 Volume magnetic susceptibility

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 asHere ${\mu }_B$ is the Bohr magneton. If its $B$ is a prescribed vacuum/applied magnetic flux density $B_0={\mu }_0{H}_{\mathrm{app}}$, the dimensionless apparent slope is ${\mu }_0{\chi }_B^{\mathrm{vol}}$. 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.