  Magnetic skyrmions are stable topological solitons with complex non-coplanar
spin structures. Their nanoscopic size and the low electric currents required
to initiate and control their motion has opened a new field of research,
skyrmionics, that aims at using skyrmions as information carriers for data
storage and manipulation. Recent advances in skyrmionics prompt for a thorough
understanding of the detailed three-dimensional (3D) spin texture of a skyrmion
including skyrmion-skyrmion interactions and their coupling to surfaces and
interfaces. These properties crucially affect application-related aspects such
as the stability and mobility of skyrmions in confined structures. To date,
however, experimental techniques to measure the three-dimensional spin texture
with nanometer resolution are largely missing. We therefore adapt holographic
vector field electron tomography to the problem and report on the first
quantitative reconstruction of the 3D spin texture of skyrmions with sub-10
nanometer resolution. The reconstructed textures reveal a variety of previously
unseen local deviations from a homogeneous Bloch character within the skyrmion
tubes (SkTs), details of the collapse of the skyrmion texture at surfaces, and
a correlated modulation of the SkT in FeGe along their tube axes. The
quantitative 3D data of the magnetic induction also allow to experimentally
confirm some principles of skyrmion formation by deriving spatially resolved
maps of the magnetic energy density across these magnetic solitons.
