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Asymmetric slot waveguides with a magnetooptic material filling the slot are studied for their nonreciprocal phase shift properties. General properties and performance are first evaluated by a one-dimensional silicon slot waveguide model, to find optimal asymmetric waveguide profiles. The results are verified with a two-dimensional calculation for a realistic optimal waveguide structure. The achieved ratio of the waveguide nonreciprocal phase shift to the specific Faraday rotation of the magnetooptic material is at a level comparable with semiconductor waveguides having a garnet cladding. The geometry may be applied to silicon-based vertical slot waveguides for quasi-TE polarization, which provides integration potential with active components in Si photonic circuits.