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In a ferromagnet, the change in temperature would result in a change in spontaneous magnetisation even without an external field. But does the changing of this spontaneous magnetisation cause an induced electric field which would result in a change in conductivity? Or in short, Does heating a ferromagnet cause a change in conductivity?

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Magnetic field changing in time will create an electric field, yes. But this has nothing to do with conductivity. Conductivity is basicaly dependent on the free charges you have in your media (electrons) and ammount of these charges doesn't change in this particular phase transition. Of course, here we ignore the effect that conductivity of any material changes when you change the temperatures. This is an effect which applies not only to ferromagnets, and effect of the change depends on the type of particular material. But I assume you are not interested in generic effect of temperature changes here, but in changes of magnetisation.

So short answer is - no, going through ferromagnetic phase transition will not change conductivity of material.

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