We report on measurements of the resistivity and Hall coefficient in underdoped GdBa 2 Cu 3 O 7Ϫ␦ epitaxial thin films grown by off-axis magnetron sputtering. The films have been lithographically patterned allowing precise measurements of the temperature dependencies of the inverse Hall constant R H Ϫ1 and of the Hall angle H . We find that R H Ϫ1 is linear in temperature between 300 K and the pseudogap temperature T*, whereas cot( H ) displays a perfect T 2 temperature dependence typically between 300 and 100 K. We observe for all the samples that the temperature at which the temperature dependence of cot( H ) deviates from the T 2 behavior is correlated to the temperature at which R H displays a peak. This characteristic temperature, found to lie between T c and T*, does not depend markedly on the doping level and defines a crossover line in the temperature versus doping phase diagram. We tentatively relate these findings to recent high-frequency conductivity and Nernst effect experimental results, and we briefly discuss the possible consequences for competing theories for the pseudogap state of the cuprates.

We calculated the electronic structure of a vortex in a pseudogapped superconductor within a model featuring strong correlations. With increasing strength of the correlations, the BCS core states are suppressed and the spectra inside and outside the core become similar. If the correlations are short range, we find new core states in agreement with the observations in YBa 2 Cu 3 O 72d and Bi 2 Sr 2 CaCu 2 O 81d . Our results point to a common phenomenology for these two systems and indicate that normal-state correlations survive below T c without taking part in the overall phase coherence.

A phenomenological theory of superconductivity based on the two-body Cooperon propagator is presented. This theory takes the form of a modified Gorkov equation for the Green's function and allows one to model the effect of local superconducting correlations and long-range phase fluctuations on the spectral properties of high-temperature superconductors, both above and below T c . A model is proposed for the Cooperon propagator, which provides a simple physical picture of the pseudogap phenomenon, as well as insights into the doping dependence of the spectral properties. Numerical calculations of the density of states and spectral functions based on this model are also presented, and compared with the experimental tunneling ͑STM͒ and photoemission ͑ARPES͒ data. It is found, in particular, that the sharpness of the peaks in the density of states is related to the strength and the range of the superconducting correlations and that the apparent pseudogap in STM and ARPES can be different, although the underlying model is the same.

The various mechanisms for the magnetic relaxation of nuclei via magnetic impurities in metals are discussed and compared with each other. It is shown that two of the mechanisms proposed earlier [1, 2, 3] can be derived in a unified way in the random phase approximation, and this leads to a clear understanding of the physics involved and of the possible extensions. The possible importance of the mechanisms involving direct dipolar coupling and pseudo-dipolar coupling (via the conduction electrons) is pointed out. A comparison is made with the available data on the CuMn and the CdMn systems, and a serious discrepancy between theory and experiment is pointed out

Recent electron paramagnetic resonance (EPR) experiments on metals and alloys of high paramagnetic susceptibility (Pd and NigLa) 1 " 3 have shown an anomalous long range of the spin polarization around magnetic impurities. Wolff 4 has suggested that the exchange interaction between valence electrons in metals will increase the range of the polarization in space. By connecting the enhancement of the polarization in momentum space with the observed uniform susceptibility of the studied metal, we have found that exchange interactions can bring predicted and observed data into agreement.The susceptibility function of a system is defined by its linear response to an external magnetic field. If the system is homogeneous,where (M(q,f)), x(q,0 are the spatial Fourier transforms of (M(r,£)),x( r >0, respectively. For an electron gas, x is given by where andV is the volume of the system, 10) is the ground state of the isolated system, and T is the time ordering operator. EPR measurements of magnetic impurities in metals allow one to get some insight into the shape of this function.In a series of recent experiments, the shift and the broadening of the EPR lines of 2% Gd (im-purity A) in a matrix formed by 96% of high-susceptibility metals and 2 % of additional magnetic impurities (B) have been studied. 1 The magnetic moment of rare earth impurities was found to be practically equal to their ionic moment, contrary to transition elements, which show giant moments in solid solution in Pd alloys. 5 The deformation of the EPR line of Gd in the matrix is very sensitive to the shape of the susceptibility function. This can be best understood by thinking first of only one ion of Gd in the host metal: Each magnetic inpurity B will polarize the valence electrons of the host metal and will therefore shift the g value of the Gd ion. The magnitude of this shift will depend on the value of the susceptibility function of the host metal at the Gd site. Since the magnetic impurities are distributed at random, the statistical average over all Gd ions will give both a displacement and a deformation of the resonance line.The shift of a resonance line is defined bywhere H 0 is the center of the nonperturbed line and 1(H) the perturbed intensity line; and the mean square deviation byOne can express 5 and B in terms of x(?) = J X(r, t)dt\ s = c B n Q a yh(x>Pr 9 B = c B n 0 a 2 ±f X 2 (r)d 3 r,where eg is the concentration of magnetic impurities in the matrix, n 0 the number of lattice sites per cc, and a is a constant depending on the characteristics of the system. The value of the ratio of the shift squared to the mean square 736