We report on the first Skyrme-Hartree-Fock calculations with the tilted-axiscranking in the context of magnetic rotation. The mean field symmetries,differences between phenomenological and self-consistent methods and thegeneration of shears-like structures in the mean field are discussed.Significant role of the time-odd spin-spin effective interaction is pointedout. We reproduce the shears mechanism, but quantitative agreement withexperiment is rather poor. It may have to do with too large core polarization,lack of pairing correlations or properties of the Skyrme force.
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