Magnetism in Transition Metals

An attempt is made to distinguish "band-type magnetization" from "alignment-type magnetization" on the basis of whether the local moments associated with the Wannier functions on the atom sites are "induced" or "permanent." In general, the local moment is partially induced and partially permanent, and a criterion is suggested: A local moment is defined to be of the permanent variety if in the presence of magnetic forces (supposed characteristic of the crystal in a given circumstance) tending to produce a moment in one sense ($\hat{z}$, say) of a direction, it can maintain itself (perhaps altered in magnitude, however) in the opposite sense ($-\hat{z}$), as well as in $\hat{z}$. The internal mechanisms tending to produce permanent moments are simplified to just the $H_{\mathrm{corr}}$ of Anderson, and the external inducing mechanism are the Heisenberg interaction and a magnetic field, $H_{\mathrm{spin}}$, say. If $H_{\mathrm{corr}}$ dominates $H_{\mathrm{spin}}$, then it is shown that a local moment can maintain itself to the polarizing tendencies (whence an alignment type of magnetization calculation is appropriate), but if $H_{\mathrm{spin}}$ dominates $H_{\mathrm{corr}}$, then the local moment has only one sense possible in this environment (and a band type of calculation is appropriate). It is suggested that this distinction is relevant to transition metals.