crystal structure and magnetism

As it happens, one of the first crystal structure determinations
was conducted to answer this question. Sometime before 1920,
A. W. Hull of the GE Research Lab used x-ray diffraction
to determine the crystal structures of the three elements
that are ferromagnetic at room temperature: iron, cobalt,
and nickel. The question was whether they all had the
same crystal structure, which would suggest a direct
connection between structure and magnetism. The answer
was no: iron is body-centered cubic, cobalt is
hexagonal close packed, nickel is face-centered cubic.
Much later (1970s) it was found that non-crystalline
materials (glassy metals, amorphous alloys) can also
be ferromagnetic.
However, it is true that crystal structure affects
magnetic properties of ferromagnetic elements,
notably the magnetic anisotropy. Crystal structure
also profoundly affects the magnetic structure and
properties of antiferromagnetic and ferrimagnetic
materials.