of the stripes with superconductivity is not clear yet. It is, therefore, of interest to investigate the responses of the normal state to variations of external factors (temperature or pressure) or internal parameters (doping). Interest in the role of lattice in the pairing mechanism of HTSC has increased since the discovery of superconductivity with high transition temperature (Tc)[15] in MgB2 [57–63], the alkali metal doped C60 [64–66], and, more recently, by the very high transition temperature achieved under hydrostatic pressure in sulfur hydrides [67–70]. In the case of cuprates, several experiments (e.g., [71–79]) suggest that phonons play a substantial role in the high Tc mechanism. Phase separation has been observed using several methods in both pnictides and chalcogenides iron-based superconductors [80–86] and at the insulator to metal transition in VO2 [87–92]. It has been pointed out that this is generic feature in the proximity of topological electronic Lifshitz transitions [40,51,82] where lattice and electronic effects are both essential and key terms of the physics of these complex quantum phenomena. Therefore, the study of lattice anomalies, such as soft modes or structural instabilities, is of central interest in the investigation of the HTSC. Raman spectroscopy is one of the tools used for investigating the characteristics of the new compounds and for providing important information on the carriers through their coupling with the phonons [93], the appearance of new phases [94,95], the anharmonic coupling of the phonons [96–98], the existence and the size of a gap [99], its symmetry [100], and on crystal field excitations [101], etc. In this review, cumulative results from our systematic micro-Raman studies on two families of the cuprates (yttrium and lanthanum families) are presented. Our studies on other high Tc compounds, such as the diborides [60,62,63,102] and the pnictides [103–105] not presented here, have shown similar results with the cuprates. The role of doping, atomic substitutions, and hydrostatic pressure are examined in detail for creating phase separated domains and structural instabilities. It should be noted that our spontaneous Raman studies cannot discriminate between static and dynamic phase separated effects, and it detects them as statistically distributed in space domains.

2. The Yttrium Family Cuprates

Detailed analysis of the lattice vibration symmetry of YBa2Cu3Ox can be found in numerous publications (see e.g., [106]). The compounds have an approximate tetragonal symmetry with a small orthorhombic distortion in the superconducting phase [107]. Because of the center of inversion, the zone-center optical phonons are either Raman or IR active. The atoms of the chains (Och, Cuch) and Y have full point group site symmetry being IR-active (B2u,3u and B1u), Ba, and apical oxygen (Oap). The CuO2 plane atoms (Cupl,Opl) have lower symmetry (C2) and they participate in three phonons of Condens. Matter 2019, 4, 87 3 of 23 Condens. Matter 2019, 4, 87 3 of 23 three phonons of even symmetry Ag, B2g,3g and three phonons of odd symmetry B1u, B2u,3u (along the c, a, and b axis, correspondingly). The main difference between the orthorhombic and the tetragonal even symmetry Ag,B2g,3g and three phonons of odd symmetry B1u,B2u,3u (along the c, a, and b axis, phase are the out-of-phase vibrations of Opl atoms, which in the former case have the Ag symmetry correspondingly). The main diﬀerence between the orthorhombic and the tetragonal phase are the and in the latter case, B1g symmetry, and can be easily identified from the distinct polarization out-of-phase vibrations of O atoms, which in the former case have the A symmetry and in the latter selection rules [106]. Characteristicpl Raman spectra are shown in Figure 1a,bg for the y(cc)y and y(xx)y case, B1g symmetry, and can be easily identiﬁed from the distinct polarization selection rules [106]. scattering geometries and the strong Raman active phonons of Ag symmetry along the c-axis for Characteristic Raman spectra are shown in Figure1a,b for the y(cc)y and y(xx)y scattering geometries YBa2Cu3O7−δ are located at ≈116 cm−1 (Ba), ≈150 cm−1 (Cupl), ≈435 cm−1 (in-phase vibrations of Opl and the strong Raman−1 active phonons of Ag symmetry along the c-axis for YBa2Cu3O7 δ are located at atoms), and1 ≈502 cm (Oap).1 1 − 1 116 cm (Ba), 150 cm (Cu ), 435 cm (in-phase vibrations of O atoms), and 502 cm (Oap). ≈ − ≈ − pl ≈ − pl ≈ −

Figure 1. Typical spectra of YBa2Cu3Ox at room temperature using the 514.5 nm laser line in the y(cc)y Figure 1. Typical spectra of YBa2Cu3Ox at room temperature using the 514.5 nm laser line in the (a) and y(xx)y (b) polarization. y(cc)y (a) and y(xx)y (b) polarization. 2.1. Phase Separation from Oxygen Doping 2.1. Phase Separation from Oxygen Doping The Ag symmetry strong modes due to the Ba and Cupl atoms vary considerably in intensity withThe oxygen Ag symmetry concentration strong in modes the y(xx)y due to scattering the Ba and configuration Cupl atoms (Figure vary considerably1b) and Ba phonon in intensity has a withstrong oxygen asymmetric concentration shape in that the gradually y(xx)y scattering disappears configuration in the tetragonal (Figurephase 1b) and (x Ba6.35). phonon The has Cu a ≤ pl strongphonon asymmetric shows the oppositeshape that behavior, gradually being disappears very weak in in the the fullytetragonal oxygenized phase compounds(x ≤ 6.35). (xThe 7)Cu andpl ≈ phonongaining shows intensity the byopposite the orthorhombic behavior, being to tetragonal very weak (O-T) in the phase fully transition oxygenized (Figure compounds1). In the (x y(cc)y ≈ 7) andscattering gaining geometry, intensity theseby the phonons orthorhombic appear into all tetr oxygenagonal concentrations (O-T) phase transition without considerable (Figure 1). intensityIn the y(cc)yvariations scattering (Figure geometry,1a). In this these scattering phonons geometry, appear in the all Baoxygen phonon concentrations is symmetric, without which considerable indicates that intensitythe asymmetry variations observed (Figure in 1a). the In other this geometry scattering is geometry, due to its couplingthe Ba phonon with the is carriers.symmetric, Its intensitywhich indicatesis modified that bythe the asymmetry amount ofobserved oxygen in which the other reflects geometry the carrier is due redistribution to its coupling with with doping the carriers. between Itsthe intensity BaO and is themodified CuO2 planes. by the Atamount low doping, of oxygen the carrierswhich reflects are distributed the carrier outside redistribution the CuO2 planeswith dopingscreening between the Ba the phonon, BaO and which the CuO appears2 planes. with At very low low doping, intensity the (orcarriers it is completely are distributed absent) outside in the thexx CuO scattering2 planes polarization. screening the Exactly Ba phonon, the opposite which appears happens with to the very Cu lowpl phonon, intensity which (or it isis strongcompletely at low absent)carrier in concentrations the xx scattering and polarization. disappears with Exactly increasing the opposite doping. happens As carriers to the are Cu transferredpl phonon, to which the CuO is 2 strongplanes at they low induce carrier strong concentrations screening of theand Cu disappearspl phonon, whilewith theincreasing Ba mode doping. gains intensity As carriers (Figure are1b). transferredOxygen to the nonstoichiometry CuO2 planes they is theinduce crucial strong parameter screening controlling of the Cu suchpl phonon, a diverse while behavior the Ba mode for the gainscompound intensity as (Figure one follows 1b). the transition from YBa2Cu3O6 to YBa2Cu3O7. It is, therefore, natural to concentrateOxygen nonstoichiometry on the oxygen Raman is the activecrucial modes. parameter The controlling dependence such of the a diverse Oap mode behavior energy for on the the compoundoxygen concentration as one follows is nonlinear the transition [107]. from Roughly YBa2 described,Cu3O6 to YBa the2Cu energy3O7. It remains is, therefore, almost natural constant to in concentratethe range ofon 6.75 the< oxygenx < 7.00, Raman is reduced active in modes. the range The of dependence 6.15 < x < 6.75, of the and, O finally,ap mode for energy x < 6.15, on therethe oxygenis a sudden concentration drop in frequencyis nonlinear (Figure [107].2 a).Roughly The mode described, linewidth the exhibitsenergy remains the following almost three constant minima: in thefor range maximum of 6.75 x< values,x < 7.00, for is reduced x 6.47, in and the in range the rangeof 6.15 of < x < 6.75,6.12. and, Contrary finally, to for early x < 6.15, Raman there spectra, is a ≈ suddenwhich drop have in shown frequency a linear (Figure dependence 2a). The of mode its energy linewidth with theexhibits amount the offollowing oxygen three [108], minima: the results for in maximumFigure2 show x values, that for it remains x ≈ 6.47, practically and in the constantrange of x in < the6.12. range Contrary of 6.8 to< earlyx < 7.0Raman and, spectra, then, decreases which

