  Propagation of information encoded in spin degrees of freedom through
networks of coupled spins enables important applications in spintronics and
quantum information processing. We study control of information propagation in
networks of spin-$\tfrac{1}{2}$ particles with uniform nearest neighbour
couplings forming a ring with a single excitation in the network as simple
prototype of a router for spin-based information. Specifically optimising
spatially distributed potentials, which remain constant during information
transfer, simplifies the implementation of the routing scheme. However, the
limited degrees of freedom makes finding a control that maximises the transfer
probability in a short time difficult. We show that the structure of the
eigenvalues and eigenvectors must fulfill a specific condition to be able to
maximise the transfer fidelity, and demonstrate that a specific choice among
the many potential structures that fulfill this condition significantly
improves the solutions found by optimal control.
