Ferroelectric HfO₂ holds promise for many applications, including non-volatile on-chip memory and ferroelectric field-effect transistors. One challenge preventing the integration of ferroelectric HfO₂ into devices is the difficulty to unambiguously prepare phase-pure material without the benefits of epitaxy. Here, a new method for preparing ferroelectric HfO₂ is presented using High-Power Impulse Magnetron Sputtering (HiPIMS). HiPIMS offers a unique combination of processing parameters such as incident ion energy and gas atmosphere that are inaccessible through conventional HfO₂ synthesis by atomic layer deposition (ALD). In this work, the impact of plasma oxygen content on the crystallization, phase constitution, microstructure, and ferroelectric properties of undoped HfO₂ films deposited by HiPIMS is investigated. HfO₂ thin films were reactively sputtered with plasma oxygen content varied from 7.1 to 8.0 %. The impact of grain size on performance and phases present was assessed, and the results show that the microstructure does not strongly vary between ferroelectric and non-ferroelectric samples. It will be shown that the oxygen content in the plasma directly relates to the oxygen content in the films, as assessed by electron energy-loss spectroscopy, X-ray photoelectron spectroscopy, and positron annihilation spectroscopy. This oxygen content strongly influences phase formation and ferroelectric performance. High concentrations of neutral oxygen vacancies are identified in crystalline ferroelectric samples and allow for low leakage currents. These results show that oxygen content can be used to dictate phase nucleation and provide a path toward phase-pure polycrystalline ferroelectric HfO₂.