Spin fluctuations in cuprates as the key to high $T_c$.pdf

a r X i v : c o n d - m a t / 0 6 0 1 5 1 1 v 1 [ c o n d - m a t .s t r - e l ] 2 3 J a n 2 0 0 6 Spin fluctuations in cuprates as the key to high Tc P. Prelov?ek ?,? , I. Sega ? , A. Ram?ak ?,? and J. Bonc?a ?,? ? Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia ? J. Stefan Institute, Ljubljana, Slovenia Abstract. Spin fluctuations represent the lowest established energy scale in cuprates and are crucial for the understanding of anomalous normal state properties and superconductivity in these materials [1]. The memory-function approach to the spin response in the t-J model is described. Combined with numerical results for small systems it is able to explain the anomalous scaling at low doping and the crossover to the Fermi-liquid-like behavior in overdoped systems. Within the superconducting phase the theory reproduces the resonant peak and its peculiar double dispersion. Such spin fluctu- ations are then used as the input for the theory of superconductivity within the t-J model, where we show that an important role is played also by the next-nearest-neighbour hopping parameter t ′ . Keywords: cuprates, spin fluctuations, non-Fermi liquid, resonant peak, superconductivity PACS: 71.27.+a, 74.72.-h, 75.10.Lp INTRODUCTION The phase diagram of cuprates still represents one of the major challenges in solid state physics, both for theoreticians and experimentalists. Besides superconductivity (SC) and antiferromagnetic (AFM) ordering, several regimes with distinct electronic properties have been identified within the normal metallic phase. In this contribution, we are con- cerned with the spin dynamical response in cuprates which has been intensively studied using the inelastic neutron scattering (INS) [2, 3] and NMR relaxation experiments [4]. There is an abundant evidence that in underdoped cuprates magnetic properties are not following the usual Fermi-liquid (FL) scenario within the metallic state above the SC transition T Tc.