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Wave-diffusion theory of spin transport in metals after ultrashort-pulse excitation

Spin and charge-current dynamics after ultrafast spin-polarized excitation in a normal metal are studied theoretically using a wave-diffusion theory. It is shown analytically how this macroscopic approach correctly describes the ballistic and diffusive properties of spin and charge transport, but also applies to the intermediate regime between these two limits. Using the wave-diffusion equations we numerically analyze spin and charge dynamics after ultrafast excitation of spin polarized carriers in thin gold films. Assuming slightly spin-dependent momentum relaxation times, we find that a unified treatment of diffusive and ballistic transport yields robust signatures in the spin and charge dynamics, which are in qualitative agreement with recent experimental results [Phys. Rev. Lett 107, 076601 (2011)]. The influence of boundary effects on the temporal signatures of spin transport is also studied.