We present a combination of ab initio calculations, magnetic Compton scattering and polarized neutron experiments, which elucidate the density distribution of unpaired electrons in the kagome staircase system Co3V2O8. Ab initio wave functions were used to calculate the spin densities in real and momentum space, which show good agreement with the respective experiments. It has been found that the spin polarized orbitals are equally distributed between the t2g and the eg levels for the spine (s) Co ions, while the eg orbitals of the cross-tie (c) Co ions only represent 30% of the atomic spin density. Furthermore, the results reveal that the magnetic moments of the cross-tie Co ions, which are significantly smaller than those of the spine Co ions in the zero-field ferromagnetic structure, do not saturate by applying an external magnetic field of 2 T along the easy axis a, but that the increasing bulk magnetization originates from induced magnetic moments on the O and V sites. The refined individual magnetic moments are mu(Co_c)=1.54(4) mu_B, mu(Co_s)=2.87(3) mu_B, mu(V)=0.41(4) mu_B, mu(O1)=0.05(5) mu_B, mu(O2)=0.35(5) mu_B, and; mu(O3)=0.36(5) mu_B combining to the same macroscopic magnetization value, which was previously only attributed to the Co ions.
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