= Magnetic susceptibility
{title2=$\chi$}
{wiki}
<Magnetic susceptibility> describes how readily a <magnetic field> changes a material's <magnetization>. The field variable and normalization matter: <volume magnetic susceptibility> in the <International System of Units> is dimensionless, whereas a <derivative> of total <magnetic moment> with respect to $B$ has units of $\mathrm{J\,T^{-2}}$. A slope measured against the applied <magnetic field intensity> also depends on the sample's <demagnetizing field>.
For an isotropic, reversible linear response through the origin, write
$$
\mathbf M=\chi_v\mathbf H_{\rm int},\qquad
\mathbf B_{\rm int}=\mu_0(\mathbf H_{\rm int}+\mathbf M)
=\mu_0(1+\chi_v)\mathbf H_{\rm int}.
$$
Here $\mathbf M$ is <magnetization>, or <magnetic moment> per <volume>; $\mathbf H_{\rm int}$ is the internal <magnetic field intensity>; $\mathbf B_{\rm int}$ is the internal <magnetic flux density>; and $\mu_0$ is the <vacuum permeability>. Both $M$ and $H$ have units $\mathrm{A\,m^{-1}}$. The <magnetic permeability> is $\mu_0(1+\chi_v)$. <Classical Electromagnetism: An intermediate level course by Richard Fitzpatrick/Magnetic susceptibility and permeability>[Richard Fitzpatrick, Magnetic susceptibility and permeability, equations (866)–(868): isotropic linear response and permeability]{ref}
The <independent-moment magnetic response> below shows why one number cannot describe every field: <magnetization> approaches a <saturation magnetization>, while its <differential magnetic susceptibility> approaches zero. <Anisotropy> requires a <magnetic susceptibility tensor>; <hysteresis> requires specifying the preparation and sweep branch as well as the bias <magnetic field>, <temperature>, and timescale. The <Gouy balance> turns a small response into a measurable <force> without presuming that its readout is already the intrinsic <volume magnetic susceptibility>.
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