After Slater published his paper on Hund’s rule in 1929, almost all standard textbooks adopted his approach to explaining the origin of magnetism, specifically the stabilization of the magnetic ground state, based on electron exchange energy. However, at the time his theory was developed, computers were not available to numerically solve many-body electron systems. As a result, he overlooked a crucial factor, the nucleus-electron interaction, by assuming a uniform charge distribution for the nucleus, despite its sharp peak. It has been demonstrated that this omission leads to a significant violation of the virial theorem, which is a necessary condition for any Coulomb system. By numerically solving the Schrödinger equation while satisfying the virial theorem, it has been shown that the nucleus-electron interaction plays a fundamental role in lowering the energy of the magnetic ground state. With the virial theorem as a benchmark, it is now able to differentiate between correct and incorrect theories. One of the most striking findings is that two-level models, like the Hubbard model, which assume identical spatial wavefunctions for the magnetic ground state and for the excited state, are incorrect and should be excluded from theories of magnetism.

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Correct Theory of Magnetism

  • Yoshiyuki Kawazoe

摘要

After Slater published his paper on Hund’s rule in 1929, almost all standard textbooks adopted his approach to explaining the origin of magnetism, specifically the stabilization of the magnetic ground state, based on electron exchange energy. However, at the time his theory was developed, computers were not available to numerically solve many-body electron systems. As a result, he overlooked a crucial factor, the nucleus-electron interaction, by assuming a uniform charge distribution for the nucleus, despite its sharp peak. It has been demonstrated that this omission leads to a significant violation of the virial theorem, which is a necessary condition for any Coulomb system. By numerically solving the Schrödinger equation while satisfying the virial theorem, it has been shown that the nucleus-electron interaction plays a fundamental role in lowering the energy of the magnetic ground state. With the virial theorem as a benchmark, it is now able to differentiate between correct and incorrect theories. One of the most striking findings is that two-level models, like the Hubbard model, which assume identical spatial wavefunctions for the magnetic ground state and for the excited state, are incorrect and should be excluded from theories of magnetism.