Condens. Matter 2019, 4, 87 4 of 23

Condens.have shown Matter 2019 a ,linear4, 87 dependence of its energy with the amount of oxygen [108], the results 4in of 23 Figure 2 show that it remains practically constant in the range of 6.8 < x < 7.0 and, then, decreases with decreasing x (Figure 2a). More pronounced changes appear in the width of this phonon with a withmaximum decreasing close x to (Figure x = 6.72 anda). Morethen a pronounced decrease toward changess the appeartwo ends in (Figure the width 2a), of which this phononis a result with of a maximumthe appearance close toof xnew= 6.7 phases, and thenas discussed a decrease below. towards the two ends (Figure2a), which is a result of the appearance of new phases, as discussed below.

FigureFigure 2. 2.Apex Apex ((aa)) andand in-phasein-phase ( b)) phonon energy energy and and width width dependence dependence on on amount amount of oxygen of oxygen

contentcontent for for YBa YBa2Cu2Cu3O3Oxx.. CorrespondingCorresponding datadata forfor YY11−yyCaCayBayBa2Cu2Cu3O37O−δ 7areδ arepresented presented with with % amount % amount of of − − Ca.Ca. Error Error bars bars indicate indicate statisticalstatistical distributiondistribution of of data data from from various various microcrystallites. microcrystallites.

InIn the the YBa YBa2Cu2Cu33OOxx (Y123x) compounds, compounds, Cu Cu atoms atoms also also exist exist outside outside the the CuO CuO2 planes,2 planes, forming forming linearlinear chains chains along along the the b-axis.b-axis. As the rest rest of of the the HT HTSCSC does does not not have have such such chains, chains, it is it believed is believed that that theythey do do not not play play a a crucial crucial rolerole inin superconductivity,superconductivity, although although they they influence influence the the properties properties of the of the Y123xY123x system. system. In In thethe fullyfully occupiedoccupied chain (Y1237), (Y1237), all all oxygen oxygen atoms atoms are, are, in inprinciple, principle, located located along along thethe b-axis, b-axis, and, and, asas thethe numbernumber of oxygen atoms atoms is is decreased, decreased, there there is isalways always a tendency a tendency to form to form thermodynamicallythermodynamically stable stable structures structures [109 [109].]. Two Two such such phases phases with with Tc Tatc 60at 60 K (ortho-II,K (ortho-II, for for x x6.5), ≈ 6.5), which ≈ correspondwhich correspond to alternating to alternating full and empty full and chains, empty and chains, at 92 K (ortho-I,and at 92 fully K (ortho-I, oxygenated fully samples) oxygenated are well establishedsamples) are appearing well established as characteristic appearing plateaus as characte in theristic phase plateaus diagram in the [110 phase]. For diagram lower concentrations [110]. For (xlower6.35), concentrations a transition takes (x place ≤ to6.35), anantiferromagnetic, a transition takes non-superconducting place to an phaseantiferromagnetic, [107]. The exact ≤ stoichiometries,non-superconducting where phase the phases [107]. appear, The exact depend stoich oniometries, the preparation where the conditions phases appear, [107]. depend This is dueon to thethe existence preparation of many conditions other intermediate[107]. This is phases,due to the which existence correspond of many to diotherfferent intermediate combinations phases, of full andwhich empty correspond chains that to different are examined combinations below. Suchof full ideal and orderedempty chains microstructures that are examined can only below. be stabilized Such ideal ordered microstructures can only be stabilized after a careful annealing of the materials; after a careful annealing of the materials; otherwise the disorder will make the compound appear otherwise the disorder will make the compound appear macroscopically tetragonal [111]. The macroscopically tetragonal [111]. The changes induced in the chains from the removal of oxygen, changes induced in the chains from the removal of oxygen, have a direct effect on the position of the have a direct effect on the position of the apical oxygen, which moves away from the superconducting apical oxygen, which moves away from the superconducting CuO2 planes [110]. In terms of the CuO planes [110]. In terms of the valences, this is an indication of redistribution of charges between valences,2 this is an indication of redistribution of charges between the chains and the planes as theoxygen chains is and added the in planes the system as oxygen [100]. is addedAnother in way the systemto explain [100 the]. Anotherphase transformation way to explain from the the phase transformationantiferomagnetic from to the the antiferomagnetic superconducting to thestate superconducting was proposed state within was proposedthe phase within separation the phase separationmodel [112]. model As oxygen [112]. Asatoms oxygen are added, atoms and are holes added, are and transferred holes are to transferred the CuO2 planes, to the conducting CuO2 planes, conductingmicrodomains microdomains are formed, are which, formed, when which, there are when enough, there are connected enough, are and connected the system and becomes the system a becomessuperconductor. a superconductor. A further Aincrease further of increase holes in of the holes planes in the induces planes inducesanother anotherphase transition phase transition with withhigher higher Tc (92 Tc (92K). K).The The appearance appearance of these of these phases phases is connected is connected with with the thedistribution distribution of the of theoxygen oxygen atomsatoms in in the the chains chains along along thethe b-axisb-axis forming two- two- or or three-dimensional three-dimensional superlattices superlattices [109]. [109 Some]. Some of of thesethese structures structures have have been been observed observed (tetragonal, (tetragonal, ortho-II,ortho-II, andand ortho-IIIortho-III phases) and they they correspond correspond to x 6, x 6.5, and x 6.67 [109–111]. The effect of the removal of the chain oxygen on the Raman spectra ≈ ≈ ≈ is shown in Figure1. As discussed above, on the one hand, the relative intensity of the low frequency modes (Ba and Cupl) depends strongly on the amount of oxygen (mainly in the y(xx)y scattering Condens. Matter 2019, 4, 87 5 of 23 to x ≈ 6, x ≈ 6.5, and x ≈ 6.67 [109–111]. The effect of the removal of the chain oxygen on the Raman spectra is shown in Figure 1. As discussed above, on the one hand, the relative intensity of the low frequencyCondens. Matter modes2019, 4 (Ba, 87 and Cupl) depends strongly on the amount of oxygen (mainly in the y(xx)y5 of 23 scattering geometry), but their energy is not modified appreciably. On the other hand, the oxygen content affects very strongly both the energy and width of the apical oxygen and the in-phase geometry), but their energy is not modified appreciably. On the other hand, the oxygen content affects phonons (Figure 2). This is due to the appearance of new phases, as resonance examination of these very strongly both the energy and width of the apical oxygen and the in-phase phonons (Figure2). oxygen modes in the excitation energy range of 1.6–2.9 eV, for the tetragonal and orthorhombic This is due to the appearance of new phases, as resonance examination of these oxygen modes in Y123x system, has revealed [113]. Concerning the Ag symmetry apical oxygen phonon, it has been the excitation energy range of 1.6–2.9 eV, for the tetragonal and orthorhombic Y123x system, has found to show a strong resonance in the IR excitation for the tetragonal case, with additional modes revealed [113]. Concerning the A symmetry apical oxygen phonon, it has been found to show a strong appearing, which are absent wheng the excitation is in the visible region of spectrum [114]. Work resonance in the IR excitation for the tetragonal case, with additional modes appearing, which are carried out by Iliev et al. [94] has shown a very characteristic variation of the apical Ag phonon when absent when the excitation is in the visible region of spectrum [114]. Work carried out by Iliev et al. [94] the excitation wavelength varied from blue (482.5 nm) to red (647.1 nm) for the YBa2Cu3O6.4 has shown a very characteristic variation of the apical A phonon when the excitation wavelength compound. Our investigations confirmed this by showingg that, in the fully oxygenated ortho-I varied from blue (482.5 nm) to red (647.1 nm) for the YBa2Cu3O6.4 compound. Our investigations phase, the Oap mode does not shift with varying excitation wavelength (Figure 3a) and it is modified confirmed this by showing that, in the fully oxygenated ortho-I phase, the O mode does not shift considerably for the underdoped compound (Figure 3b) due to the differentap cross sections of the with varying excitation wavelength (Figure3a) and it is modified considerably for the underdoped coexisting phases, with the lower Tc phases being in resonance with lower energy compound (Figure3b) due to the di fferent cross sections of the coexisting phases, with the lower T excitations [113,114]. c phases being in resonance with lower energy excitations [113,114].

