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

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.

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 [3,4,5,6,7,8,9,10,11], nikelates [12,13], A15 alloys [14], and cuprates [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52] 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.

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 (T_c) [15] in MgB₂ [57,58,59,60,61,62,63], the alkali metal doped C60 [64,65,66], and, more recently, by the very high transition temperature achieved under hydrostatic pressure in sulfur hydrides [67,68,69,70]. In the case of cuprates, several experiments (e.g., [71,72,73,74,75,76,77,78,79]) 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 [80,81,82,83,84,85,86] and at the insulator to metal transition in VO₂ [87,88,89,90,91,92]. 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 [96,97,98], 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 T_c compounds, such as the diborides [60,62,63,102] and the pnictides [103,104,105] 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 YBa₂Cu₃O_x 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 (O_ch, Cu_ch) and Y have full point group site symmetry being IR-active (B_2u,3u and B_1u), Ba, and apical oxygen (O_ap). The CuO₂ plane atoms (Cu_pl, O_pl) have lower symmetry (C2) and they participate in three phonons of even symmetry A_g, B_2g,3g and three phonons of odd symmetry B_1u, B_2u,3u (along the c, a, and b axis, correspondingly). The main difference between the orthorhombic and the tetragonal phase are the out-of-phase vibrations of O_pl atoms, which in the former case have the A_g symmetry and in the latter case, B_1g symmetry, and can be easily identified from the distinct polarization selection rules [106]. Characteristic Raman spectra are shown in Figure 1a,b for the y(cc)y and y(xx)y scattering geometries and the strong Raman active phonons of A_g symmetry along the c-axis for YBa₂Cu₃O_7−δ are located at ≈116 cm⁻¹ (Ba), ≈150 cm⁻¹ (Cu_pl), ≈435 cm⁻¹ (in-phase vibrations of O_pl atoms), and ≈502 cm⁻¹ (O_ap).

2.1. Phase Separation from Oxygen Doping

The A_g symmetry strong modes due to the Ba and Cu_pl atoms vary considerably in intensity with oxygen concentration in the y(xx)y scattering configuration (Figure 1b) and Ba phonon has a strong asymmetric shape that gradually disappears in the tetragonal phase (x ≤ 6.35). The Cu_pl phonon shows the opposite behavior, being very weak in the fully oxygenized compounds (x ≈ 7) and gaining intensity by the orthorhombic to tetragonal (O-T) phase transition (Figure 1). In the y(cc)y scattering geometry, these phonons appear in all oxygen concentrations without considerable intensity variations (Figure 1a). In this scattering geometry, the Ba phonon is symmetric, which indicates that the asymmetry observed in the other geometry is due to its coupling with the carriers. Its intensity is modified by the amount of oxygen which reflects the carrier redistribution with doping between the BaO and the CuO₂ planes. At low doping, the carriers are distributed outside the CuO₂ planes screening the Ba phonon, which appears with very low intensity (or it is completely absent) in the xx scattering polarization. Exactly the opposite happens to the Cu_pl phonon, which is strong at low carrier concentrations and disappears with increasing doping. As carriers are transferred to the CuO₂ planes they induce strong screening of the Cu_pl phonon, while the Ba mode gains intensity (Figure 1b).

Oxygen nonstoichiometry is the crucial parameter controlling such a diverse behavior for the compound as one follows the transition from YBa₂Cu₃O₆ to YBa₂Cu₃O₇. It is, therefore, natural to concentrate on the oxygen Raman active modes. The dependence of the O_ap mode energy on the oxygen concentration is nonlinear [107]. Roughly described, the energy remains almost constant in the range of 6.75 < x < 7.00, is reduced in the range of 6.15 < x < 6.75, and, finally, for x < 6.15, there is a sudden drop in frequency (Figure 2a). The mode linewidth exhibits the following three minima: for maximum x values, for x ≈ 6.47, and in the range of x < 6.12. Contrary to early Raman spectra, which have shown a linear dependence of its energy with the amount of oxygen [108], the results in 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 maximum close to x = 6.7 and then a decrease towards the two ends (Figure 2a), which is a result of the appearance of new phases, as discussed below.

