Magnetic instabilities in Kondo insulators

Kondo insulators such as ${\mathrm{Ce}}_3$ ${\mathrm{Bi}}_4$ ${\mathrm{Pt}}_3$ and CeNiSn are small-gap semiconductor compounds. We consider a stoichiometric Kondo insulator described by the symmetric Anderson lattice without orbital degeneracy and on average two electrons per site. We use a Gutzwiller-type mean-field approximation formulated in terms of four slave bosons per site in analogy with Kotliar and Ruckenstein’s approach for the Hubbard model. A hybridization gap on the scale of the Kondo temperature opens in the paramagnetic phase, giving rise to the semiconducting properties at low temperatures. The paramagnetic solution is stable for sufficiently small U, but not stable with respect to a metallic ferromagnetic phase if U>1.54V (first-order transition) and antiferromagnetic long-range order for U>0.45V (second-order transition). In zero field the energy of the antiferromagnetic phase is always lower than the energy of the ferromagnetic state. Quantum fluctuations and the Ruderman-Kittel-Kasuya-Yosida interaction are expected to stabilize the paramagnetic and antiferromagnetic phases as compared to the ferromagnetic one. We also discuss the effects of a strong magnetic field.