High-field slope correction of hysteresis loops: are we doing it correctly?

Presentation of magnetic hysteresis data has long been a standard component of paleomagnetic, rock magnetic, and environmental magnetic publications. It has become standard practice to correct the high-field slope of hysteresis loops using a line fit through data points between 70 and 100% of the maximum applied field. Implicit to this approach is that the magnetization is considered saturated if the loop is closed at the point at which 70% of the maximum applied field is reached. This approach treats hysteresis overly simplistically because it assumes that the irreversible magnetization, which is what gives rise to hysteresis, is the only relevant part of the magnetization. The reversible component of magnetization is also important; this component approaches saturation non-linearly following the so-called law of approach to saturation, where the magnetization continues to increase due to rotation of magnetic moments parallel to the applied field, which is resisted by the anisotropy of the material. Various mathematical formulations exist for the law of approach to saturation. Use of this law is not straightforward for geological materials because terms in the respective equations depend on the material analysed and must be approximated, which becomes problematical for samples with mixed magnetic components. Alternatively, hysteresis loops can be fitted and extrapolated to high fields to estimate the approach to saturation using hyperbolic functions. We illustrate issues associated with linear slope correction at 70–100% of the maximum applied field by comparing hysteresis parameters estimated using approach to saturation fitting with various maximum applied fields. In all cases, for maximum fields used typically in mineral magnetic studies (e.g., 1 T), conventional slope correction underestimates the saturation magnetization M_s and overestimates the ratio of the saturation remanent magnetization M_rs to M_s. Hysteresis loop undersaturation is likely to be widespread in mineral magnetic studies with inadequate slope correction probably causing a large uncertainty in published hysteresis parameters. We recommend routine application of approach to saturation fitting of hysteresis loops, which can help to better estimate M_s and M_rs/M_s, as well as help to indicate whether a maximum applied field is sufficient to achieve magnetic saturation.