In the YBa₂Cu₃O_x (Y123x) compounds, Cu atoms also exist outside the CuO₂ planes, forming linear chains along the b-axis. As the rest of the HTSC does not have such chains, it is believed that they do not play a crucial role in superconductivity, although they influence the properties of the Y123x system. In the fully occupied chain (Y1237), all oxygen atoms are, in principle, located along the b-axis, and, as the number of oxygen atoms is decreased, there is always a tendency to form thermodynamically stable structures [109]. Two such phases with T_c at 60 K (ortho-II, for x ≈ 6.5), which correspond to alternating full and empty chains, and at 92 K (ortho-I, fully oxygenated samples) are well established appearing as characteristic plateaus in the phase diagram [110]. For lower concentrations (x ≤ 6.35), a transition takes place to an antiferromagnetic, non-superconducting phase [107]. The exact stoichiometries, where the phases appear, depend on the preparation conditions [107]. This is due to the existence of many other intermediate phases, which correspond to different combinations of full and empty chains that are examined below. Such ideal ordered microstructures can only be stabilized after a careful annealing of the materials; otherwise the disorder will make the compound appear macroscopically tetragonal [111]. The changes induced in the chains from the removal of oxygen, have a direct effect on the position of the apical oxygen, which moves away from the superconducting CuO₂ planes [110]. In terms of the valences, this is an indication of redistribution of charges between the chains and the planes as oxygen is added in the system [100]. Another way to explain the phase transformation from the antiferomagnetic to the superconducting state was proposed within the phase separation model [112]. As oxygen atoms are added, and holes are transferred to the CuO₂ planes, conducting microdomains are formed, which, when there are enough, are connected and the system becomes a superconductor. A further increase of holes in the planes induces another phase transition with higher T_c (92 K). The appearance of these phases is connected with the distribution of the oxygen atoms in the chains along the b-axis forming two- or three-dimensional superlattices [109]. Some of these structures have been observed (tetragonal, ortho-II, and ortho-III phases) and they correspond to x ≈ 6, x ≈ 6.5, and x ≈ 6.67 [109,110,111]. 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 frequency modes (Ba and Cu_pl) depends strongly on the amount of oxygen (mainly in the y(xx)y 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 phonons (Figure 2). This is due to the appearance of new phases, as resonance examination of these oxygen modes in the excitation energy range of 1.6–2.9 eV, for the tetragonal and orthorhombic Y123x system, has revealed [113]. Concerning the A_g symmetry apical oxygen phonon, it has been found to show a strong resonance in the IR excitation for the tetragonal case, with additional modes appearing, which are absent when the excitation is in the visible region of spectrum [114]. Work carried out by Iliev et al. [94] has shown a very characteristic variation of the apical A_g phonon when the excitation wavelength varied from blue (482.5 nm) to red (647.1 nm) for the YBa₂Cu₃O_6.4 compound. Our investigations confirmed this by showing that, in the fully oxygenated ortho-I phase, the O_ap mode does not shift with varying excitation wavelength (Figure 3a) and it is modified considerably for the underdoped compound (Figure 3b) due to the different cross sections of the coexisting phases, with the lower T_c phases being in resonance with lower energy excitations [113,114].