Figure 3. Apex and in-phase oxygen modes excited with various laser lines for optimal doped (a) and Figure 3. Apex and in-phase oxygen modes excited with various laser lines for optimal doped (a) and underdoped (b) compounds. underdoped (b) compounds. Other measurements also suggest the coexistence of phases [115]. Since the apical oxygen mode Other measurements also suggest the coexistence of phases [115]. Since the apical oxygen mode is very sensitive to the chain ordering [93,116] and its width shows minimum values around x 6, is very sensitive to the chain ordering [93,116] and its width shows minimum values around x ≈ 6, x 6.47, and x 7 (Figure1a), one could assume that at least three phases are present. But the x ≈ 6.47, and x ≈ 7 (Figure 1a), one could assume that at least three phases are present. But the resonance measurements have revealed the existence of four peaks located at 502 cm 1, 493 cm 1, resonance measurements have revealed the existence of four peaks located at 502 cm−−1, 493 cm−−1, 486 cm 1, and 476 cm 1 that correspond to four coexisting phases. The higher and the lower energy 486 cm−1, and 476 cm−−1 that correspond to four coexisting phases. The higher and the lower energy peaks certainly correspond to ortho-I and the tetragonal x 6 phases. From our measurements and peaks certainly correspond to ortho-I and the tetragonal x ≈≈ 6 phases. From our measurements and other measurements on x 6.5, it is clear beyond any doubt that the 493 cm 1 is a superstructure other measurements on x ≈≈ 6.5, it is clear beyond any doubt that the 493 cm−1 is −a superstructure peak peak due to the ortho-II phase (doubling of unit cell with half occupation of the chains). In order to due to the ortho-II phase (doubling of unit cell with half occupation of the chains). In order to delineate the origin of the 486 cm 1 peak, we consistently carried out a deconvolution of all Raman delineate the origin of the 486 cm−−1 peak, we consistently carried out a deconvolution of all Raman spectra from 30 samples of varying oxygen concentrations with 16O and 23 samples with 18O, and spectra from 30 samples of varying oxygen concentrations with 16O and 23 samples with 18O, and the the results are presented in Figure4 (similar results exist for 18O in [98]). It appears that the 486 cm 1 results are presented in Figure 4 (similar results exist for 18O in [98]). It appears that the 486 cm−1 peak− peak corresponds to a phase in the tetragonal doping region. From the similarity in energy, the corresponds to a phase in the tetragonal doping region. From the similarity in energy, the superstructure (S) peak at 486 cm 1 could correspond to the breathing (0.5, 0.5, 0) mode [117], but then superstructure (S) peak at 486 cm− −1 could correspond to the breathing (0.5, 0.5, 0) mode [117], but it should peak around x 6.25, contrary to the deconvolution results (Figure4). A better guess is the ≈ 2 √2ao 2 √2ao c diagonal superlattice phase based on the amount of oxygen [118–120]. In order to × × extract more information from the Raman spectra, as shown in Figure5, we plotted a histogram of Condens. Matter 2019, 4, 87 6 of 23 then it should peak around x ≈ 6.25, contrary to the deconvolution results (Figure 4). A better guess is the 22ao × 22ao × c diagonal superlattice phase based on the amount of oxygen [118–120]. In Condens. Matter 2019, 4, 87 6 of 23 order to extract more information from the Raman spectra, as shown in Figure 5, we plotted a histogram of the peak positions for the apex and in-phase modes. A preference appears for certain thewavenumbers, peak positions which for correspond the apex and (from in-phase Figure modes. 2) to the A preferencephases indicated appears in forFigure certain 5. The wavenumbers, ortho-I and whichortho-II correspond phases (fromare clear, Figure 2while) to the phasesthe superstructure indicated in Figure S peak5. The seems ortho-I andto ortho-IIcorrespond phases to arex ≈ clear,1/8 ( while22a theo × superstructure22ao × c) phase. S peak seemsFurthermore, to correspond there are to x indications1/8 (2 √2a oof 2other√2a ophasesc) phase. for ≈ × × Furthermore,wavenumbers there pointing are indications to an ortho-III of other (x = phases6.67) or for even wavenumbers higher phases pointing [121]. In to a an systematic ortho-III (ximaging= 6.67) orof eventhe higherspatial phasesordering [121 of]. Inthe a systematicoxygen chains imaging in ofYBa the2Cu spatial3O6+y, orderingby micro of theX-ray oxygen diffraction chains inmeasurements, YBa2Cu3O6+ ythe, by phase micro separated X-ray diff regionsraction measurements,have been detected the phase[122–124]. separated For y = regions 0.33, the have ortho-II been detectedphase was [122 clearly–124]. detected For y = 0.33,embedded the ortho-II in more phase disord wasered clearly regions detected [124]. embedded For y = 0.67, in more nano-puddles disordered regionscorresponding [124]. For to y y == 0.50.67, + 1/8 nano-puddles were found correspondingcorresponding to to ythe= 0.5 ortho-VIII+ 1/8 were puddles found of corresponding alternating five to thefilled ortho-VIII and three puddles empty oxygen of alternating wires every five filled eight and rows three [122]. empty Other oxygen networks wires were every created eight by rows thermal [122]. Othermanipulation networks [123]. were Unfortunately, created by thermal no Raman manipulation data exist [ 123on ].the Unfortunately, same compounds no Raman for comparison, data exist onbut theour same studies compounds agree with for these comparison, results and but at our least studies the one-eighth agree with oxygen these resultsordering and seems at least to be the a one-eighthpreferential oxygen oxygen ordering ordering seems for to both be a preferentialthe YBa2Cu oxygen3O6 and ordering the YBa for both2Cu3O the6.5 YBastable2Cu 3phases.O6 and theFurthermore, YBa2Cu3O the6.5 stableregions phases. assigned Furthermore, to OIII phase the in regions Figure assigned 5 possibly to OIIIconsist phase of several in Figure other5 possibly phases consistsimilar ofto severalthe ones other discovered phases similarby X-ray to theimaging ones discovered[122,123]. This by X-raycan explain imaging the [122 less,123 pronounced]. This can explainnature of the the less OIII pronounced peaks in Figure nature of5 for the both OIII peaksthe apex in Figure and the5 for in-phase both the modes. apex and Finally, the in-phase there is modes.another Finally,peak in there the is anotheroverdoped peak region, in the overdopedas strongly region, indicated as strongly from indicatedthe in-phase from themode in-phase and modediscussed and below. discussed below.

FigureFigure 4.4. Relative amounts of coexisting phasesphases inin YBaYBa22Cu3OOxx compoundcompound at at different diﬀerent doping doping levels. levels.

Condens. Matter 2019, 4, 87 7 of 23 Condens. Matter 2019, 4, 87 7 of 23

FigureFigure 5.5. HistogramsHistograms ofof apexapex andand in-phasein-phase peakpeak positionspositions ofof YBaYBa22CuCu33Ox showingshowing various phases phases..

