Collective Oscillations in a Simple Metal. I. Spin Waves

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Abstract
Using the Landau theory of Fermi liquids, we analyze the paramagnetic behavior of the alkali metals at low temperatures. An integral formulation of the kinetic equations is derived, and this is solved for arbitrary wavelengths (within the limits of Landau's theory), for arbitrary direction of propagation and retaining an arbitrarily large number of the Landau interaction coefficients. We derive a practical algorithm for obtaining the transverse and longitudinal susceptibilities; this enables us to discuss, with the generality just outlined, all of the collective magnetization modes, as well as the features of individual-particle excitations in a simple metal with spherical Fermi surface. The effects of scattering from dilute, random impurities are also included. We catalog systematically the dispersion properties as well as the oscillator strengths of all of these waves. Comparison of the results with the experiments of Schultz and Dunifer is described, and the feasibility of observing the various spin-wave modes is discussed.