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, 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, 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 other measurements on x ≈ 6.5, it is clear beyond any doubt that the 493 cm⁻¹ is a superstructure peak 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 spectra from 30 samples of varying oxygen concentrations with ¹⁶O and 23 samples with ¹⁸O, and the results are presented in Figure 4 (similar results exist for ¹⁸O in [98]). It appears that the 486 cm⁻¹ peak 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 it should peak around x ≈ 6.25, contrary to the deconvolution results (Figure 4). A better guess is the 2$\sqrt{2}$a_o × 2$\sqrt{2}$a_o × c diagonal superlattice phase based on the amount of oxygen [118,119,120]. In 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 wavenumbers, which correspond (from Figure 2) to the phases indicated in Figure 5. The ortho-I and ortho-II phases are clear, while the superstructure S peak seems to correspond to x ≈ 1/8 (2$\sqrt{2}$a_o × 2$\sqrt{2}$a_o × c) phase. Furthermore, there are indications of other phases for wavenumbers pointing to an ortho-III (x = 6.67) or even higher phases [121]. In a systematic imaging of the spatial ordering of the oxygen chains in YBa₂Cu₃O_6+y, by micro X-ray diffraction measurements, the phase separated regions have been detected [122,123,124]. For y = 0.33, the ortho-II phase was clearly detected embedded in more disordered regions [124]. For y = 0.67, nano-puddles corresponding to y = 0.5 + 1/8 were found corresponding to the ortho-VIII puddles of alternating five filled and three empty oxygen wires every eight rows [122]. Other networks were created by thermal manipulation [123]. Unfortunately, no Raman data exist on the same compounds for comparison, but our studies agree with these results and at least the one-eighth oxygen ordering seems to be a preferential oxygen ordering for both the YBa₂Cu₃O₆ and the YBa₂Cu₃O_6.5 stable phases. Furthermore, the regions assigned to OIII phase in Figure 5 possibly consist of several other phases similar to the ones discovered by X-ray imaging [122,123]. This can explain the less pronounced nature of the OIII peaks in Figure 5 for both the apex and the in-phase modes. Finally, there is another peak in the overdoped region, as strongly indicated from the in-phase mode and discussed below.

As seen in Figure 2b, the in-phase O_pl mode energy and linewidth values remain constant in the range of 6.00 < x < 6.40. At higher doping levels, the energy monotonically decreases, while the linewidth increases almost linearly and, finally, it softens by ~8 cm⁻¹ close to optimal doping (Figure 2b). An analysis of the Raman measurements shows that microcrystallites of the two different phases could be found within the same compound with the in-phase phonon energy either corresponding to the optimally or the overdoped concentration. This is the reason for the increased error bars (the statistical distribution from measurements from several microcrystallites) for the overdoped data of in-phase phonon energy in Figure 2b. The EXAFS [125] and neutron [126] scattering measurements have shown that, at exactly this oxygen concentration, there is a sudden modification in the buckling of the CuO₂ planes with a reduction in T_c [127]. Apparently, this softening is related to the change in the buckling. Therefore, we conclude that two phases coexist for x ≥ 6.94 and only the relative amount of each phase varies with oxygen content [127]. It should be stressed that the miscibility gap, seen as a split-off peak below 435 cm⁻¹ in Figure 5 (in-phase mode), is observed even between microcrystals of the same sample, i.e., x = 6.940. This fact underlines the martensitic character of the phase transition. A similar softening has been observed for the ¹⁸O samples [98], and in samples where the La has been substituted in half by another rare earth (La_0.5R_0.5Ba₂Cu₃O^x) [128], but not in the homologous series Pr_0.5R_0.5Ba₂Cu₃O_x [129]. It has been shown that the softening is not related to the amount of doping, as the alternative way of doping by Ca substitution (Y_xCa_1−xBa₂Cu₃O_y) does not induce such a softening ([130] and following session). As La has the tendency of attracting more oxygen atoms, the softening must be attributed to structural modifications induced by the excess of oxygen atoms.

