Magnetic impurities in a correlated electron system with spin-triplet pairing

Abstract

We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a δ -function spin-exchange potential. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). 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 the impurities and the Kondo exchange coupling. In the zero-field ground state the spin-triplet states are effectively free bosons and a threshold band splitting Δ is required to break up a triplet pair. The gap of the unpaired electron excitations is gradually reduced by the band splitting and closes at Δ . For a splitting larger than Δ 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 as well as to gradually align the spins of the spin-triplets with the field. Spin- 1 2 impurities always enhance the gap Δ , while with impurities of higher spin the gap decreases if the coupling between the triplets and impurities is weak (small Kondo temperature), but increases otherwise. For small T K the gap is closed at a critical concentration x cr and the two electron bands have different populations. For x > x cr we obtain a zero-magnetization phase with three coexisting components, namely, itinerant ferromagnetism of unpaired electrons, antiferromagnetism of the impurities and superconducting fluctuations of ferromagnetically correlated spin triplets. The critical exponents of correlation functions are also briefly discussed in the conformal field theory limit.