AsAs seen in Figure Figure 22b,b, the in-phase in-phase O Oplpl modemode energy energy and and linewidth linewidth values values remain remain constant constant in the in therange range of 6.00 of 6.00 < x<

2.2. PhaseThe BSeparation1g mode from is sensitiveAtomic Substitutions to atomic substitutions for yttrium and its broadening was used to measure the superconducting gap by tuning the phonon energy across the gap The B1g mode is sensitive to atomic substitutions for yttrium and its broadening was used to energymeasure for the carefully superconducting chosen raregap by earth tuning substitutions the phonon [131 energy]. By across studying the gap a seriesenergy of for rare carefully earth substitutions, La0.5R0.5Ba2Cu3O7 δ [128], R0.5Pr0.5Ba2Cu3O7 δ [129], Y1 xLaxBa2Cu3O7 δ [132], and chosen rare earth substitutions− [131]. By studying a− series of− rare earth substitutions,− Y1 xPrxBa2Cu3O7 δ [133], it has also been found that the B1g mode splits into two or three bands, La−0.5R0.5Ba2Cu3O7−δ− [128], R0.5Pr0.5Ba2Cu3O7−δ [129], Y1−xLaxBa2Cu3O7−δ [132], and depending on the difference of the atomic radii of substituting species and this is related to the Y1−xPrxBa2Cu3O7−δ [133], it has also been found that the B1g mode splits into two or three bands, superconductingdepending on the property. difference On theof the one atomic hand, inradii all theseof substituting cases, the XRD species studies and could this is not related discriminate to the moresuperconducting than one component, property. although On the modifications one hand, in theall interatomicthese cases, distances the XRD at critical studies di ffcoulderences not of thediscriminate ion size havemore beenthan foundone component, [128]. This although indicates modifications that any phase in separationthe interatomic in those distances systems at critical differences of the ion size have been found [128]. This indicates that any phase separation in those systems occurred at distances smaller than the coherence length of XRD. On the other hand,

Condens. Matter 2019, 4, 87 8 of 23

Condens. Matter 2019, 4, 87 8 of 23 occurred at distances smaller than the coherence length of XRD. On the other hand, Raman measurementsRaman measurements with smaller with smaller coherent coherent length length could could clearly clearly detect detect the the multiphase multiphase structure structure ofof the compoundsthe compounds [128 ,[128,129,132,133].129,132,133]. Characteristic Characteristic spectra spectra for for the the evolution evolution of of the the strong strong modes modes with with rare rare earth substitution for Y1−xLaxBa2Cu3O7−δ are shown in Figure 6 [132]. Similar Raman spectra have earth substitution for Y1 xLaxBa2Cu3O7 δ are shown in Figure6[ 132]. Similar Raman spectra have been found for the other −substitutions [128,129,133].− been found for the other substitutions [128,129,133].

Figure 6. Raman spectra from selected La concentrations for polarizations along the c-axis (a) or the Figure 6. Raman spectra from selected La concentrations for polarizations along the c-axis (a) or the ab-plane (b). ab-plane (b). Concerning the other modes, the apex oxygen mode in Figure6 shifts continuously depending on Concerning the other modes, the apex oxygen mode in Figure 6 shifts continuously depending the average ionic radius of the substituting rare earth elements, in agreement with the results from on the average ionic radius of the substituting rare earth elements, in agreement with the results the system RBa2Cu3O7 δ [134]. The in-phase mode is more or less insensitive to rare earth (Figure6), from the system RBa2−Cu3O7−δ [134]. The in-phase mode is more or less insensitive to rare earth although there might be variations, as much as 7 to 8 cm 1, if the oxygen content varies slightly below (Figure 6), although there might be variations, as much −as 7 to 8 cm−1, if the oxygen content varies or above the optimal doping value (Figure6). In addition, the Cu phonon is not modiﬁed by the slightly below or above the optimal doping value (Figure 6). In addition,pl the Cupl phonon is not substitution.modified by Thethe substitution. Ba phonon also The doesBa phonon not vary also in do energy,es not butvary its in intensity energy, but has its been intensity strongly has quenched been instrongly the xx polarizationquenched in bythe Prxx substitution polarization [by128 Pr,129 substitution], which is [128,129], due to the which partial is substitutiondue to the partial of Pr for Ba,substitution explaining of the Pr unexpectedfor Ba, explaining strong the reduction unexpected in T cstrongin that reduction case [133 ].in TheTc in most that sensitivecase [133]. is The the B1g modemost thatsensitive follows is the one- B1g mode or two-mode that follows behavior one- or [ 135two-mode] depending behavior on [135] the radius depending diﬀerence on the ofradius thetwo atomsdifference [128 ,129of the]. As two seen atoms in Figure [128,129].6b, thisAs phononseen in Figure splits into6b, this two phonon or three splits bands, into which two apparentlyor three correspondbands, which to apparently the end members correspond and to an the intermediate end members one. and In an the intermediate case of Y1 one.xPr xInBa the2CuO case7 δof, the − − transitionY1−xPrxBa2 temperatureCuO7−δ, the transition decreases temperature as Pr substitutes decreases for yttrium as Pr substitutes up to 60%, for and yttrium above that,up to the 60%, compound and doesabove not that, superconduct the compound (Figure does7). Plottingnot superconduct the relative (F amountigure 7).of Plotting the various the re phaseslative asamount induced of the by the Bvarious1g phonon phases mode, as itinduced is observed by the that B1g T cphonondoes not mode, follow it is the observed evolution that of theTc does relative not amountfollow the of the intermediateevolution of mixedthe relative state, amount which of is thethe leadingintermediat phasee mixed up to state, 80% Prwhich content, is the where leading the phase compound up to is 80% Pr content, where the compound is not superconducting (Figure 7). This is proof that both the not superconducting (Figure7). This is proof that both the pure Pr123 (Y 1 xPrxBa2CuO7 δ) and the − − intermediatepure Pr123 (Y mixed1−xPrxBa phases2CuO7 are−δ) and not superconductingthe intermediate mixed and the phases superconductivity are not superconducting in these compounds and the is superconductivity in these compounds is only due to the percolation via the Y123 only due to the percolation via the Y123 (YBa2Cu3O7 δ) phase. (YBa2Cu3O7−δ) phase. −

Condens. Matter 2019, 4, 87 99 of of 23 Condens. Matter 2019, 4, 87 9 of 23

Figure 7. Relative intensity of the three phases as obtained from the B1g-symmetry phonon.

Figure 7.7. Relative intensity of the three phases as obtained fromfrom thethe BB1g1g-symmetry-symmetry phonon. Because, in YBa2CuOx, there is no way to add more oxygen beyond x = 7, overdoping can be achievedBecause, by Ca in YBasubstitutes2CuOCuOxx, ,there therefor yttrium.is is no no way way This to to add substitution more oxygenoxyge hasn two beyond effects; x = 7,an overdoping increase of can holes be achievedcreating overdoping, byby CaCa substitutes substitutes and creation for for yttrium. yttrium. of strains This This substitution from substitution the size has twodifferencehas etwoffects; effects;between an increase an the increase ofCa holes and of creatingY holesions. overdoping,creatingFurthermore, overdoping, and the creationlocal and electric of creation strains field frominof thestrains the CuO size from2 planes diff theerence from size between thedifference Y/Ca the and between Ca Ba and sites Y the is ions. modified, Ca Furthermore, and Y which ions. theFurthermore,could local possibly electric the field localaffect in electric thethe CuO phasefield2 planes in separationthe from CuO the2 planes Yobserved/Ca from and Ba thein sites Y/Cathe is and modified,rare Ba earth sites which issubstitutions modified, could possibly which for acouldyttriumffect thepossibly [128,129]. phase separationaffect The resultsthe observed phase of the in separationCa the substitution rare earth observed substitutions on the in strong the for rarephonon yttrium earth modes [128 substitutions,129 for]. Thethe resultsy(xx)y for ofyttriumscattering the Ca [128,129].substitution polarization The on areresults the shown strong of thein phononFigure Ca substitution 8. modes The A forg-symmetry on the the y(xx)y strong modes, scattering phonon due polarization tomodes Ba and for Cu2, arethe are showny(xx)y not inscatteringmodified Figure8 considerably.polarization The A g-symmetry areby shownthe Ca modes, insubstitution Figure due to8. BaThe (Fig and Aureg-symmetry Cu2, 8) implying are not modes, modified that dueCa considerablydoesto Ba not and substitute Cu2, by are the notfor Ca substitutionmodifiedisovalent considerablyBa. (Figure The relative8) implying by theintensity Ca that substitution Caof doesthe Cu2 not (Fig substituteto ureBa 8)in implyingthe for isovalentxx polarization that Ba. Ca Thedoes is relative alsonot substitutenot intensity modified for of theisovalentbecause Cu2 tothe Ba. Ba excess inThe the relativedoping xx polarization continuesintensity is alsoofscreening the not Cu2 modified the to CuBa2 because inatoms the xx[130]. the polarization excess In the doping Ca substitutionis continuesalso not screeningmodifiedfor the Y thebecauseoverdoped Cu2 atomsthe region,excess [130 ].dopingthe In theenergy continues Ca substitutionof the screening Oap phonon for the the Y Cudecreases overdoped2 atoms (Figure [130]. region, In 2a) thethe following energyCa substitution of the Obell-shapedap forphonon the Y decreasesoverdopedtrend of T (Figurec . region,The 2widtha) the following energyof the thephononof bell-shapedthe O remainsap phonon trend close decreases of to T cits. The value (Figure width for of2a)the the followingortho-I phonon phase remainsthe bell-shaped(Figure close 2a), to itstrendverifying value of T forthatc. The the the ortho-Iwidth substantial of phase the increase phonon (Figure 2in remainsa), the verifying width close with that to oxygenits the value substantial doping for the in increase ortho-I pure YBa inphase2 theCu 3 widthO(Figurex is due with 2a), to oxygenverifyingthe ordering doping that of the inthe substantial pure chain YBa oxygen2Cu increase3O atoms.x is duein the to width the ordering with oxygen of the chaindoping oxygen in pure atoms. YBa2Cu3Ox is due to the ordering of the chain oxygen atoms.

