Magnetic instability of a highly degenerate Kondo lattice

The large-degeneracy (N) limit of the periodic Anderson model is studied within a model in which the hybridization matrix elements $v_k$,m are treated as angle dependent. The resulting effective heavy-fermion Fermi surface is multisheeted, with quasi-one-dimensional bands. A spin-density-wave instability with wave vector 2$k_f$ is shown to arise below a critical value of the effective Schrieffer-Wolff coupling constant J=$v^2$/‖${\varepsilon }_f^0$‖, where ${\varepsilon }_f^0$ is the unrenormalized f-level energy. The dependence of this critical coupling $J_c$ on crystal field splitting is shown to be quite weak. For systems with J close to $J_c$, the effects of zero-point spin-density-wave fluctuations are shown to decrease the heavy-fermion mass at T=0. For increasing temperature, this decrease is rapidly washed out, leading to an initial increase of the low-temperature γ value. This behavior provides an interpretation of specific-heat observations in ${\mathrm{CeAl}}_3$ and ${\mathrm{CeCu}}_2$ ${\mathrm{Si}}_2$. The effect of applied field and pressure on the specific heat are discussed in the context of this theory.