  Improving our understanding of the physical coupling between type-II
superconductors (SC) and soft ferromagnetic materials (SFM), is root for
progressing onto the application of SC-SFM metastructures in scenarios such as
magnetic cloaking, magnetic shielding, and power transmission systems. However,
in the latter some intriguing and yet unexplained phenomena occurred, such as a
noticeable rise in the SC energy losses, and a local but not isotropic
deformation of its magnetic flux density. These phenomena, which are in
apparent contradiction with the most fundamental theory of electromagnetism for
superconductivity, i.e., the critical state theory (CST), have remained
unexplained for about 20 years, given place to the acceptance of the
controversial and yet paradigmatic existence of the so-called overcritical
current densities. Therefore, aimed to resolve these long-standing problems, we
extended the CST by incorporating a semi-analytical model for cylindrical
monocore SC-SFM heterostructures, setting the standards for its validation with
a variational approach of multipole functionals for the magnetic coupling
between Sc and SFM materials. It is accompanied by a comprehensive numerical
study for SFM sheaths of arbitrary dimensions and magnetic relative
permeabilities $\mu_{r}$, ranging from $\mu_{r}=5$ (NiZn ferrites) to
$\mu_{r}=350000$ (pure Iron), showing how the AC-losses of the SC-SFM
metastructure radically changes as a function of the SC and the SFM radius for
$\mu_{r} \geq 100$. Our numerical technique and simulations revealed also a
good qualitative agreement with the magneto optical imaging observations that
were questioning the CST validness, proving therefore that the reported
phenomena for self-field SC-SFM heterostructures can be understood without
including the ansatz of overcritical currents.
