  We report on lateral spin-caloric transport (LSCT) of electron spin packets
which are optically generated by ps laser pulses in the non-magnetic
semiconductor n-GaAs at $T\leq35$K. LSCT is driven by a local temperature
gradient induced by an additional cw heating laser. The spatio-temporal
evolution of the spin packets is probed using time-resolved Faraday rotation.
We demonstrate that the local temperature-gradient induced spin diffusion is
solely driven by a non-equilibrium hot spin distribution, i.e. without
involvement of phonon drag effects. Additional electric field-driven spin drift
experiments are used to verify directly the validity of the non-classical
Einstein relation for moderately doped semiconductors at low temperatures for
near band-gap excitation.
