Thermomagnetic data analysis#
These notebooks support the analysis of thermomagnetic data.
Thermomagnetic Curves This notebook plots and analyzes data from high-temperature susceptibility experiments.
Nota bene: We do not provide Curie Temperature estimation by the “two-tangent” method, as proposed for spontaneous magnetization Mₛ(T) curves by Grommé et al. (1969). Fabian et al. (2013) explain this well:
“The importance of the difference between determining Tc from Mₛ(T) and χ-T is pointed out by Petrovský and Kapicka (2006), where methods to determine Tc from measurements of the initial susceptibility are analyzed. They conclude that the two-tangent method is not suitable for χ-T and can considerably overestimate Tc. The physical origin of χ-T close to Tc is more challenging than that of Mₛ(T), because a number of low-field effects are important for χ-T, but become negligible in the higher fields used to infer Mₛ(T). The variation of m depends not only on the variation of Mₛ(H,T) with field H, it also contains a contribution from a rotation of the ordered moment with respect to an easy magnetization axis, and contributions from thermally activated switching of small independent – but already magnetically ordered – regions (e.g., SP particles). In large bulk material, domain-wall movement contributes to χ-T even slightly below Tc. In nanoparticles, the inhomogeneity of Mₛ due to the different exchange coupling of inner and surface atoms is of additional importance.”
And from Petrovský and Kapicka (2006):
“…susceptibility for T > Tc and T < Tc increases to infinity, and we have to use analytical formulas developed for susceptibility behavior above the Curie point. Here, due to the geometry of the susceptibility curve, the two-tangent method will always yield temperature above the inflection point, which is higher than the temperature at which the substance starts to obey the paramagnetic Curie-Weiss law. The resulting error in Tc (or TN1) can be on the order of several degrees to several tens of degrees. Therefore, in the case of temperature dependence of magnetic susceptibility, application of the two-tangent method is not justified.”
Furthermore:
“In the case of synthetic magnetite and hematite, with sharp Hopkinson peak, the difference between transition temperatures determined using the two-tangent method and Curie-Weiss paramagnetic law is in the order of some few degrees. In the case of samples with wide susceptibility maximum and gradual decrease, reflecting e.g., wide distribution of grain sizes, or in the case of substituted hematite, application of the two-tangent method to susceptibility curves overestimates the transition temperature by several tens of degrees.”