= Volume magnetic susceptibility
{title2=$\chi_v=M/H_{\rm int}$}
<Volume magnetic susceptibility> is the dimensionless ratio of longitudinal <magnetization> to internal <magnetic field intensity> in a linear regime through the origin. Positive response gives <paramagnetism>. Always distinguish <magnetization> $M=\mathcal M/V$ from total <magnetic moment> $\mathcal M$: dividing by <volume> changes the normalization. Mass-normalized and mole-normalized values likewise require the <mass density> or the <volume> per <amount of substance> before comparison with $\chi_v$.
In the existing <Pauli paramagnetism> formula, $M$ denotes total <magnetic moment>, and $g(E_F)$ is the total <spin-summed density of states>. Relabel that response as
$$
\chi_B^{\rm tot}=\left(\frac{\partial\mathcal M}{\partial B}\right)_T
=\mu_B^2g(E_F),\qquad
\chi_B^{\rm vol}=\frac{\chi_B^{\rm tot}}{V}.
$$
Here $\mu_B$ is the <Bohr magneton>. If its $B$ is a prescribed vacuum/applied <magnetic flux density> $B_0=\mu_0H_{\rm app}$, the dimensionless apparent slope is $\mu_0\chi_B^{\rm vol}$. It agrees approximately with intrinsic $\chi_v$ only when the <demagnetizing field> correction and magnetic feedback are negligible. The existing <Curie's law> formula also uses a total-<magnetic moment>, $B$-derivative convention; its $N$ counts moments rather than giving a <number density>.
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