2.2. Phase Separation from Atomic Substitutions

The B_1g mode is sensitive to atomic substitutions for yttrium and its broadening was used to measure the superconducting gap by tuning the phonon energy across the gap energy for carefully chosen rare earth substitutions [131]. By studying a series of rare earth substitutions, La_0.5R_0.5Ba₂Cu₃O_7−δ [128], R_0.5Pr_0.5Ba₂Cu₃O_7−δ [129], Y_1−xLa_xBa₂Cu₃O_7−δ [132], and Y_1−xPr_xBa₂Cu₃O_7−δ [133], it has also been found that the B_1g mode splits into two or three bands, depending on the difference of the atomic radii of substituting species and this is related to the superconducting property. On the one hand, in all these cases, the XRD studies could not discriminate more than one component, although modifications in the interatomic distances 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, Raman measurements with smaller coherent length could clearly detect the multiphase structure of the compounds [128,129,132,133]. Characteristic spectra for the evolution of the strong modes with rare earth substitution for Y_1−xLa_xBa₂Cu₃O_7−δ are shown in Figure 6 [132]. Similar Raman spectra have been found for the other substitutions [128,129,133].

Concerning the other modes, the apex oxygen mode in Figure 6 shifts continuously depending on the average ionic radius of the substituting rare earth elements, in agreement with the results from the system RBa₂Cu₃O_7−δ [134]. The in-phase mode is more or less insensitive to rare earth (Figure 6), although there might be variations, as much as 7 to 8 cm⁻¹, if the oxygen content varies slightly below or above the optimal doping value (Figure 6). In addition, the Cu_pl phonon is not modified by the substitution. The Ba phonon also does not vary in energy, but its intensity has been strongly quenched in the xx polarization by Pr substitution [128,129], which is due to the partial substitution of Pr for Ba, explaining the unexpected strong reduction in T_c in that case [133]. The most sensitive is the B_1g mode that follows one- or two-mode behavior [135] depending on the radius difference of the two atoms [128,129]. As seen in Figure 6b, this phonon splits into two or three bands, which apparently correspond to the end members and an intermediate one. In the case of Y_1−xPr_xBa₂CuO_7−δ, the transition temperature decreases as Pr substitutes for yttrium up to 60%, and above that, the compound does not superconduct (Figure 7). Plotting the relative amount of the various phases as induced by the B_1g phonon mode, it is observed that T_c does not follow the evolution of the relative amount of the intermediate mixed state, which is the leading phase up to 80% Pr content, where the compound is not superconducting (Figure 7). This is proof that both the pure Pr123 (Y_1−xPr_xBa₂CuO_7−δ) and the intermediate mixed phases are not superconducting and the superconductivity in these compounds is only due to the percolation via the Y123 (YBa₂Cu₃O_7−δ) phase.

Because, in YBa₂CuO_x, there is no way to add more oxygen beyond x = 7, overdoping can be achieved by Ca substitutes for yttrium. This substitution has two effects; an increase of holes creating overdoping, and creation of strains from the size difference between the Ca and Y ions. Furthermore, the local electric field in the CuO₂ planes from the Y/Ca and Ba sites is modified, which could possibly affect the phase separation observed in the rare earth substitutions for yttrium [128,129]. The results of the Ca substitution on the strong phonon modes for the y(xx)y scattering polarization are shown in Figure 8. The A_g-symmetry modes, due to Ba and Cu2, are not modified considerably by the Ca substitution (Figure 8) implying that Ca does not substitute for isovalent Ba. The relative intensity of the Cu2 to Ba in the xx polarization is also not modified because the excess doping continues screening the Cu2 atoms [130]. In the Ca substitution for the Y overdoped region, the energy of the O_ap phonon decreases (Figure 2a) following the bell-shaped trend of T_c. The width of the phonon remains close to its value for the ortho-I phase (Figure 2a), verifying that the substantial increase in the width with oxygen doping in pure YBa₂Cu₃O_x is due to the ordering of the chain oxygen atoms.

