Experimental determination of the Landau Fermi-liquid-theory parameters: Spin waves in sodium and potassium

Abstract

This paper presents the results of a study made on spin waves in high-purity sodium and potassium foils at cryogenic temperatures (1.4-10°K). The measurements were made using the microwave transmission technique at $X$-band microwave frequencies. Spin waves in an alkali metal are a mode of excitation of the conduction electrons that exists solely due to the interactions, or many-body effects, among the electrons. We present a description of the general properties of the spin waves, such as their dependence upon sample purity, temperature, magnetic field orientation, thickness, and other relevant parameters. By comparing the experimental data with detailed theoretical line-shape formulas derived from the Landau Fermi-liquid theory, we are able to deduce values for the first three Legendre coefficients of the spin-dependent part of the Landau interaction function. The values are $B_0=-0.215\mathrm{}\pm 0.03$, $B_1=-0.005\mathrm{}\pm 0.04$, and $B_2=0.0\mathrm{}\pm 0.05$ for sodium; and $B_0=-0.285\mathrm{}\pm 0.02$, $B_1=-0.06\mathrm{}\pm 0.03$, and $B_2=0.0\mathrm{}\pm 0.05$ for potassium. The numbers we obtained are compared with results from other methods, both experimental and theoretical, where applicable. A discussion of the difficulties encountered in determining the coefficients is given along with a description of the experimental techniques we have used. Finally, we consider how these measurements might be extended in the future to yield further information on interacting conduction-electron systems.