  Particle-like topological magnetic defects that can propagate in all spatial
directions open a new dimension for design of magnetic memory and data
processing devices. We show that three-dimensional magnetic skyrmions can be
stabilized in non-collinear antiferromagnets, such as the Fe-langasite,
Ba$_3$TaFe$_3$Si$_2$O$_{14}$. Spins in the crystallographic unit cell of this
material form a 120-degree ordering transformed by competing exchange
interactions into a short-period spiral, which in turn forms a basis for
complex large-scale magnetic superstructures stabilized by
Dzyaloshinskii-Moriya interactions and applied magnetic fields. We derive an
effective continuum model describing modulated states of Fe-langasite at the
100 nm scale and explore its magnetic phases and topological defects. The order
parameter space of this model is similar to that of superfluid $^{3}$He-A and
the three-dimensional topological defect is closely related to the Shankar
monopole and hedgehog soliton in the Skyrme model of baryons.