Figure 9 shows that the decrease in energy of the apical oxygen mode is due to the increase in the distance of the O_ap from the CuO₂ planes. Apparently, the extra carriers introduced in the CuO₂ planes from the Ca substitution induce redistribution of charges between CuO₂ planes and CuO chains repelling the apical oxygen from CuO₂ planes. Although the data are limited, it seems that there is a stepwise increase in the CuO₂-O_ap distance with Ca overdoping. Since the accurately measured amount of oxygen does not vary appreciably with Ca substitution (Figure 10) and the width of the apex mode is almost the same as for the ortho-I phase (Figure 2), this effect could not be due to coexisting phases from chain ordering. Possibly, it indicates the tendency of O_ap to stay at discrete positions along the c-axis as in a double well potential, or equivalently discrete charge transfers from chains to the superconducting planes. Such an important effect requires further investigation using several Ca concentrations and fully oxygenated samples.

The in-phase vibrations of O_pl atoms are strongly dampened by oxygen doping, with their energy reducing and the width increasing with x in pure Y123x compound (Figure 2b). The overdoping with Ca further increases the width and to a lesser degree decreases the energy (Figure 2b), although the presence of the phonon softening at oxygen overdoping complicates the effect. The relative amount of the softened phase located at 428 cm⁻¹ in the Ca substituted compounds to the total counts of in-phase mode, correlates very well with the amount of oxygen and not with the concentration in Ca (Figure 10). The EXAFS measurements have indicated that the carriers introduced by Ca do not reside at the CuO₂ (or the BaO) planes, but the Ca atoms act as pinning centers for these excess carriers [136]. In such a case, the continuous reduction in T_c with the amount of Ca could be a result of percolation from the separation into at least two phases (Figure 8), a pure YBa₂Cu₃O_7−δ and a mixed one not superconducting. In the studies of the R1_1−xR2_xBa₂Cu₃O_7−δ systems, we have observed that the B_1g-mode splits into two or three modes that correspond to two end compounds and a mixed phase. In the Ca case, in addition to the B_1g-symmetry mode of YBa₂Cu₃O_7−δ which is gradually reduced in intensity with the amount of Ca, another mode of A_g-symmetry at ≈322 cm⁻¹ appears to gain intensity with the substitution, but its energy remains unaffected by the amount of Ca. This extra mode must correspond to the mixed phase. On the basis of the B_1g phonon energy dependence on the ion size [128,129,132], we can deduce that it could roughly correspond to a Y_0.5Ca_0.5Ba₃O_7−δ phase.

Furthermore, there is a very weak mode at ≈312 cm⁻¹ activated by the Ca substitution (Figure 8). In the pure YBa₂Cu₃O₇ system, there is a mode of B_2g,3g symmetry due to vibrations of the yttrium ions. The substitution of heavier yttrium atoms by Ca should induce a shift of ≈5% in frequency as compared with the 10% difference observed. It is, therefore, unlikely that the two modes are related and most likely the ≈312 cm⁻¹ mode corresponds to an ideal CaBa₂Cu₃O_x phase, which is unstable as a free compound.

2.3. Pressure Induced Lattice Effects

As detected by the softening of the in-phase mode (Figure 2b) and confirmed by other measurements [125,126], YΒ₂Cu₃O_7−δ at optimal doping with maximum T_c is at the edge of a lattice instability undergoing a small lattice distortion. Systematic Raman studies on various high Tc cuprates have revealed nonlinear lattice distortions and lattice instabilities induced by the application of hydrostatic pressure [137,138,139,140,141], which correlate with the non-monotonic pressure dependence of T_c. This is not surprising because it is well accepted that structural and electronic inhomogeneities constitute intrinsic properties of cuprate superconductors [10,142,143]. The Raman study of hydrostatically compressed YBa₂Cu₃O_y (Y123x) and YBa₂Cu₄O₈ (Y1248) cuprates revealed deviations from an expected linear behavior in the phonon characteristics indicating lattice instabilities [139,144] at those pressures where T_c dependence shows saturation or nonlinear behavior [145,146]. Synchrotron angle-dispersive powder diffraction measurements with dense sampling on optimally doped Y1237 and Y1248 [147] superconductors verified the Raman results showing clear deviation of the lattice constants from the expected equation of states (EOS) followed by a strong hysteresis effect in the same pressure range, which disappear in the non-superconducting PrBa₂Cu₃O₇ (Pr1237) [147].

