Longitudinal conduction electron spin waves (Larmor waves) in tungsten

The 9.1 GHz microwave transmission spectrum against magnetic field of a high-purity tungsten single crystal coated with ferromagnetic layers is investigated. A strong transmission peak at the ferromagnetic resonance of the coating layers is attributed to longitudinal single electron spin waves (Larmor waves). The wavelength of the spin waves was determined from the magnetic field angle dependence of the transmission peak and by applying simple considerations the Fermi velocity around the [111] direction was derived. To test the idea of longitudinal waves the Fermi velocity in the (110) plane was calculated by using an ab initio band calculation. The effects of spin-orbit and electron-phonon interactions are discussed and it is concluded that taking into consideration these effects and the uncertainties in deriving the Fermi velocity, the phenomenon observed is qualitatively well described by longitudinal spin waves. The experiment also supports a phenomenological model of the coupling of magnetisations at a paramagnetic-ferromagnetic interface. (author)