Two-fluid behavior of the Kondo lattice in the $1/N$ slave boson approach.*

It has been recently shown by Nakatsuji, Pines, and Fisk [S. Nakatsuji, D. Pines, and Z. Fisk, Phys. Rev. Lett. \textbf {92}, 016401 (2004)] from the phenomenological analysis of experiments in Ce$_{1-x}$La$_x$CoIn$_5$ and CeIrIn$_5$ that thermodynamic and transport properties of Kondo lattices below coherence temperature can be very successfully described in terms of a two-fluid model, with ``Kondo gas" (interacting magnetic moments) and ``Kondo liquid" (heavy electron Fermi liquid) contributions. We analyze thermodynamic properties of Kondo lattices using $1/N$ slave boson treatment of the periodic Anderson model and show that these two contributions indeed appear below the coherence temperature. We find that the ``Kondo gas" contribution to thermodynamics corresponds to thermal excitations into the flat portion of the energy spectrum. As a result, the relative fraction of ``Kondo gas" depends exponentially on temperature, rather than linearly in experiment.