ELSEVIER Journal of Magnetism and Magnetic Materials 140-144 (1995) 1273-1274 Journal of magnetism , J H and magnetic , 4 ~ materials Spin susceptibility of correlated systems beyond random phase approximation Karol I. Wysokifiski *, T. Domafiski Institute of Physics, M. Curie Sktodowska University, ul. RadziszewskiegoI OA, PL-20 031 Lublin, Poland Abstract The spin susceptibility has been calculated for systems described by the 'correlated hopping' model. RPA and Hubbard-Jain approximations are used in the weak and strong coupling limits. Carrier concentration dependence of susceptibility in strong coupling limit agrees with experiments on copper oxides. The purpose of this paper is to present the results of our study of the nature of magnetic excitations in a system described by the 'correlated hopping' model [1,2]. We use the method which in principle enables us to go beyond the Random Phase Approximation (RPA). It is based on spe- cial type of decoupling of the Green's functions defined in the Hilbert subspace of empty and singly occupied sites. The method has been originally proposed by Hubbard and Jain [3] for the system described by the standard Hubbard Hamiltonian. Here we apply it to a more general model, which despite of the kinetic and on-site repulsion U terms possesses a term Kij(ni_ o. -F nj_,,_)c~,,_cj,,, which pro- motes the hopping of spin o- electron (hole) from site j to i provided one of the sites is occupied by spin -o- electron (hole). The Kij term has been shown to induce the superconductivity in the system [1,2]. This model which is supposed to describe carriers in the two dimensional square lattice has few parameters. These are the values of U, K measured in the units of bandwidth D and the electron concentration n. In this contribution we limit our discussion to the static w = 0 limit of the frequency and wave vector q dependent sus- ceptibility x(q, o~). We omit here all the technical details which can be found in Ref. [4], where x(q, w) has been studied in weak (U <D) and strong (U > D) coupling limits. Here we merely discuss some of the results. The normal state susceptibility of high temperature superconductors does depend on carrier concentration in a nonmonotonous manner [5], taking on a maximum value for some nonzero concentration of holes. Moreover its temperature dependence shows different behavior for the * Corresponding author. Fax: +48-81-33 669; email: karol@golem.umcs.lublin.pl. underdoped and overdoped samples [6] (i.e. samples with carrier concentration lower or higher than the optimal doping leading to the highest superconducting transition temperature). In Fig. 1 we show the carrier concentration and wave vector q dependence of the susceptibility for K/D = 1 and U >> D at temperature T= 0.01D. As seen in the figure, susceptibility for point qM = (aT, aT) of the two-dimen- sional Brillouin zone (we take the lattice constant a = 1) is strongly enhanced for some value of n. For small hole concentrations and at low temperatures x(q) shows a pronounced peak which indicates strong antiferromagnetic fluctuations. It is important to note that the increase of the value of K increases this peak. On the other hand, the increase of K strongly reduces susceptibility for small carrier concentrations n < 0.6, increases it around the peak n ~ 0.6 and leads to very minute changes at higher concen- trations (see Fig. 2). Fig. 1. Static, wave vector dependent susceptibility in the strong coupling limit (U >> D) for the main directions of the square, two-dimensional Brillouin zone and carrier concentration n ~ [0, 1] for K/D = 1, T = O.O1D. 0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00665-2