Study of ultrasonic attenuation for the Kondo and magnetic effects in heavy fermion systems

Abstract

The heavy fermion (HF) systems draw considerable attention due to their cooperative phenomena and anomalous properties arising out of the huge effective mass. A heavy fermion system is described by a model Hamiltonian consisting of the Kondo lattice model in addition to the Heisenberg-type spin-spin interaction among the localised electrons. The Hamiltonian is treated in the mean-field approximation to find the Kondo singlet parameter λ and the short-ranged f-electron correlation parameter Γ. In order to investigate ultrasonic absorption in the system, we consider the phonon interaction with the bare f-electrons, and the phonon coupling to the Kondo singlets. Further, the phonon Hamiltonian is considered in the harmonic approximation. The phonon Green’s function is calculated in closed form. The imaginary part of the phonon self-energy describes the ultrasonic attenuation for the HF systems. The calculated ultrasonic attenuation clearly displays the f-electron correlation region separated by the Kondo singlet state at low temperatures. The correlation transition temperature and the Kondo temperature are located at dips in the temperature-dependent ultrasonic attenuation. The parameter dependence of the attenuation is investigated by varying the physical parameters of the HF systems and the wave frequency, and the experimental observations are explained on the basis of the model calculations.