FigureFigure 8. 8.Raman Raman spectra spectra of of Y Y1 1−yyCayBa22CuCu33OOx xforfor the the y(xx)y y(xx)y scattering scattering polarization. polarization. − Figure 8. Raman spectra of Y1−yCayBa2Cu3Ox for the y(xx)y scattering polarization. Figure9 9 shows shows thatthat thethe decreasedecrease inin energyenergy ofof thethe apicalapical oxygenoxygen modemode isis duedue toto thethe increaseincrease inin the distancedistanceFigure 9 ofof shows thethe OO apthatap from the thedecrease CuO2 planes.in energy Apparently, Apparently, of the apical the oxygen extra carriers mode is introduced due to the inin increase thethe CuOCuO in22 planesthe distance fromfrom the ofthe the Ca Ca substitutionO substitutionap from the induce CuO induce2 redistributionplanes. redistribution Apparently, of charges of thecharges betweenextra between carriers CuO 2introducedCuOplanes2 planes and in CuO andthe chains CuOCuO2 planeschains repellingfrom the theCa substitutionapical oxygen induce from CuOredistribution2 planes. Althoughof charges the between data are CuO limited,2 planes it seems and CuO that chains repelling the apical oxygen from CuO2 planes. Although the data are limited, it seems that

Condens. Matter 2019, 4, 87 10 of 23

Condens. Matter 2019, 4, 87 10 of 23 repelling the apical oxygen from CuO2 planes. Although the data are limited, it seems that there is therea stepwise is a stepwise increase inincrease the CuO in 2the-Oap CuOdistance2-Oap withdistance Ca overdoping.with Ca overdoping. Since the accuratelySince the accurately measured measuredamount of amount oxygen doesof oxygen not vary does appreciably not vary with apprec Ca substitutioniably with Ca (Figure substitution 10) and the(Figure width 10) of theand apex the widthmode of is almostthe apex the mode same is as almost for the the ortho-I same phaseas for th (Figuree ortho-I2), thisphase e ﬀ (Figureect could 2), not this be effect due tocould coexisting not be duephases to coexisting from chain phases ordering. from Possibly, chain ordering. it indicates Possibly, the tendency it indicates of O theap to tendency stay at discrete of Oap to positions stay at discretealong the positions c-axis as along in a double the c-axis well potential,as in a double or equivalently well potential, discrete or charge equivalently transfers discrete from chains charge to transfersthe superconducting from chains planes. to the Such superconducting an important eplanﬀectes. requires Such an further important investigation effect requires using several further Ca investigationconcentrations using and several fully oxygenated Ca concentrations samples. and fully oxygenated samples.

FigureFigure 9. 9.Modiﬁcation Modification of of the the Cu Cuplpland andO Oapap distance inin ÅÅ forfor thethe YY11−yyCaCayyBaBa2Cu2Cu3O3Ox compound.x compound. −

TheThe in-phasein-phase vibrationsvibrations of of O plOplatoms atoms are are strongly strongly dampened dampened by oxygen by oxygen doping, doping, with their with energy their energyreducing reducing and the widthand the increasing width increasing with x in pure with Y123x x in compound pure Y123x (Figure compound2b). The (Figure overdoping 2b). withThe overdopingCa further increases with Ca the further width increases and to a lesserthe width degree and decreases to a lesser the energy degree (Figure decreases2b), although the energy the (Figurepresence 2b), of thealthough phonon the softening presence at of oxygen the phonon overdoping softening complicates at oxygen the overdoping eﬀect. The complicates relative amount the 1 effect.of the softenedThe relative phase amount located of at the 428 cmsoftened− in thephase Ca substitutedlocated at compounds428 cm−1 in to the the Ca total substituted counts of compoundsin-phase mode, to the correlates total counts very wellof in-phase with the mode, amount correlates of oxygen very and well not with thethe concentrationamount of oxygen in Ca and(Figure not 10with). The the EXAFS concentration measurements in Ca (Figure have indicated 10). The thatEXAFS the measurements carriers introduced have by indicated Ca do not that reside the carriersat the CuO introduced2 (or the BaO)by Ca planes, do not but reside the Ca at atomsthe CuO act2 as (or pinning the BaO) centers planes, for thesebut the excess Ca carriersatoms act [136 as]. pinningIn such acenters case, the for continuousthese excess reduction carriers [136]. in Tc Inwith such the a amountcase, the of continuous Ca could be reduction a result ofin percolationTc with the amountfrom the of separation Ca could be into a result at least of twopercolation phases from (Figure the8 ),separation a pure YBa into2Cu at 3leastO7 δ twoand phases a mixed (Figure one not8), − asuperconducting. pure YBa2Cu3O7−δIn and the a studiesmixed one of the not R1 superconducting.1 xR2xBa2Cu3O 7Inδ thesystems, studies we of havethe R1 observed1−xR2xBa2 thatCu3O the7−δ − − systems,B1g-mode we splits have into observed two or that three the modes B1g-mode that correspondsplits into two to two or three end compounds modes that andcorrespond a mixed to phase. two endIn the compounds Ca case, in and addition a mixed to the phase. B1g-symmetry In the Ca mode case, of in YBa addition2Cu3O 7toδ thewhich B1g-symmetry is gradually mode reduced of − 1 YBain intensity2Cu3O7−δ withwhich the is amount gradually of Ca,reduced another in modeintensity of Awithg-symmetry the amount at 322of Ca, cm −anotherappears mode to gain of ≈ Aintensityg-symmetry with at the ≈ substitution,322 cm−1 appears but its to energy gain intensity remains una withﬀected the substitution, by the amount but of Ca.its energy This extra remains mode unaffectedmust correspond by the toamount the mixed of Ca. phase. This extra On the mode basis must of the correspond B1g phonon to energythe mixed dependence phase. On on the the basis ion ofsize the [128 B1g,129 phonon,132], weenergy can deduce dependence that it on could the roughly ion size correspond [128,129,132], to a we Y0.5 canCa0.5 deduceBa3O7 δthatphase. it could − roughly correspond to a Y0.5Ca0.5Ba3O7−δ phase.

Condens. Matter 2019, 4, 87 11 of 23 Condens. Matter 2019, 4, 87 11 of 23

−11 FigureFigure 10.10. Relative intensity of 428 cmcm− modemode and and its its correlation correlation with with amount amount of of oxygen. oxygen.

Furthermore, there isis aa veryvery weakweak modemode atat ≈312 cm −11 activatedactivated by by the the Ca Ca substitution substitution (Figure (Figure 88).). ≈ − In thethe purepure YBaYBa22Cu3OO77 system,system, there there is is a mode ofof BB2g,3g2g,3g symmetrysymmetry due due to to vibrations of the yttrium ions. The The substitution of of heavier yttrium atoms by Ca should induce a shiftshift ofof ≈5% in frequency as ≈ compared with the 10% didifferenceﬀerence observed. It is, th therefore,erefore, unlikely that the two modes are related 1 and most likelylikely thethe ≈312 cm −1 modemode corresponds corresponds to an ideal CaBa2Cu3OOxx phase,phase, which which is is unstable as ≈ − 2 3 a free compound.

