  We introduce a model of a quantum walk on a graph in which a particle jumps
between neighboring nodes and interacts with independent spins sitting on the
edges. Entanglement propagates with the walker. We apply this model to the case
of a one dimensional lattice, to investigate its magnetic and entanglement
properties. In the continuum limit, we recover a Landau-Lifshitz equation that
describes the precession of spins. A rich dynamics is observed, with regimes of
particle propagation and localization, together with spin oscillations and
relaxation. Entanglement of the asymptotic states follows a volume law for most
parameters (the coin rotation angle and the particle-spin coupling).
