  We investigate the geometry of classical Hamiltonian systems immersed in a
magnetic field in three-dimensional Riemannian configuration spaces. We prove
that these systems admit non-trivial symplectic-Haantjes manifolds, which are
symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These
geometric structures allow us to determine separation variables for known
systems algorithmically; besides, the underlying St\"ackel geometry is used to
construct new families of integrable Hamiltonian models immersed in a magnetic
field.
