Spontaneous Band Magnetism

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Abstract
With sharply defined, critical overlap integrals Δc and Δcf for a localized‐electron ⇆ collective‐electron transition and for spontaneous band ferromagnetism, the conditions for band ferromagnetism to occur are: Δc <Δb <Δcf, and Δc <Δab <Δcf <Δb, where the overlap integrals Δab <Δb are each proportional to the bandwidths of antibonding and bonding bands, respectively. Spontaneous magnetism also depends upon the electron/atom ratio: Half‐filled bands may exhibit antiferromagnetism, but not ferromagnetism. If Δc <Δb <Δcf, bands less than one‐quarter filled may exhibit ferromagnetism with magnetization ≤ ndμB per atom and a distributed spin density as in ZrZn2, where nd, nh, and nab are numbers of electrons, holes, and antibonding electrons per atom. Bands more than three‐quarters filled may be ferromagnetic with a localized atomic moment of nhμB. Bands more than half‐filled and less than three‐quarters filled give a localized atomic moment of nhμB, if Δc <Δb <Δcf, and are either ferromagnetic or exhibit a spiral‐spin configuration. However, if Δc <Δab <Δcf <Δb, ferromagnetism with a reduced atomic moment of nabμB per atom is predicted. The spin density is localized, but a small negative‐spin density may occur at large distances from the atom. It is indicated how these ideas can account satisfactorily for the spontaneous magnetism, atomic moments, and spin‐density distributions in first‐row transition metals.

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