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Critical thickness for itinerant ferromagnetism in ultrathin films of SrRuO$_3$

Ultrathin films of the itinerant ferromagnet SrRuO$_3$ were studied using transport and magnto-optic polar Kerr effect. We find that below 4 monolayers the films become insulating and their magnetic character changes as they loose their simple ferromagnetic behavior. We observe a strong reduction in the magnetic moment which for 3 monolayers and below lies in the plane of the film. Exchange-bias behavior is observed below the critical thickness, and may point to induced antiferromagnetism in contact with ferromagnetic regions.