Figure 11 presents the comparative results on the hydrostatic pressure dependence of the lattice parameters a, b, and c for the three compounds (superconducting Y1237, Y1248, and non-superconducting Pr1237). At the bottom of the figure, the corresponding relative strain is depicted for the three cases. Full symbols correspond to the measurements to increase the pressure and open symbols for those obtained on pressure release. It was found, as expected, that the compressibility along the a-, b-, and c-axis is anisotropic, with the c-axis exhibiting the strongest reduction upon pressure [147]. The main result is the strong deviation of the pressure dependence of the c-axis that starts around 3.7 GPa and extends to 8 to 10 GPa (Figure 11). The deviation also exists in the same pressure range for the other two axes, but it is much smaller. 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 from similar modifications in the interatomic distances such as the Ba distance from the basal plane, the Cu2-O_pl bond length, and the Cu2-Cu1 distance along the c-axis [147]. Concerning the relative strain calculated from the (113) line, it shows three pressure regions (Figure 1, bottom). Up to ~3 GPa, the data among the three compounds agree following the expected slight increase in the line width and, in the region ~3 to 8 GPa, there is a change in the slope only in the two superconducting compounds (Y1237 and Y1248) to be followed by a further increase in slope at higher pressures, which is common in all three cases. It seems that at the critical pressure range of ~3–8 GPa, something happens to the lattice which affects the carriers related to superconductivity. Above ~8 GPa, there must be another effect which is common to all compounds.

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 O_ap, O_in-ph, Ba, and Cu2 atoms. The clear anomaly and the plateau around 3 GPa observed in Y1237 is absent for Pr1237 and the results agree with the X-ray diffraction measurements (Figure 11) and the modifications in the interatomic distances [147]. Raman data have shown that, even for the ortho-II phase, a similar anomaly exists in the A_g-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.

The c-axis modification with pressure is a result of interatomic bond length changes resulting from pressure-induced charge redistribution or internal strains in the structure. Charge redistribution among the planes has been found to occur in the case of chemical pressure [148] affecting T_c and must certainly play some role in the observed effects. The correlation of the structural characteristics with Raman spectral modifications of the in-phase O_pl and O_ap phonon modes (Figure 12) and corresponding changes of T_c [145,146] imply that the trigger of the lattice instabilities lies among the CuO₂ and BaO planes. The average Cu2-O_pl bond distance is almost constant in the low pressure region, up to ~1.5 GPa, it decreases for increasing pressure up to 3.7 GPa, remains almost constant in the range of 3.7 GPa < p < 8 GPa, and decreases further for p > 8 GPa [149]. The fractional coordinate z of the Ba atom along the c-axis also shows similar modifications at the same pressures (Figure 13, bottom). In the low-pressure region, up to ~1.5 GPa, the fractional coordinate z of Ba decreases almost linearly with pressure. With increasing pressure, z increases and levels off for 3.7 GPa < p < 8 GPa, indicating that the Ba atom moves away from the basal plane. For p > 8 GPa, z is decreasing indicating that Ba atom is again pushed towards the basal plane. Upon pressure release, the movement of the Ba atom clearly shows a hysteresis effect (Figure 13). The Cu2-Cu1 distance in the perovskite block hosting the Ba atom shows similar deviations from linear behavior at the same pressures (3.7 GPa and ~8 GPa, top of Figure 13). Since this distance is related to the transfer of carriers from the CuO chains to the CuO₂ superconducting planes, its abnormal 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 T_c.

