The influence of quenched disorder on the competition between ordered states separated by a first-order transition is investigated. A phase diagram with features resembling quantum-critical behavior is observed, even using classical models. The low-temperature paramagnetic regime consists of coexisting ordered clusters, with randomnly oriented order parameters. Extended to manganites, this state is argued to have a colossal magnetoresistance effect. A scale T * for cluster formation is discussed. This is the analog of the Griffiths temperature, but for the case of two competing orders, producing a strong susceptibility to external fields. Cuprates may have similar features, compatible with the large proximity effect of the very underdoped regime.PACS numbers: 75.30.Kz Complex phenomena such as "colossal" magnetoresistance (CMR) in manganites and high temperature superconductivity (HTS) in cuprates have challenged our understanding of correlated electrons [1]. Recent developments unveiled a previously mostly ignored aspect of doped transition-metal-oxides (TMO): these systems are intrinsically inhomogeneous, even in the best crystals. (i) The evidence in the CMR context is overwhelming. Experiments and theory provide a picture where competing ferromagnetic (FM) and charge-ordered (CO) states form microscopic and/or mesoscopic coexisting clusters [2,3]. Exciting recent experiments [4] identified features referred to as a "quantum critical point" (QCP) [5] -defined as the drastic reduction of ordering temperatures near the zero temperature (T=0) transition between ordered states -by modifying the A-site cation mean-radius r A by chemical substitution at fixed hole density (left inset of Fig. 1). The paramagnetic state in the QCP region -where the Curie temperature T C is the lowest -is crucial to understand CMR phenomenology, producing the largest CMR ratio [1,2,3]. (ii) In the HTS context, scanning tunneling microscopy (STM) studies of superconducting (SC) Bi2212 revealed a complex surface with nm-size coexisting clusters [6]. Underdoped cuprates also appear to be inhomogeneous [7]. In addition, a "colossal" proximity effect (CPE) was reported on underdoped YBa 2 Cu 3 O 6+x over large distances [8].In this paper, the competition between two ordered states in the presence of quenched disorder is investigated. These states are assumed sufficiently "different" that their low-T transition in the clean limit has firstorder characteristics. The approach has similarities with the classical work of Imry and Ma [9]. From the general considerations, doped TMOs are here considered, with intrinsic disorder caused by chemical substitution. For Mn-oxides, a possible rationalization of the CMR effect is discussed, with predictions including a scale T * for cluster formation -the analog of the Griffiths temperature [10] but in the regime of competing orders. For underdoped Cu-oxides, a similar inhomogeneous picture is proposed. The calculations are mainly carried out using a two dimensional (2D) toy model of Ising spins, but ...

Previous theoretical investigations of colossal magnetoresistance (CMR) materials explain this effect using a "clustered" state with preformed ferromagnetic islands that rapidly align their moments with increasing external magnetic fields. While qualitatively successful, explicit calculations indicate drastically different typical resistivity values in two- and three-dimensional lattices, contrary to experimental observations. This conceptual bottleneck in the phase-separated CMR scenario is resolved here considering the cooperative nature of the Mn-oxide lattice distortions. This effectively induces power-law correlations in the quenched disorder used in toy models with phase competition. When these effects are incorporated, resistor-network calculations reveal very similar results in two and three dimensions, qualitatively modifying previous scenarios and solving the puzzle.

A recent vast experimental and theoretical effort in manganites has shown that the colossal magnetoresistance effect can be understood based on the competition of charge-ordered and ferromagnetic phases. The general aspects of the theoretical description appear to be valid for any compound with intrinsic phase competition. In high temperature superconductors, recent experiments have shown the existence of intrinsic inhomogeneities in many materials, revealing a phenomenology quite similar to that of manganese oxides. Here, the results for manganites are briefly reviewed with emphasis on the general aspects. In addition, theoretical speculations are formulated in the context of Cu-oxides by mere analogy with manganites. This includes a tentative explanation of the spin-glass regime as a mixture of antiferromagnetic and superconducting islands, the rationalization of the pseudogap temperature T * as a Griffiths temperature where clusters start forming upon cooling, the prediction of "colossal" effects in cuprates, and the observation that quenched disorder may be far more relevant in Cu-oxides than previously anticipated.