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Based on the two-variable polynomial model of magnetization, magnetic entropychange of bilayered manganites with $327$-structure and its scaling behaviourwith respect to applied magnetic fields are investigated. It's found that theCurie temperature, which is defined as the point at which the partialderivative of magnetization with respect to temperature reaches its maximum, isdifferent from the temperature of peak magnetic entropy change. Thus amean-field model can not apply to this kind of manganites. In contrast to whathas been found in manganites with the $113$-structure, the scaling behaviour atthe Curie temperature in manganites with $327$-structure is much different fromthat at the temperature of peak magnetic entropy. It's also found that thetemperature dependence of the scaling exponent under weak fields is distinctfrom that under strong fields.This difference is attributed to an crossoverfrom one-step transition under weak fields to two-step transition under strongfields.

Scaling behaviour of magnetic entropy change in bilayered manganites by two-variable polynomials fitting to magnetization