  Geometrical frustration arised in spin ices leads to fascinating emergent
physical properties. Nowadays there is a wide diversity of the artificial
structures, mimicking spin ice at the nanoscale and demonstrating some new
effects. Most of the nanoscaled spin ices are two dimensional. Ferromagnetic
inverse opal-like structures (IOLS) are among inspiring examples of the
three-dimensional system exhibiting spin ice behaviour. However detailed
examination of its properties is not straightforward. Experimental technique
which is able to unambiguously recover magnetization distribution in 3D
mesoscaled structures is lacking. In this work we used an approach based on
complementary exploiting of small-angle neutron diffraction technique and
micromagnetic simulations. External magnetic field was applied along three main
directions of the IOLS mesostructure. Comparison of the calculated and measured
data allowed us to determine IOLS magnetic state. The results are in good
agreement with the spin ice model. Moreover influence of the demagnetizing
field and vortex states on the magnetizing process were revealed. Additionally,
we speculate that this approach can be also applied to other 3D magnetic
mesostructures.
