青山学院大学 物理学科 コロキウム

1999年度 第三回

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(世話人・久保 健・学内23108・学外03−5384−2649)



講演者:A.C.M. Green 氏(Dept. of Mathematics, Imperial College, London)

日時: 8月31日(火) 午後4時から
場所: 青山学院大学 理工学部 一号館 五階 1538号室

講演題目: A Many-Body CPA Theory of Manganites
要旨:
The double exchange (DE) model for the colossal magnetoresistance (CMR) manganites is studied; we go beyond other theories by considering quantum local spins $S$. An equation for the one-electron Green function is obtained using a many-body coherent potential approximation (CPA). This CPA, derived by decoupling equations of motion, is based on Hubbard's scattering correction approximation for the Hubbard model. It takes account of dynamical scattering, the exchange of angular momentum between local and conduction electrons, in a local approximation. Our CPA is exact in the atomic limit for all band-filling $n$, reduces to Kubo's one-electron dynamical CPA in the empty-band limit $n\rightarrow 0$, and reduces to dynamical mean field theory (DMFT) in the classical spin limit $S\rightarrow\infty$.

The electronic structure and resistivity $\rho$ of the paramagnetic state are calculated. We find, using the elliptical approximation to the bare density of states (DOS), that $\rho$ is orders of magnitude too small to agree with experiment. This confirms that the bare DE model is inadequate as a model for CMR materials. The much larger value for $\rho$ calculated by Furukawa is found to be due to his Lorentzian approximation for the bare DOS. We also calculate the magnetic susceptibility $\chi$ of the paramagnetic state, working in the strong-coupling limit $J\rightarrow\infty$ and calculating all correlation functions appearing in the CPA Green function equations self-consistently. We find no transition to ferromagnetism for any $S$ and unphysical deviations from the Curie law at half-filling. The reasons for this failure of our approximation are identified and a modification is proposed which gives a transition to ferromagnetism for all $S$ and the correct Curie law behaviour of $\chi$ at half-filling.


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