Spontaneous vortex phase (SVP) is an exotic quantum matter in which quantized superconducting vortices form in the absence of external magnetic field. Although being predicted theoretically nearly 40 years ago, its rigorous experimental verification still appears to be lacking. Here we present low-field magnetic measurements on single crystals of the iron-based ferromagnetic superconductor Eu(Fe$_{0.91}$Rh$_{0.09}$)$_{2}$As$_{2}$ which undergoes a superconducting transition at $T_mathrm{sc}$ = 19.6 K followed by a magnetic transition at $T_mathrm{m}$ = 16.8 K. We observe a characteristic first-order transition from a Meissner state within $T_mathrm{m}<T<T_mathrm{sc}$ to an SVP below $T_mathrm{m}$, under a magnetic field approaching zero. Additional isothermal magnetization and ac magnetization measurements at $Tll T_mathrm{sc}$ confirm that the system is intrinsically in a spontaneous-vortex ground state. The unambiguous demonstration of SVP in the title material lays a solid foundation for future imaging and spectroscopic studies on this intriguing quantum matter.
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