2.3. Pressure Induced Lattice Effects Effects As detected by the softening of the in-phasein-phase mode (Figure 2b)2b) andand confirmedconfirmed byby otherother measurements [125,126], YB2 2Cu3 3O7−δ7 δ at optimal doping with maximumc Tc is at the edge of a measurements [125,126], YΒ Cu O −at optimal doping with maximum T is at the edge of a lattice latticeinstability instability undergoing undergoing a small a small lattice lattice distortion. distortion. Systematic Systematic Raman Raman studies studies on on various various high high Tc Tc cuprates havehave revealed revealed nonlinear nonlinear lattice lattice distortions distor andtions lattice and instabilitieslattice instabilities induced byinduced the application by the ofapplication hydrostatic of pressurehydrostatic [137 –pressure141], which [137–141], correlate wh withich thecorrelate non-monotonic with the pressure non-monotonic dependence pressure of Tc. Thisdependence is not surprising of Tc. This because is not it issurprising well accepted because that structuralit is well andaccepted electronic that inhomogeneities structural and electronic constitute intrinsicinhomogeneities properties constitute of cuprate intrinsic superconductors properties of [cuprate10,142,143 superconductors]. The Raman study[10,142,143]. of hydrostatically The Raman compressedstudy of hydrostatically YBa2Cu3Oy (Y123x) compressed and YBa YBa2Cu2Cu4O3O8 (Y1248)y (Y123x) cuprates and YBa revealed2Cu4O8 deviations (Y1248) cuprates from an expectedrevealed lineardeviations behavior from in thean phononexpected characteristics linear behavior indicating in the lattice phonon instabilities characteristics [139,144 ]indicating at those pressures lattice whereinstabilities Tc dependence [139,144] showsat those saturation pressures or nonlinear where T behaviorc dependence [145,146 shows]. Synchrotron saturation angle-dispersive or nonlinear powderbehavior di [145,146].ffraction measurementsSynchrotron angle-dispersive with dense sampling powder on optimallydiffraction doped measurements Y1237 and Y1248with dense [147] superconductorssampling on optimally verified doped the Raman Y1237 results and Y1248 showing [147] clear superconductors deviation of the verified lattice constantsthe Raman from results the expectedshowing clear equation deviation of states of the (EOS) lattice followed constants by afr strongom the hysteresis expected equation effect in theof states same (EOS) pressure followed range, whichby a disappearstrong hysteresis in the non-superconducting effect in the PrBasame2 Cupressure3O7 (Pr1237) range, [147 ].which disappear in the non-superconductingFigure 11 presents PrBa the2Cu comparative3O7 (Pr1237) results[147]. on the hydrostatic pressure dependence of the latticeFigure parameters 11 presents a, b,the and comparative c for the results three on compounds the hydrostatic (superconducting pressure dependence Y1237, of Y1248, the lattice and non-superconductingparameters a, b, and Pr1237). c for Atthe the three bottom compounds of the figure, (superconducting the corresponding Y1237, relative Y1248, strain and is depictednon-superconducting for the three cases.Pr1237). Full At symbols the bottom correspond of the to thefigure, measurements the corresponding to increase relative the pressure strain and is opendepicted symbols for the for three those cases. obtained Full on symbols pressure correspond release. It wasto the found, measurem as expected,ents to that increase the compressibility the pressure alongand open the a-,symbols b-, and for c-axis those is anisotropic,obtained on withpressure the c-axis release. exhibiting It was thefound, strongest as expected, reduction that upon the pressurecompressibility [147]. along The main the a-, result b-, and is the c-axis strong is anisotropic, deviation of with the pressurethe c-axis dependence exhibiting the of thestrongest c-axis thatreduction starts aroundupon pressure 3.7 GPa and[147147]. extends The to 8main to 10 result GPa (Figureis the 11strong). The deviation deviation alsoof the exists pressure in the samedependence pressure of rangethe c-axis for thethat other starts two around axes, 3.7 but GPa it is muchand extends smaller. to It8 isto interesting10 GPa (Figure that there 11). The is a substantialdeviation also hysteresis exists in eff ectthe withsame the pressure data following range for the the decompression other two axes, the expectedbut it is much EOS. The smaller. nonlinear It is interesting that there is a substantial hysteresis effect with the data following the decompression the expected EOS. The nonlinear evolution of the lattice constants, with the applied pressure, originates

Condens. Matter 2019, 4, 87 12 of 23

Condens. Matter 2019, 4, 87 12 of 23 evolution of the lattice constants, with the applied pressure, originates from similar modifications fromin the similar interatomic modifications distances in such the interatomic as the Ba distance distance froms such the as basal the Ba plane, distance the Cu2-Ofrom thepl bond basal length,plane, theand Cu2-O the Cu2-Cu1pl bond distancelength, and along the the Cu2-Cu1 c-axis [distance147]. Concerning along the the c-axis relative [147]. strain Concerning calculated the from relative the strain(113) line,calculated it shows from three the pressure (113) line, regions it shows (Figure thr1,ee bottom). pressure Up regions to ~3 GPa, (Figure the data1, bottom). among theUp threeto ~3 GPa,compounds the data agree among following the three the compounds expected slight agree increase following in the lineexpected width slight and, increase in the region in the ~3 line to width8 GPa, and, there in is the a change region in~3 the to 8 slope GPa, only there in is the a ch twoange superconducting in the slope only compounds in the two (Y1237 superconducting and Y1248) compoundsto be followed (Y1237 by a furtherand Y1248) increase to be in followed slope at higher by a further pressures, increase which in is slope common at higher in all threepressures, cases. whichIt seems is thatcommon at the criticalin all pressurethree cases. range It ofseems ~3–8 GPa,that at something the critical happens pressure to the range lattice of which ~3–8 affGPa,ects somethingthe carriers happens related to to superconductivity. the lattice which Aboveaffects ~8the GPa, carriers there related must be to another superconductivity. effect which isAbove common ~8 GPa,to all there compounds. must be another effect which is common to all compounds.

Figure 11. Pressure dependence of the lattice constants (a (a-,-, b-, and c-axis) and lattice strain (bottom

graphs) for for YBa 22CuCu33OO7−δ7 (Y1237),δ (Y1237), PrBa PrBa2Cu2Cu3O73−δO 7(Pr1237),δ (Pr1237), and andYBa2 YBaCu42OCu8 (Y1248)4O8 (Y1248) compounds. compounds. Full − − (empty)Full (empty) symbols symbols for increasing for increasing (decreasing) (decreasing) pressure. pressure.

Figure 12 presents the comparative results of Raman measurements among superconducting Y1237 and non-superconducting Pr1237 for the strong A g-symmetry phonons that involve the Oap,, Oin-phin-ph, ,Ba, Ba, and and Cu2 Cu2 atoms. atoms. The The clear clear anomaly anomaly and and the the plateau plateau around around 3 3 GPa GPa observed observed in in Y1237 Y1237 is is absent for Pr1237 and the results results agree with the X-ray diffraction diﬀraction measurem measurementsents (Figure 11)11) and the modificationsmodiﬁcations in in the interatomic distances [147]. [147]. Raman Raman data data have have shown shown that, that, even even for for the ortho-II phase, a similar anomaly exists in the Ag-symmetry phonon modes [147]. Although no hydrostatic Raman pressure data exist for the Y1236 compound, the absence of this anomaly for Pr1237 supports the hypothesis that this effect is related with the carriers.

