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I was wondering what the technical term is for some metal(like a refrigerator door) that is not magnetic on its own like neodymium but when there is a magnet in its vicinity, it attracts to the magnet. Neodymium has a polarity but these metals don't have one, they just stick to a magnet. Is it called ferromagnetism?

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As far as I know there is no single term to refer to a material that is attracted by magnetism but not a magnet. Rather, there are terms that describe a material's magnetic behaviour regardless of its magnetized state.

There are a few versions. Ferromagnetic, paramagnetic, and diamagnetic.

Ferromagnetic is like iron it will be attracted to other magnets, but can also be magnetized and turned into a permanent magnet.

Paramagnetic and diamagnetic materials can't be turned into permanent magnets. The difference might be considered nitty gritty and I'm not qualified to comment.

But it sounds like you're asking for a specific term for a material that is ferromagnetic, but not currently magnetized. I don't know of one.

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