  Harnessing spins as carriers for information has emerged as an elegant
extension to the transport of electrical charges. The coherence of such spin
transport in spintronic circuits is determined by the lifetime of spin
excitations and by spin diffusion. Fermionic quantum gases are a unique system
to study the fundamentals of spin transport from first principles since
interactions can be precisely tailored and the dynamics is on time scales which
are directly observable. In particular at unitarity, spin transport is dictated
by diffusion and is expected to reach a universal, quantum-limited diffusivity
on the order of hbar/m. Here, we study the non-equilibrium dynamics of a
two-dimensional Fermi gas following a quench into a metastable, transversely
polarized spin state. Using the spin-echo technique, we measure the yet lowest
transverse spin diffusion constant of 0.25(3) hbar/m. For weak interactions, we
observe a coherent collective transverse spin-wave mode that exhibits mode
softening when approaching the hydrodynamic regime.
