I'm wondering if a ferromagnet is heated under a constant opposite external field, will the zero net magnetization occur BEFORE the Curie temperature because the external field cancel out the original magnetization before the material become completely paramagnetic? At Curie temperature the magnetization cannot be zero because of the magnetization due to external field.
And what happens if it's cooled under the same constant external field ? It will certainly gain a magnetization the same direction as the external field, but at what magnitude ? the magnetic susceptibility become infinite when approaching Tc.