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The phase diagram of Sr3Ru2O7 contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties - a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrell-Larkin-Ovchinnikov state. Based on a microscopic theory of Stoner magnetism we derive a Ginzburg-Landau expansion where the magnetisation transverse to the applied field can become spatially inhomogeneous. We show that this reproduces the observed phase diagram of Sr3Ru2O7.

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