  Strongly correlated materials are expected to feature unconventional
transport properties, such that charge, spin, and heat conduction are
potentially independent probes of the dynamics. In contrast to charge
transport, the measurement of spin transport in such materials is highly
challenging. We observed spin conduction and diffusion in a system of ultracold
fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong
interactions, spin diffusion is driven by super-exchange and
doublon-hole-assisted tunneling, and strongly violates the quantum limit of
charge diffusion. The technique developed in this work can be extended to
finite doping, which can shed light on the complex interplay between spin and
charge in the Hubbard model.
