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Magnetic domain tuning and the emergence of bubble domains in the bilayer manganite La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ (x=0.32)

We report a magnetic force microscopy study of the magnetic domain evolution in the layered manganite La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ (with $x=0.32$). This strongly correlated electron compound is known to exhibit a wide range of magnetic phases, including a recently uncovered biskyrmion phase. We observe a continuous transition from dendritic to stripe-like domains, followed by the formation of magnetic bubbles due to a field- and temperature dependent competition between in-plane and out-of-plane spin alignments. The magnetic bubble phase appears at comparable field- and temperature ranges as the biskyrmion phase, suggesting a close relation between both phases. Based on our real-space images we construct a temperature-field phase diagram for this composition.