A Kinematical Theorem on Ferromagnetism

概要

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In most of the existing theories of ferromagnetism there is a wide-spread view of elementary excitations in non-relativistic ferromagnets. The view is that the transverse excitations accompanying spin reversals consist of the spin wave excitations (Goldstone modes) and the individual particle ones (Stoner modes) and these latter excitations lead to the energy gaps called exchange splitting. This picture, originally given by approximate theories, is extended to the concept of non-quasi-degeneracy which is expected to be valid in rigorous theories of heavily interacting particle systems exhibiting ferromagnetism, provided that the notion of exchange splitting is not entirely wrong. If the non-quasi-degeneracy condition is accepted, a difficulty is found in reconciling ferromagnetism with a kinematical requirement imposed upon any non-relativistec system. The requirement is a modified version of the f-sum rule. In the case of complete ferromagnetism the difficulty can be brought forth on a rigorous mathematical basis. It is concluded that complete ferromagnetism cannot appear in the ground states satisfying the condition of non-quasi-degeneracy so long as <Ψ_0|J_+(x')(H-E_0)^<-1>J_-(x")|Ψ_0>≫0, where J_±(x') is the transverse spin current flowing through the plane x=x'. We advocate the ansatz that this inequality is always valid--an undoubted proposition.
理論物理学刊行会の論文
1973-10-25