The magnetism in the ferromagnetic superconductor UCoGe has been studied using a combination of magnetic Compton scattering, bulk magnetization, X-ray magnetic circular dichroism and electronic structure calculations, in order to determine the spin and orbital moments. The experimentally observed total spin moment, $M_s$, was found to be -0.24 $pm$ 0.05~$mu_B$ at 5~T. By comparison with the total moment of 0.16 $pm$ 0.01~$mu_B$, the orbital moment, $M_l$, was determined to be 0.40 $pm$ 0.05~$mu_B$. The U and Co spin moments were determined to be antiparallel. We find that the U 5textit{f} electrons carry a spin moment of U$_s approx$ -0.30~$mu_B$ and that there is a Co spin moment of Co$_s approx$ 0.06~$mu_B$ induced via hybridization. The ratio U$_l/$U$_s$, of $-1.3 pm 0.3$, shows the U moment to be itinerant. In order to ensure an accurate description of the properties of 5textit{f} systems, and to provide a critical test of the theoretical approaches, it is clearly necessary to obtain experimental data for both the spin and orbital moments, rather than just the total magnetic moment. This can be achieved simply by measuring the spin moment with magnetic Compton scattering and comparing this to the total moment from bulk magnetization.
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