Magnetic and thermal properties of nanoscale heavy-fermion particles

Abstract

The heavy-fermion state in some rare-earth and actinide compounds arises from a hybridization of extended conduction states with strongly correlated localized f states. The properties of the heavy fermions are those of a Fermi liquid with small Fermi energy of the order of ${T}_{K}.$ In nanosized particles, however, the conduction states have discrete energy levels and the energy spacing leads to an additional energy scale that competes with the Kondo temperature. A small heavy-fermion particle is considered, described by the Anderson model in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, so that only two electronic configurations---namely, ${f}^{0}$ and ${f}^{1}$---are allowed. A mean-field approximation with one slave boson per f site is used to study the susceptibility, the entropy, and the specific heat at low temperatures. All quantities increase rapidly with T as a consequence of exponential activations due to the discreteness of the energy spectrum until the heavy-electron state is formed. The possibility of ferromagnetic order is investigated using the formulation of Kotliar and Ruckenstein in terms of three auxiliary bosons per site. The mean-field approximation yields several possible magnetic phases for the ground state as a function of the f-level position. In the strongly mixed-valent regime the transition from the paramagnetic to the ferromagnetic phase is signaled as a function of temperature by a diverging susceptibility. It is concluded that the thermal and magnetic properties of very small heavy-fermion particles are quite different from those of bulk heavy-fermion material.