Theory of laser-induced ultrafast superdiffusive spin transport in layered heterostructures

Femtosecond laser excitation of a ferromagnetic material creates energetic spin-polarized electrons that have anomalous transport characteristics. We develop a semiclassical theory that is specifically dedicated to capture the transport of laser-excited nonequilibrium (NEQ) electrons. The randomly occurring multiple electronic collisions, which give rise to electron thermalization, are treated exactly and we include the generation of electron cascades due to inelastic electron-electron scatterings. The developed theory can, moreover, treat the presence of several different layers in the laser-irradiated material. The derived spin-dependent transport equation is solved numerically and it is shown that the hot NEQ electron spin transport occurs neither in the diffusive nor ballistic regime, it is superdiffusive. As the excited spin majority and minority electrons in typical transition-metal ferromagnets (e.g., Fe, Ni) have distinct, energy-dependent lifetimes, fast spin dynamics in the femtosecond (fs) regime is generated, causing effectively a spin current. As examples, we solve the resulting spin dynamics numerically for typical heterostructures, specifically, a ferromagnetic/nonmagnetic metallic layered junction (i.e., Fe/Al and Ni/Al) and a ferromagnetic/nonmagnetic insulator junction (Fe or Ni layer on a large band-gap insulator as, e.g., MgO). For the ferromagnetic/nonmagnetic metallic junction where the ferromagnetic layer is laser-excited, the computed spin dynamics shows that injection of a superdiffusive spin current in the nonmagnetic layer (Al) is achieved. The injected spin current consists of screened NEQ, mobile majority-spin electrons and is nearly 90% spin-polarized for Ni and about 65% for Fe. Concomitantly, a fast demagnetization of the ferromagnetic polarization in the femtosecond regime is driven. The analogy of the generated spin current to a superdiffusive spin Seebeck effect is surveyed.