From quantum mechanics to micromagnetics

To clarify some of the terminology, concepts and fundamental models which are essential to computational micromagnetics, this section will briefly discuss some of these. More detailed accounts can be found in Brown (1963), O'Handley (1999), Aharoni (2000) and Blundell (2001).

Figure 2.1: As the area in which a bit can be stored decreases, the overall storage capacity increases in $\mathcal{O}(1/n^2)$ assuming a square bit of edge length $n$; the scale on the right indicates the capacity of a four-platter double-sided 3.5'' hard disk, ignoring spindle size and actuation overheads.

Figure 2.2: A three-platter IDE hard disk drive, manufactured by Fujitsu in 1999

The magnetic moment is derived from the angular momentum of electrons in an atom. For free atoms, this is a combination of electron spin and orbital momentum (O'Handley, 1999):

$$\mbox{\boldmath {$\mu$}} = -g\mu_{B}(\ensuremath{\mathbf{L}}+\ensuremath{\mathbf{S}})$$ (2.1)

$\mu$A magnetic moment $g$The generalised Landé factor, $\approx$2 $\mu_{B}$The Bohr magneton, 9.2741$\times$10$^{-24}$ A$\cdot$m$^2$ $\ensuremath{\mathbf{S}}$The electron spin $\ensuremath{\mathbf{L}}$The orbital momentum

where $\mu$ is the magnetic moment, $g$ is the generalised Landé factor ($\approx$2), $\mu_{B}$ is the Bohr magneton (9.2741$\times$10$^{-24}$ A$\cdot$m$^2$), $\ensuremath{\mathbf{L}}$ is the orbital momentum and $\ensuremath{\mathbf{S}}$ is the electron spin.

When materials are solids, the spin component $\ensuremath{\mathbf{S}}$ dominates the magnetic moment. The magnetic moment per atom for the important 3d transition metals are shown in table 2.1.