Simulation of Ultrafast Spin-Dependent Hot-Electron Transport in Metallic Multilayers

Spin currents in metallic heterostructures can play an important role in connection with ultrafast demagnetization in ferromagnetic materials, as optically excited hot electrons contribute to the non-equilibrium magnetization over the whole range of a multilayer structure. Here, we present our results on two approaches to this problem. First, we apply the Boltzmann transport equation in the homogeneous metal part of a ferromagnet/metal-bilayer and determine the microscopic distribution function of the spin-polarized hot carriers excited in an adjacent magnetic layer. To solve the Boltzmann equation, we reduce the computational domain to an effectively two-dimensional phase space. Carrier-carrier scattering and interactions with phonons are included at the level of a relaxation-time approximation. We have also derived semi-classical equations of motion for the carriers using a particle-in-cell approach. With this approach, we calculate the dynamics of the electrons travelling through the whole bilayer structure, using as input velocities and electronic lifetimes from ab-initio calculations. \\ D.~M.~Nenno, S.~Kaltenborn and H.~C.~Schneider, Phys.~Rev.~B 94, 115102 (2016)