Questions about Curie Temperature Characteristics

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korneld
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Is the curie temperature of a ferromagnetic material constant? Are there any factors that will raise it or lower it? For instance, what happens if my piece of iron is already in a strong magnetic field? Is the curie temperate higher, then?
 
I am a layman of magnetism. Curie temperature comes from strong magnetic interaction between atoms so the environment condition has less effects on it, I assume. However strong magnetic field in environment would help atoms to have orders and raise Curie temperature at least qualitatively.