Spin Susceptibility in High - TC Superconductivity

Mi Umo

doi:10.4314/gjpas.v18i3-4.12

Abstract

Spin- current loop fluctuations is proposed as the mechanism of holes pairing in high temperature superconductors using the assumption of the coexistence of short-ranged antiferromagnetism with superconductivity and the Anderson’s superexchange theory. The spin-spin correlation function is calculated using the Kubo-Mori relaxation function and the magnetic susceptibility equation is derived in terms of force correlation. Also a Bardeen –Cooper-Schrieffer (BCS) type of equation is solved for the transition temperature (Tc). KEY WORDS: Superconductivity, cuprates, superexchange, susceptibility.

Highlights

The problem of formation and stabilization of ferromagnets(FM) and antiferromagnets (AFM) was explained by Hubbard(Hubbard, 1963)
The first high temperature superconductor was discovered in 1986 in the ceramic La2-xSrxCuO4, where the parent compound is AFM (Bednorz, Muller,1986).It was soon observed that it is the CuO plane that is responsible for the pairing of holes, coherence and superconductivity
),the ground state of the parent compound has electrons taken from or holes added to the Cu sites

Summary

INTRODUCTION

The problem of formation and stabilization of ferromagnets(FM) and antiferromagnets (AFM) was explained by Hubbard(Hubbard, 1963). One of the holes hops to the neighbouring Cu-A site resulting in Cu3+ (3d9).The remaining hole is in direct exchange with Cu-B ion with exchange integral J.This process is the superexchange mechanism and is based on Hunds rules It portrays the AFM interaction between two sublattice Cu spins as due to mediation of the ligand oxygen. To lower the kinetic energy, a hole’s spin hooks up with the random Cu moment to form a quasiparticle, two such quasiparticles reach out to each other magnetically to form spin singlet pairs with d-wave symmetry This process is made clearer in the quantum mechanics of entanglements, where for the AFM subsystems A,B the classical correlation for the density matrix is given as.

The Fourier transform of the equation of motion is

26 We can differentiate the last expression to obtain