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Ferromagnetism is an iconic example of a first-order phase transition taking place in spatially extended systems and is characterized by hysteresis and the formation of domain walls. In this paper we demonstrate that an extended atomic superfluid in the presence of a coherent coupling between two internal states exhibits a quantum phase transition from a para- to a ferromagnetic state. The nature of the transition is experimentally assessed by looking at the phase diagram as a function of the control parameters, at hysteresis phenomena, at the magnetic susceptibility and the magnetization fluctuations around the critical point. We show that the observed features are in good agreement with mean-field calculations. Additionally, we develop experimental protocols to deterministically generate domain walls that separate spatial regions of opposite magnetization in the ferromagnetic state. Thanks to the enhanced coherence properties of our atomic superfluid system compared to standard condensed matter systems, our results open the way towards the study of different aspects of the relaxation dynamics in isolated coherent many-body quantum systems., Comment: 16 pages, 9 figures