  We examine the maximum entanglement reached by an initially fully aligned
state evolving in an XY Heisenberg spin chain placed in a uniform transverse
magnetic field. Both the global entanglement between one qubit and the rest of
the chain and the pairwise entanglement between adjacent qubits is analyzed. It
is shown that in both cases the maximum is not a monotonous decreasing function
of the aligning field, exhibiting instead a resonant behavior for low
anisotropies, with pronounced peaks (a total of [n/2] peaks in the global
entanglement for an $n$-spin chain), whose width is proportional to the
anisotropy and whose height remains finite in the limit of small anisotropy. It
is also seen that the maximum pairwise entanglement is not a smooth function of
the field even in small finite chains, where it may exhibit narrow peaks above
strict plateaus. Explicit analytical results for small chains, as well as
general exact results for finite n-spin chains obtained through the
Jordan-Wigner mapping, are discussed.
