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We report the first observation of two-dimensional incommensurate magnetic fluctuations in the layered metallic perovskite Sr3Ru2O7. The wavevectors where the magnetic fluctuations are strongest are different from those observed in the superconducting single layer ruthenate Sr2RuO4 and appear to be determined by Fermi surface nesting. No antiferromagnetic ordering is observed for temperatures down to 1.5K. For temperatures T<20K, the fluctuations become predominately ferromagnetic. Our inelastic neutron scattering measurements provide concrete evidence of the coexistence of competing interactions in Sr3Ru2O7 and of the low energy scale of the fluctuations.

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