Extracting magnetic Landau coefficients from an Arrott plot ($a={\mu }_0{X}_0,b={\mu }_0/S$)

If physical ordinate is $Y=M^2$ and abscissa $X=H/M$, slope $S=dY/dX$ and horizontal intercept $X_0$ give $b={\mu }_0/S$ and $a={\mu }_0{X}_0$. Any displayed squared-magnetisation scale must be converted before using S. For example, an ordinate unit $(10^4\mathrm{A}{\mathrm{m}}^{-1}{)}^2$ equals $10^8{\mathrm{A}}^2{\mathrm{m}}^{-2}$, not $10^4$. With a free-energy density, the resulting units are $[a]=\mathrm{H}{\mathrm{m}}^{-1}$ and $[b]=\mathrm{J}\mathrm{m}{\mathrm{A}}^{-4}$. Curvature or differing isotherm slopes limits the accuracy of a constant-coefficient fit.