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When a magnetic field ${\bf H}$ is turned on from zero, a piece of material, not previously magnetized, exhibits a magnetization ${\bf M}$ due to ${\bf H}$.

According to ${\bf M} = \chi {\bf H}$, this would happen instantaneusly. But that's hard to believe, because magnetic moments, inside the bulk of the material, should take some time to turn around themselves.

Suppose ${\bf H}$ is varying with time, such as ${\bf H}\propto e^{-i\omega t}$. If $\omega$ is high enough, a temporal phase shift between ${\bf M}$ and ${\bf H}$ should occur, due to the time taken by the magnetic dipoles to turn around.

So, what is the frequency range where ${\bf M} = \chi {\bf H}$ should be used, as if ${\bf M}$ would follow ${\bf B}$ instantaneously?

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    $\begingroup$ There is a distinction between the ambient field and the field inside the material exposed to the ambient field. $\textbf{M}=\chi\textbf{H}$ refers to the $\textbf{H}$ field inside the material. $\endgroup$ – Ben Crowell Nov 27 '18 at 1:22

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