  We explicitly construct a symplectomorphism that relates magnetic twists to
the invariant hyperk\"ahler structure of the tangent bundle of a Hermitian
symmetric space. This symplectomorphism reveals foliations by (pseudo-)
holomorphic planes, predicted by vanishing of symplectic homology. Furthermore,
in the spirit of Weinstein's tubular neighborhood theorem, we extend the
(Lagrangian) diagonal embedding of a compact Hermitian symmetric space to an
open dense embedding of a specified neighborhood of the zero section. Using
this embedding, we compute the Gromov width and Hofer-Zehnder capacity of these
neighborhoods of the zero section.
