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Field-temperature phase diagram of magnetic bubbles spanning charge$/$orbital ordered and metallic phases in La$_{1-x}$Sr$_x$MnO$_3$ ($x = 0.125$)

We report formation of magnetic textures in the ferromagnetic (FM) phase of La$_{1-x}$Sr$_x$MnO$_3$ for $x =$ 0.125; these textures are magnetic bubbles, magnetic stripe domains, and forced FM states. In situ Lorentz microscopy (LM) observations show that magnetic bubbles exist in the FM insulating phase accompanying the formation of the charge$/$orbital ordering (CO$/$OO). Furthermore, stable magnetic bubbles still exist in an intermediate temperature region between the CO$/$OO ($T_{CO} =$ 155 K) and FM ($T_c =$ 190 K) transition temperatures. These magnetic bubbles are believed to originate from the magnetocrystalline anisotropy and the dipole-dipole interaction in the FM phase. Based on in situ LM observations as a function of both temperature and the strength of the external magnetic field applied, a magnetic field-temperature phase diagram is constructed, exhibiting the stabilizing regions of the magnetic bubbles in the FM phase of La$_{0.875}$Sr$_{0.125}$MnO$_{3}$.