Condens. Matter 2019, 4, 87 13 of 23

phase, a similar anomaly exists in the Ag-symmetry phonon modes [147]. Although no hydrostatic Raman pressure data exist for the Y1236 compound, the absence of this anomaly for Pr1237 supports Condens.the hypothesis Matter 2019 that, 4, 87 this eﬀect is related with the carriers. 13 of 23

FigureFigure 12. 12. RoomRoom temperature temperature pressure RamanRaman datadata forfor thethe A Agg-symmetry-symmetry phonons phonons of of the the YBa YBa2Cu2Cu3O3O77−δδ − (Y1237,(Y1237, triangles) triangles) and and PrBa PrBa2CuCu33OO7−δ7 (Pr1237,δ (Pr1237, squares) squares) systems. systems. − TheThe c-axis modificationmodification withwith pressure pressure is is a resulta result of interatomicof interatomic bond bond length length changes changes resulting resulting from frompressure-induced pressure-induced charge redistributioncharge redistribution or internal strainsor internal in the structure.strains Chargein the redistributionstructure. Charge among redistributionthe planes has beenamong found the toplanes occur has in the been case found of chemical to occur pressure in the [148 case] aff ofecting chemical Tc and pressure must certainly [148] affectingplay some Tc role and in must the observed certainly e ffplayects. some The correlation role in th ofe observed the structural effects. characteristics The correlation with Ramanof the structuralspectral modifications characteristics of with the in-phaseRaman spectral Opl and modifications Oap phonon modes of the (Figurein-phase 12 O) andpl and corresponding Oap phonon modeschanges (Figure of Tc [12)145 ,and146] corresponding imply that the changes trigger ofof theTc [145,146] lattice instabilities imply that lies the among trigger the of CuOthe lattice2 and instabilitiesBaO planes. lies The among average the Cu2-O CuOpl2 bondand BaO distance planes. is almost The average constant Cu2-O in thepl low bond pressure distance region, is almost up to constant~1.5 GPa, in it the decreases low pressure for increasing region, pressureup to ~1.5 up GPa, to 3.7 it GPa, decreases remains for almost increasing constant pressure in the up range to 3.7 of GPa,3.7 GPa remains< p < almost8 GPa, constant and decreases in the range further of 3.7 for GPa p > <8 p GPa < 8 [GPa,149]. and The decreases fractional further coordinate for p > z 8 of GPa the [149].Ba atom The along fractional the c-axis coordinate also shows z of the similar Ba atom modifications along the c-axis at the also same shows pressures similar (Figure modifications 13, bottom). at theIn the same low-pressure pressures region,(Figure up13, to bottom). ~1.5 GPa, In thethe fractional low-pressure coordinate region, z up of Bato decreases~1.5 GPa, almostthe fractional linearly coordinatewith pressure. z of WithBa decreases increasing almost pressure, linearly z increases with pressure. and levels With off increasingfor 3.7 GPa pressure,< p < 8 z GPa, increases indicating and levelsthat the off Ba for atom 3.7 GPa moves < p away< 8 GPa, from indicating the basal that plane. the Ba For atom p > 8moves GPa, zaway is decreasing from the basal indicating plane. that For Ba p >atom 8 GPa, is again z is decreasing pushed towards indicating the basal that plane. Ba atom Upon is again pressure pushed release, towards the movement the basal of plane. the Ba Upon atom pressureclearly shows release, a hysteresis the movement effect (Figure of the 13Ba). atom The Cu2-Cu1 clearly shows distance a inhysteresis the perovskite effect block(Figure hosting 13). The the Cu2-Cu1Ba atom showsdistance similar in the deviations perovskite from block linear hosting behavior the Ba atatom the sameshows pressures similar deviations (3.7 GPa andfrom ~8 linear GPa, behaviortop of Figure at the 13 same). Since pressures this distance (3.7 GPa is relatedand ~8 GPa, to the top transfer of Figure of carriers 13). Since from this the distance CuO chains is related to the to theCuO transfer2 superconducting of carriers planes,from the its abnormalCuO chains modification to the CuO with2 superconducting pressure is certainly planes, connected its abnormal with an modification with pressure is certainly connected with an irregular transfer of carriers to the CuO2 planes. Therefore, the data point to lattice instability at a critical pressure, which affects the carrier distribution and Tc.

Condens. Matter 2019, 4, 87 14 of 23

irregular transfer of carriers to the CuO2 planes. Therefore, the data point to lattice instability at a critical pressure, which aﬀects the carrier distribution and Tc. Condens. Matter 2019, 4, 87 14 of 23

FigureFigure 13.13.Pressure Pressure dependence dependence for for Y1237 Y1237 of Baof atomBa atom z-relative z-relative position position (as compared (as compared with the with c-axis) the andc-axis) the and Cu2-Cu1 the Cu2-Cu1 distance distance in Å (open in Å triangles, (open triangles, for decompression). for decompression).

TheThe newnew phase phase and and the latticethe lattice anomalies anomalies could notcoul bed relatednot be with related a non-hydrostatic with a non-hydrostatic environment ofenvironment the transmitting of the medium. transmitting Although medium. the Although line width th ofe theline luminescencewidth of the luminescence line of ruby and line the of XRDruby lineand widththe XRD cannot line width provide cannot a definite provide proof a definite of a hydrostatic proof of a hydrostatic medium, no medium, broadening no broadening was observed was beforeobserved the before 12.7 GPa the pressure. 12.7 GPa Furthermore, pressure. Furtherm the two-dimensionalore, the two-dimensional (2D) patterns (2D) in thepatterns synchrotron in the detectorsynchrotron do not detector bear any do signnot ofbear a non-hydrostaticany sign of a no pressuren-hydrostatic for the pressure lines of thefor mainthe lines phase. of Thisthe main is in completephase. This agreement is in complete with all agreement measurements with performed all measurements up to now performed that do not up provide to now any that evidence do not forprovide a non-hydrostatic any evidence environment for a non-hydrostatic in the methanol-ethanol environment mixture in the for methanol-ethanol pressures up to 10mixture GPa [150 for]. Itpressures was also up not to related 10 GPa to [150]. any oxygen It was deficiency,also not rela asted the to apex any mode oxygen of thedeficiency, Raman spectraas the apex indicate mode fully of oxygenatedthe Raman spectra compounds indicate (Figure fully4 oxygenated). In order to compound investigates (Figure the e ff ect4). In of order doping to andinvestigate the transmitting the effect medium, the La2 xSrxCuO4 system has been examined at hydrostatic pressures by Raman spectroscopy of doping and the− transmitting medium, the La2−xSrxCuO4 system has been examined at hydrostatic forpressures selected by doping Raman levels spectroscopy using the samefor selected methanol-ethanol doping levels transmitting using the medium same methanol-ethanol and synchrotron XRDtransmitting with two medium different media,and synchrotron i.e., a mixture XRD of methanol-ethanol with two different and neon media, [151 ].i.e., a mixture of methanol-ethanolConcerning the and e ffneonect of[151]. the transmitting medium, it was found that Tc gradually increases whenConcerning Bi2Sr2CaCu the2O8 effectis exposed of the to transmitting methanol at roommedium, temperature, it was found reaching that the Tc maximumgradually Tincreasesc after a monthwhen Bi [1522Sr2].CaCu The2 wholeO8 is exposed process to could methanol be accelerated at room substantiallytemperature, underreaching hydrostatic the maximum pressures. Tc after But a in the same work no change in Tc was detected for the La2 xSrxCuO4 and YBa2Cu3O7 compounds. month [152]. The whole process could be accelerated substantially− under hydrostatic pressures. But Inin anotherthe same systematic work no change investigation in Tc was of the detected effect of for methanol the La2−x onSrx LaCuO2 x4Sr andxCuO YBa4,2 itCu was3O7 discoveredcompounds. that In − +3 theanother adsorption systematic of methanol investigation depends of the on effect the amount of methanol of Sr via on theLa2− smallerxSrxCuO Cu4, it wasions discovered in the compound, that the whichadsorption facilitate of methanol intercalation depends and the on whole the amount effect peaks of Sr around via the x =smaller0.2 doping Cu+3 [ 153ions]. Again,in the compound, hydrostatic pressurewhich facilitate should accelerateintercalation and and possibly the whole modify effect the process.peaks around Synchrotron x = 0.2 XRD doping data [153]. collected Again, on thehydrostatic same La 2pressureCuO4 compound should accelerate with a mixture and poss of methanol-ethanolibly modify the process. and neon Synchrotron have really XRD detected data dicollectedfferences on that the begin same around La2CuO 74 to compound 8 GPa [151 ].with This a pressuremixture regionof methanol-ethanol almost coincides and with neon the have anomalies really observeddetected indifferences both Y1237 that and begin Pr1237 around (Figure 7 to11 ),8 stronglyGPa [151]. suggesting This pressure that the region origin almost of this ecoincidesffect is related with tothe the anomalies presence observed of methanol. in both For Y1237 some and reason Pr1237 in Y1248 (Figure no 11), such strongly effect has suggesting been observed that the (Figure origin 11 of) this effect is related to the presence of methanol. For some reason in Y1248 no such effect has been observed (Figure 11) and this requires further high-pressure investigation using another transmitting medium. In any case, the effect observed both Y1237 and Y1248 at lower pressures (~3 to 4 GPa, Figure 11) must be related to an intrinsic instability of the lattice in these compounds, independent of the transmitting medium.

