  We discuss the stability of ferromagnetic long-range order in
three-dimensional classical XY ferromagnets upon substitution of a small subset
of equally oriented bonds by impurity bonds, on which the ferromagnetic
exchange J_perp > 0 is replaced by a strong antiferromagnetic coupling J_imp <
0. In the presence of a single impurity bond, once the absolute value of the
frustrating coupling J_imp < 0 exceeds a threshold J_c > 0, the ground state
becomes two-fold degenerate, corresponding to either clockwise or anticlockwise
canting of the spins in the vicinity of the impurity bond. In the presence of a
small concentration of impurity bonds, the effective low-energy Hamiltonian is
that of Ising variables encoding the sense of rotation of the local canting
around the impurities. Those degrees of freedom interact through a dipolar
interaction mediated by spin waves. A ferromagnetic Ising ground state
indicates the instability of the XY ferromagnet towards a spiral state with a
wave vector proportional to the concentration of impurity bonds. To analyze
under which circumstances such a ground state arises, we study first impurities
forming superlattices. For a subclass of those, we can rigorously establish the
existence of spiral order. For another class of superlattices, the Ising
variables order ferromagnetically in planes perpendicular to the orientation of
impurity bonds, but antiferromagnetically parallel to it, which results in a
fan-like XY ground state. Second, we consider the case when the impurity bonds
are randomly distributed on the three-dimensional host lattice according to a
Poisson process. We show the phenomenon of spiral order by disorder with an
ordering wave vector proportional to the impurity concentration. The analytical
predictions are confirmed by Monte Carlo simulations and are relevant for
magnetic materials such as YBaCuFeO_5.
