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We investigate the effect of substituting Si for Ge in the ferromagnetic superconductor UCoGe. Dc-magnetization, ac-susceptibility and electrical resistivity measurements on polycrystalline UCoGeSi samples show that ferromagnetic order and superconductivity are progressively depressed with increasing Si content and simultaneously vanish at a critical concentration . The non-Fermi liquid temperature variation in the electrical resistivity near and the smooth depression of the ordered moment point to a continuous ferromagnetic quantum phase transition. Superconductivity is confined to the ferromagnetic phase, which provides further evidence for magnetically mediated superconductivity.

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