Analytical parametrization for magnetization of Gadolinium based on scaling hypothesis

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Gadolinium, which has a Curie temperature of 293 K, has been served as the reference material for the room-temperature magnetic energy conversion. Using the scaling hypothesis and university class of phase transition, we propose an analytical parametrization of Gd magnetization (M(T,H)) for fields up to 5 T and temperatures between 250 and 340 K. The key step is to fit the single-variable scaling function, beyond the leading divergent term, that well describes the entire two-variable M(T,H) near the Curie temperature. Constraints of the scaling function are derived and are used to construct the parametrization form. A stable fitting algorithm based on separating the length scale is introduced. The final expression is analytical, well defined at Curie temperature, and is validated by comparing to experiments including the magnetization and the specific heat. The proposed parametrization turns the knowledge of scaling hypothesis into an efficient and accurate scheme that quantitatively describes the material near the second-order transition. This advantage can become significant when considering realistic applications.