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Magnetic susceptibility $\chi_m$ is defined by following relation:

$$\vec{M}=\chi_m \vec{H}$$

where $\vec{M}$ is the magnetization density and $\vec{H}$ is the magnetizing field, defined by $\vec{H}=\frac{1}{\mu_0} \vec{B}-\vec{M}$. It is often said that for diamagnetic and paramagnetic materials, $\chi_m$ is a very small number with respect to 1. For ferromagnetic materials it is often said that $\chi_m$ is not small and not constant. I imagine that "not constant" here means that susceptibility depends on the modulus of $\vec{H}$ so that the previous equation is not linear anymore (right?).

Question: why is previous relation (definition of $\chi_m$) appliable to ferromagnetic materials? This relation in fact implies that magnetization and $\vec{H}$ field are always parallel (point by point). This should not be true for ferromagnets, that could have a permanent magnetization, independent from applied magnetizing field...

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What is actually implied for ferromagnetic materials is $\mathbf{M} = \chi_\mathrm{m}(\mathbf{H})\mathbf{H}$, which turn the material's response to the field non-linear, as you have stated. For an anisotropic material, $\chi_\mathrm{m}$ is naturally a tensor, which should describe the magnetic domains. Notice that high intensity fields are, in principle, capable of magnetizing the material in a single direction -- making it isotropic, but not necessarily homogeneous.

In case you are not familiar with, I would recommend you take a look at hysteresis as well, which is very important for ferromagnetic materials and their applications.

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