Condens. Matter 2019, 4, 87 15 of 23 and this requires further high-pressure investigation using another transmitting medium. In any case, the effect observed both Y1237 and Y1248 at lower pressures (~3 to 4 GPa, Figure 11) must be related to Condens. Matter 2019, 4, 87 15 of 23 an intrinsic instability of the lattice in these compounds, independent of the transmitting medium. Concerning the La2 xSrxCuO4 compound, synchrotron XRD and Raman data indicate Concerning the La2−xSrxCuO4 compound, synchrotron XRD and Raman data indicate modificationsmodifications with with pressure pressure that that depend depend on on the the amount amount of Sr of doping Sr doping [151]. [151 The]. top The section top section of Figure of Figure 14 presents the results for the c-axis of La Sr CuO and pure La CuO systems. For the 14 presents the results for the c-axis of La1.85Sr0.151.85CuO0.154 and pure4 La2CuO4 systems.2 4 For the x = 0.15 xcase,= 0.15 the case,XRD the measurements XRD measurements show a deviation show a deviation around 3 around GPa, which 3 GPa, disappears which disappears for the case for theof pure case of pure La CuO . As in the cases of yttrium systems, it also shows a hysteresis effect (Figure 14). La2CuO4. As2 in the4 cases of yttrium systems, it also shows a hysteresis effect (Figure 14). The bottom Theportion bottom of Figure portion 14 of presents Figure 14the presents pressure the depende pressurence dependence of the La/Sr of mode the La for/Sr modethe case for of the x case= 0.15. of xSomething= 0.15. Something similar, but similar, a smaller but a effect, smaller happens effect, happensfor the apex for the phonon apex phonon[151]. It [is151 clear]. It that is clear Raman that dataRaman indicate data indicate a deviation a deviation from linear from pressure linear pressure dependence dependence at ~3 GPa, at ~3 i.e., GPa, the i.e.,same the pressure same pressure where wherethe c-axis the deviates c-axis deviates from normal from normal EOS. EOS.Preliminary Preliminary high-pressure high-pressure Raman Raman measurements measurements show show that thethat effect the e ffdependsect depends strongly strongly on the on amount the amount of dopi of dopingng [151]. [151 Similar]. Similar conclusions conclusions are obtained are obtained from from the FWHMthe FWHM of the of the004, 004, 103, 103, and and110 110diffraction diffraction lines lines [151]. [151 ].

Figure 14.14. Top: dependencedependence ofof thethe c-axisc-axisfor for La La1.851.85SrSr0.150.15CuO44 atat increasing (triangles), decreasing (circles) pressures,pressures, andand for for increasing increasing pressure pressure of of La La2CuO2CuO4 (squares).4 (squares).Bottom: Bottom:pressure pressure dependence dependence of ofthe the La /La/SrSr phonon phonon energy energy (triangles) (triangles) and and width width (circles) (circles) of Laof 1.85La1.85Sr0.15Sr0.15CuOCuO4.4.

The eeffectffect originatesoriginates from from an an anomalous anomalous pressure pressure dependence dependence of the of apicalthe apical oxygen oxygen position position along alongthe c-axis. the Thec-axis. La /Sr-O(2)The La/Sr-O(2) and Cu-O(2) and bondCu-O(2) length bond modifications length modifications along the c-axis along are the indications c-axis are of indicationscharge redistribution of charge withredistribution hydrostatic with pressure hydrostati [154].c Itpressure is also interesting [154]. It is that also the interesting tolerance that factor, the t, tolerancecalculated factor, from thet, calculated average distance from the of average the La-O distance bond lengths,of the La-O as compared bond lengths, with as those compared of the Cu-O with √ thoseones [t of= thedLaO Cu-O/ 2 donesCuO] [t and = d associatedLaO/ 2 dCuO with] and charge associated redistribution with charge [155 redi], alsostribution shows an[155], anomaly also shows at ~2 anGPa anomaly for the optimallyat ~2 GPa for doped the optimally compound. doped Furthermore, compound. the Furthermore, tolerance factor the appearstolerance to factor jump appears among todi ffjumperent among almost different equidistant almost values equidistant discontinuously values [discontinuously151]. Although the[151]. statistics Although is not the good statistics enough is notto verify good thisenough effect to and verify draw this final effect conclusions, and draw thisfinal could conclusions, be related this to could the abrupt be related changes to the observed abrupt changes observed for the Cupl-Oap in the system Y1−yCayBa2Cu3O7 (Figure 9), and the plateaus observed in the Raman measurements under hydrostatic pressure (Figure 12). Such effects could be described as a signature of a stepwise modification of the carrier concentration in the superconducting planes, as in topologically distinct states.

Condens. Matter 2019, 4, 87 16 of 23

for the Cupl-Oap in the system Y1 yCayBa2Cu3O7 (Figure9), and the plateaus observed in the Raman − measurements under hydrostatic pressure (Figure 12). Such eﬀects could be described as a signature of a stepwise modiﬁcation of the carrier concentration in the superconducting planes, as in topologically distinct states.

3. Conclusions Raman studies on a series of cuprates were presented showing lattice distortions induced either by chemical doping or by applying hydrostatic pressure. From the spectral modifications (frequency and width) of the apex and in-phase phonons of the yttrium compounds it was found that the oxygen non-stoichiometry is related with the ordering of the chain oxygen atoms creating separation into submicron phases with varying transition temperature. Our Raman and more recent measurements [122–124] prove that these phases coexist in the YBa2Cu3Ox compounds and only the relative amount of the phases varies with doping. Just above the optimum doping, another lattice effect was discovered from the softening of the in-phase mode, which is related to a slight reduction of the transition temperature and originates from a sudden change in the CuO2 buckling, as verified by other techniques [125,126]. From the study of the Raman active B1g mode it was found that rare earth substitution for yttrium in the same series of superconductors induces a separation into superconducting and non-superconducting phases. Depending on the relative size and the kind of the substituting rare earth element this affects the ability of the compound to superconduct and the transition temperature. Overdoping by Ca substitution for Y shows a very similar phase separation behavior. Hydrostatic pressure was found to create small lattice distortions in YBa2Cu3O7 and YBa2Cu4O8 compounds, which are absent for the non-superconducting PrBa2Cu3O7 system. The same happens for the La2 xSrxCuO4 series, which again disappear in the pure non-superconducting La2CuO4 system. − Raman studies under hydrostatic pressure in the Bi-cuprates [141] also indicate pressure-induced lattice anomalies at low hydrostatic pressures. In all cases, there are indications for charge redistribution, which apparently affects the carrier concentration in the superconducting planes and modifies Tc. Raman studies on other high Tc compounds, such as the diborides [60,62,63,102] and the pnictides [103–105], have revealed phase separation and local lattice distortions. This is an indication that the observed effects possibly characterize most of the high temperature superconductors. In all cases, (cuprates, pnictides, and diborides) the lattice anomalies are accompanied by modifications in the transition temperature, indicating some connection between the two effects. It is unclear whether the observed effects are related to the pairing mechanism, although the lattice modifications or the phase separation phenomena apparently induce charge redistribution between the superconducting and the insulating planes in the studied layered structured superconductors. They certainly show that the lattice degrees of freedom participate in the related phenomena to an extent that needs to be clarified.

Funding: This research received no external funding. Conﬂicts of Interest: The author declares no conﬂict of interest.

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