Defect moment of antiferromagnets yields the highest remanent coercivity observed among minerals, and previous studies have been unable to reach saturation of isothermal remanent magnetization (IRM) in some goethite and hematite, even up to 20 Teslas, using resistive Bitter magnets. To go further, acquisition of IRM at room temperature has been monitored on various natural and synthetic goethite and hematite samples in pulsed magnetic fields up to 57 Teslas. "Coarse" hematite is saturated around 5 T, and low unblocking temperature (TB, i.e. with low crystallinity or Al substitution) goethites saturate around 20 T. Higher TB goethites and a Mn-bearing fine-grained hematite are still not saturated even at 57 T, with only 2 to 10 percent of the maximum IRM acquired in 3 T. Half acquisition fields are mostly above 10 T. This indicates that usual rock magnetic techniques strongly underestimate the contribution of such minerals to remanence. IRM acquisition is strongly irreversible: in some samples a 57 T backfield is unable to erase a previous 38 T IRM. A field induced defect diffusion model is put forward to account for remanence acquisition in these materials.