The new phase and the lattice anomalies could not be related with a non-hydrostatic environment of the transmitting medium. Although the line width of the luminescence line of ruby and the XRD line width cannot provide a definite proof of a hydrostatic medium, no broadening was observed before the 12.7 GPa pressure. Furthermore, the two-dimensional (2D) patterns in the synchrotron detector do not bear any sign of a non-hydrostatic pressure for the lines of the main phase. This is in complete agreement with all measurements performed up to now that do not provide any evidence for a non-hydrostatic environment in the methanol-ethanol mixture for pressures up to 10 GPa [150]. It was also not related to any oxygen deficiency, as the apex mode of the Raman spectra indicate fully oxygenated compounds (Figure 4). In order to investigate the effect of doping and the transmitting medium, the La_2−xSr_xCuO₄ system has been examined at hydrostatic pressures by Raman spectroscopy for selected doping levels using the same methanol-ethanol transmitting medium and synchrotron XRD with two different media, i.e., a mixture of methanol-ethanol and neon [151].

Concerning the effect of the transmitting medium, it was found that T_c gradually increases when Bi₂Sr₂CaCu₂O₈ is exposed to methanol at room temperature, reaching the maximum T_c after a month [152]. The whole process could be accelerated substantially under hydrostatic pressures. But in the same work no change in T_c was detected for the La_2−xSr_xCuO₄ and YBa₂Cu₃O₇ compounds. In another systematic investigation of the effect of methanol on La_2−xSr_xCuO₄, it was discovered that the adsorption of methanol depends on the amount of Sr via the smaller Cu⁺³ ions in the compound, which facilitate intercalation and the whole effect peaks around x = 0.2 doping [153]. Again, hydrostatic pressure should accelerate and possibly modify the process. Synchrotron XRD data collected on the same La₂CuO₄ compound with a mixture of methanol-ethanol and neon have really detected differences that begin around 7 to 8 GPa [151]. This pressure region almost coincides with the anomalies observed in both Y1237 and Pr1237 (Figure 11), strongly suggesting that the origin 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.

Concerning the La_2−xSr_xCuO₄ compound, synchrotron XRD and Raman data indicate modifications with pressure that depend on the amount of Sr doping [151]. The top section of Figure 14 presents the results for the c-axis of La_1.85Sr_0.15CuO₄ and pure La₂CuO₄ systems. For the x = 0.15 case, the XRD measurements show a deviation around 3 GPa, which disappears for the case of pure La₂CuO₄. As in the cases of yttrium systems, it also shows a hysteresis effect (Figure 14). The bottom portion of Figure 14 presents the pressure dependence of the La/Sr mode for the case of x = 0.15. Something similar, but a smaller effect, happens for the apex phonon [151]. It is clear that Raman data indicate a deviation from linear pressure dependence at ~3 GPa, i.e., the same pressure where the c-axis deviates from normal EOS. Preliminary high-pressure Raman measurements show that the effect depends strongly on the amount of doping [151]. Similar conclusions are obtained from the FWHM of the 004, 103, and 110 diffraction lines [151].

The effect originates from an anomalous pressure dependence of the apical oxygen position along the c-axis. The La/Sr-O(2) and Cu-O(2) bond length modifications along the c-axis are indications of charge redistribution with hydrostatic pressure [154]. It is also interesting that the tolerance factor, t, calculated from the average distance of the La-O bond lengths, as compared with those of the Cu-O ones [t = d_LaO/$\sqrt{2}$d_CuO] and associated with charge redistribution [155], also shows an anomaly at ~2 GPa for the optimally doped compound. Furthermore, the tolerance factor appears to jump among different almost equidistant values discontinuously [151]. Although the statistics is not good enough to verify this effect and draw final conclusions, this could be related to the abrupt changes observed for the Cu_pl-O_ap in the system Y_1−yCa_yBa₂Cu₃O₇ (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.

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 [122,123,124] prove that these phases coexist in the YBa₂Cu₃O_x 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 B_1g 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 La_2−xSr_xCuO₄ 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 T_c.

Raman studies on other high T_c compounds, such as the diborides [60,62,63,102] and the pnictides [103,104,105], 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.