Disorder and frustration effects on the metal insulator transition in the Y1-xAxBa2Cu3O6+y system (A=Eu,Nd,Ca) from the clean to the dirty limit.

Copper perovskites give rise to one of the most surprising phenomena in solid state physics, that is the highest-temperature known superconductivity (up to 140 K) in a material on the verge of becoming an insulator. Since their discovery in 1986, they have attracted the attention of the scientific community both for the possibility of applications, and from the point of view of the fundamental physics. After 25 years the applications exist, although they are fewer than one hoped, and many properties have been clari ed, including the non conventional origin of superconductivity. Nowadays cuprates are among the best known materials in condensed matter and yet the detailed nature of the high-Tc superconductivity is elusive. The cuprate properties are determined by the electronic behaviour of the CuO2 planes, characteristic of their structures. One of the distinctive features of these compounds is that it is possible to vary their properties by acting on their stoichiometry. Starting from an antiferromagnetic (AF) Mott-Hubbard insulating parent compound (TN=400 K) it is possible to reach a high-Tc superconducting phase (Tc=100 K) in an almost continuous fashion. This is accomplished by doping charge carriers into the CuO2 planes. All cuprates show a long range AF phase in the parent compound. Their Néel temperature TN is reduced upon doping, in a way that is dependent on the specific compound. When the Néel order is fully suppressed, a so called cluster spin glass phase (CSG) sets in, characterized by very low order temperatures (Tg <30 K) and short magnetic correlation length. The CSG phase gives way to the strongly correlated superconductor (SC), and these two orders coexist nanoscopically for a sizeable range of doping. The passage from the AF to the SC phase through the CSG corresponds to a metal to insulator transition (MIT), and understanding how doping and disorder infl uence this transition may help to unveil the high- Tc superconductivity mechanism. In particular in the literature disorder on the CuO2 planes appears to have a strongly in uence on the MIT, and on the CSG phase, whose nature is actually debated. Disorder on the CuO2 planes can be varied by the controlled substitution of an adjacent cation with another of different valence and size, providing two independent parameter to control the MI transition: disorder by localized Coulomb impurities and random localized distortions. In this work we decided to investigate extensively the low-doping range, starting from the undistorted clean limit case of YBa2Cu3O6+y, where the charge doping on the CuO2 layers is obtained by the introduction of oxygen atoms farther removed from such planes. Besides pure YBa2Cu3O6+y (Y100% in the following) we addressed other compositions. In particular two additional compositions were chosen to investigate the effect of small lattice distortions on the magnetic phase diagram by substitution of Y with a rare earth: Y0:92Eu0:08Ba2Cu3- O6+y (Eu8%), yielding a very small mismatch of the cation radii, and Y0:925Nd0:075Ba2Cu3- O6+y (Nd7.5%), yielding equivalent mismatch to that of the Y0:95Ca0:05Ba2Cu3O6+y (Ca5%) substitution. We further chose to investigate increasing Ca compositions in the Y1-xCaxBa2Cu3O6+y compound (x= 0.01, 0.05, 0.065, 0.08, 0.11, 0.14 and 0.18). Differently from the (Y3+)-isovalent Eu and Nd substitutions, Ca2+ introduces a strong Coulomb disordered perturbation. For each Ca content (i.e. fixed disorder) we spanned several dopings by varying the oxygen con- tent, therefore isolating the disorder from the doping effects. All the samples studied in this work are polycrystalline materials that we prepared in our synthesis laboratory. Many techniques have been exploited in preliminary analysis of the compounds. X-ray dicffraction and neutron scattering for structural analysis, resistivity and thermopower for transport, iodometric titration for chemistry, SQUID magnetometry for superconductivity. We selected muon spin spectroscopy (muSR) as a local probe sensitive both to static magnetic order and to the presence of a ux-lattice in the superconducting state. This technique reveals a number of evident trends, showing that the isovalent substitution a ects negligibly both the magnetic behavior and the MI transition, while Ca replacement has a marked in uence on both the magnetic and superconductive behaviour, suggesting this in uence to be speci cally linked to the introduction of a charged impurity. I conclude this abstract by summarizing the main results for the clean and dirty limit cuprates. First of all we have extensively investigated YBCO in the antiferromagnetic low doping region as a model for the clean limit cuprates. Since the in fuence of disorder induced by Nd and Eu is found to be negligible (clean limit), we extract the parameters of the low temperature re-entrant and of the thermally activated regimes from the whole set of data. The crossover between these two regimes is undoubtedly associated with the thermal activation of both spin and charge degrees of freedom. This is implemented in a single phenomenological model for the temperature and doping dependence of the reduced moment m(h;T), which fits our data throughout the entire investigated range. Our analysis leads to the identification of a common ground state for very different doping regimes at the two sides of the metal-insulator transition, the re-entrant antiferromagnetic phase (on the left) and the so-called cluster spin glass phase coexisting with superconductivity (on the right). Since this unique ground state shows characteristics of a well ordered phase, not distinctive of a disordered spin glass, we dub this unique state a quenched antiferromagnet (QAF). In the QAF state the ordered magnetic moment is subject to negligible frustration and it follows the same trend of magnetic site dilution. Conversely the fast drop of TN(h) and of the staggered moment, mA(h) are characteristic of the thermally activated antiferromagnetic phase (TAAF). Since the AF superexchange itself is not reduced by doping this indicates that a mechanism leading to strong frustration must be present. In the text I present a qualitative discussion of the possible connection between the frustration in the TAAF state and either spiral states or stripes. Furthermore, we indicate that the main boundaries in the clean-limit phase diagram, de- scribing the two main order parameters, magnetic and superconducting, both follow parabolic curves, sharing a zero temperature intersection at h = hc = hs. This behaviour identi es at hc = 0:056 a quantum critical point for the cuprates clean limit. The QCP is then superseded by the QAF behavior of the real-world compound at low temperatures. The dirty limit case is de ned by the Coulomb perturbation due to the controlled Ca sub- stitutions in the proximity of the CuO2 layers. Here the identi cation of the low temperature magnetic states with the QAF extends to the window of pure CSG state characteristic of the dirty compounds. This state is unique, and common to both the clean and dirty limits, and is characterized by charge localization and a magnetism just diluted by doping and almost insensitive to disorder. On the contrary the high temperature states, i.e. the TAAF and SC regimes, are strongly infl uenced by the Coulomb-impurity-driven disorder introduced by Ca, that progressively unveils the underlying QAF. On the left side of the QCP, the suppression of the TAAF state appears to be enhanced by disorder, that amplifies the disruptive effect of thermal activation. It suddenly falls the TAAF state into the underlying QAF via a first order transition, pushing aside the relative critical hole concentration hc(x) proportionally to x. On the right side of the QPC the effect of disorder appears to be nearly symmetric. It raises the threshold hs(x) for the onset of a superconducting condensate ns, by reducing the hole density available for superconductivity. However all the holes injected in the system contribute to the room temperature properties, indicating again some form of charge carriers temperature activation, hidden to resistivity measurements by the superconductor. It is interesting to note that whereas disorder suppresses both TAAF and SC, it does not modify the metallic character of high temperature transport, corresponding to the so called bad metal state. This state appears by thermal activation on the left of the QCP, but it is one of the two T = 0 ground states on the right, where SC sets in. For low temperatures the bad metal is very sensitive to charged impurity disorder, leading to the suppression of both its competing AF and SC order parameters, but not of its bad metal character. We have therefore produced a 3D-phase diagram, where the additional Coulomb disorder axis x, disentangled from doping, is shown to be a fundamental ingredient in the description of such complex systems.