Sound Attenuation in Magnetic Metals

Abstract

The anomalous sound attenuation due to spin fluctuations near the magnetic phase transition temperatures in itinerant magnets and the rare earth metals is theoretically studied. By applying Tsuneto and Kadanoff and Falko's formulas, the attenuation coefficient is calculated. The calculated results explain the critical anomalies observed in magnetic metals such as Ni and Gd. By comparing the results with that for insulating magnets, the expression of the exchange striction is obtained. The effect of magnetic field on the critical attenuation is discussed. ferro­ magnets. In this paper, we formulate the attenuation coefficient clue to spin fluc­ tuations and show that the expression of the coefficient in itinerant electron systems is essentially the same as that in localized spin systems. Through this study, the meaning of the exchange strictive interaction in itinerant magnets is clarified. Tsuneto, 8J and Kadanoff and Falko 9J have given an expression for the attenu­ ation coefficient applicable to the system in which the electronic state is strongly modified from the free electron state by impurity and electron-electron interaction. We apply their formula and obtain the critical attenuation coefficients near the magnetic phase transition temperatures in itinerant magnets (§ 2) and the rare earth metals (§ 3). In our formalism, the attenuation coefficient is expressed in terms of the correlation functions of electron-hole pairs. The excitation energy of electron-hole pair is renormalized due to spin fluctuations and the spectral den­ sities at low energies are extremely enhanced near the critical temperature. This enhancement causes the critical attenuation of sound. vVhen the results obtained in §§ 2 and 3 are compared with that of localized spin systems, the meaning of the exchange striction in magnetic metals becomes clear as will be shown in § 4. In the final section (§ 5), the effect of external magnetic field on the attenuation is discussed. In this paper, we neglect the spin­ orbit coupling.