Kondo insulators like ${\mathrm{Ce}}_3$${\mathrm{Bi}}_4$${\mathrm{Pt}}_3$ and CeNiSn are compounds with small-gap semiconductor properties. The Kondo insulator is described by the nondegenerate symmetric Anderson lattice with, on average, two electrons per site within Kotliar and Ruckenstein’s mean-field approximation in terms of four slave bosons per site. A Kondo hole is the charge neutral substitution of a rare earth or actinide atom by a nonmagnetic analog. An isolated Kondo hole gives rise to a bound state in the gap, which pins the Fermi level and has magnetic properties. A finite concentration of Kondo holes generates an impurity band in the gap of the semiconductor. The low-temperature thermodynamic and transport properties are determined by the impurity band. The interplay of the f-electron correlations with the impurity band is studied in the paramagnetic phase. On a bipartite lattice the pure Kondo insulator is unstable to long-range antiferromagnetism for U≳${\mathit{U}}_{\mathit{c}}$ and to ferromagnetism in sufficiently large magnetic fields. A small concentration of Kondo holes reduces the threshold for the antiferromagnetic transition, giving rise to reentrance, but does not substantially affect ferromagnetism. © 1996 The American Physical Society.

• Received 28 May 1996

DOI:https://doi.org/10.1103/PhysRevB.54.12324