The energy (per unit volume) required to magnetize a ferromagnetic material to saturation...

The energy (per unit volume) required to magnetize a ferromagnetic material to saturation (Es) is defined by the following equation:

that is, Es is equal to the product of m0 and the area under an M-versus-H curve, to the point of saturation referenced to the ordinate (or M) axis—for example, in Figure 20.17, the area between the vertical axis and the magnetization curve to Ms. Estimate Es values (in J/m3) for single-crystal iron in [100], [110], and [111] directions.

Figure 20.17 Magnetization curves for single crystals of iron and nickel. For both metals, a different curve was generated when the magnetic field was applied in each of [100], [110], and [111] crystallographic directions.

(Adapted from K. Honda and S. Kaya, “On the Magnetisation of Single Crystals of Iron,” Sci. Rep. Tohoku Univ., 15, 721 (1926); and from S. Kaya, “On the Magnetisation of Single Crystals of Nickel,” Sci. Rep. Tohoku Univ., 17, 639 (1928).)