Spin-gapped two-band correlated electron system with magnetic impurities

Abstract

We consider an integrable model consisting of two parabolic bands of electrons of equal mass interacting via a δ-function exchange potential. The exchange is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet. Without destroying the integrability we introduce a finite concentration of mixed-valent impurities with two magnetic configurations of spin S and (S+ 1 2 ) , respectively, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the correlated host with impurities and discuss the ground state properties as a function of magnetic field, the crystalline field splitting of the bands, the concentration of impurities and the Kondo exchange coupling. The attractive interaction in the host leads to Cooper-pair-like bound states, and a magnetic field larger than a critical one H c is required to break up the singlet pairs. The spin-gap is gradually reduced by a magnetic field and closes at H c. For H> H c a fraction of the electrons is spin-polarized. The impurities are antiferromagnetically correlated with each other and the effect of a magnetic field is to suppress these correlations, which are totally quenched at the saturation field H s. Depending on the off-resonance shift θ of the impurities the spin-gap may decrease or increase linearly with the concentration of impurities. For small θ and a weak interaction among the electrons the spin-gap is closed at a critical concentration x cr. For x> x F> x cr ferromagnetism is induced, so that three phases coexist, namely itinerant ferromagnetism, ferrimagnetism of the impurity spins and superconducting fluctuations. The constructive interference between antiferromagnetic and superconducting fluctuations for large θ could be related to the spin-compensation of the impurity spins among each other and the dominating forward scattering of the impurities. The critical exponents of correlation functions are also briefly discussed in the conformal field theory limit.