Localized vs Collective Descriptions of Magnetic Electrons

Spontaneous band magnetism occurs as a transitional electron state, in the thermodynamic sense, between a localized‐electron (or small‐polaron) state and a conventional collective‐electron state. The localized‐electron state is well described by crystal‐field theory, together with superexchange and double‐exchange theories. Conventional band theory neglects electron correlations, except in the superconducting state. In the transitional state, electron correlations introduce not only the exchange interactions responsible for spontaneous magnetism, but also a deep minimum, if not an energy gap, in the density‐of‐states vs energy for half‐filled bands. Since Umklapp processes stabilize antiferromagnetic vs ferromagnetic order as the Fermi surface approaches a Brillouin‐zone boundary, it is possible to construct a semiempirical phase diagram for various electronic states in the space $n_d$ , $b$ , $T$ , where $n_d$ is the number of electrons per $d$ orbital per atom, $b$ is the transfer energy, and $T$ is the temperature. Magnetic data that illustrate a few significant features of this diagram are discussed briefly, and it is pointed out that spontaneous band magnetism is a relatively rare phenomenon because the transitional state occurs over only a small range of $b$ .