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Abstract Some rock and soil samples exhibit significant loss of magnetic susceptibility (χ) with increasing applied field amplitude even at relatively low (10–100s of A/m) fields, a behavior which remains unexplained. Exceptionally strong negative field‐dependence of susceptibility (χ_HD) is present in sandstones and altered intermediate‐felsic igneous rocks in several cores from the northeastern Oklahoma subsurface. These same rocks also show elevated frequency‐dependence of susceptibility (χ_FD), with reasonable correlation ofχ_HDtoχ_FD, and frequency‐dependentχ_HD. Results from multiple characterization methods indicate that strongly negativeχ_HDin these rocks is linked to a yet‐unidentified phase which begins the approach to magnetic saturation in low fields (<1 mT/800 A/m), shows elevatedχ_FDto low temperatures, is unstable at high temperatures, possesses significant anisotropy of magnetic susceptibility, and becomes paramagnetic above ∼83°C. Clear associations with fluid alteration features indicate that this material may be highly relevant to rock alteration, diagenetic, and environmental studies.