d および f電子系における原子軌道磁気モーメント

Atomic Orbital Magnetic Moments in d and f Electron Systems

Shishidou Tatsuya

The orbital magnetic moment and related phenomena in the 3d and 5f electron systems are examined by the Hartree-Fock approximation (HFA). We will show that the faithful treatment for the exchange interaction is crucially important in describing the orbital magnetism in solids.

First, the atomic ground states of magnetic ions are summarized and the applications of HFA are given to examine its validity in describing magnetic quantities. It is shown that HFA reproduces Hund's first and second rules in the 3d and 4f systems. The third rule is not reproduced in the less than half filling case. In the 3d ions, however, the crystal-field effect, i.e., some kind of the solid-state effect, makes HFA to be a good approximation. In the uranium ions, where the 5f spin-orbit interaction is so large, HFA gives their ground state fairly reasonably.

Encouraged by these results, we apply the tight-binding HF method to the insulating CoO in order to study its possible antiferromagnetic structure and orbital state. CoO is well known to exhibit the second kind of antiferromagnetic structure, which is in general described by the four wave vectors {Qi}. It is still an open question whether the single- Q structure or multiple-Q structure is realized in CoO. Our calculation, which takes into consideration the 3d spin-orbit interaction and the intra-atomic full 3d-3d multipole inter action, shows interesting results; in addition to a collinear single-Q structure, a noncollinear quadruple-Q one, both of which are compatible with the neutron diffraction experiment, are obtained as stable HF solutions. The magnitude of the Co orbital magnetic moment is shown to be as large as ~ 1μB. Relationship between the orbital magnetism and the band-gap formation is explained.

In free atoms, their ground states have no relation to the monopole Coulomb interaction represented by the Slater integral F0, and the other multipole terms determine their magnetic state. In solids, however, the orbital magnetic moment shows strong dependence on F0, even in metallic phase. By considering simple systems, the enhancement mechanism of the orbital moment through F0 is discussed in detail.

Finally, the electronic structure of the ferromagnetic compound US is examined. The U 5f spin and orbital magnetic moments are calculated on the basis of the extended Hubbard model and HFA. Our tight-binding model includes the U 6p, 5f, 6d and 7s orbitals and the S 3s, 3p and 3d ones, and the intra-atomic 5f-5f multipole interaction and the spin-orbit interaction in the 5f state are taken into account. Most of parameters involved in the model are determined by fitting with the energy of Bloch electrons in the paramagnetic state obtamed by a first-principles calculation based on the local density approximation (LDA). The calculated magnetic quantities are in good agreement with available experimental results. The magnetic circular dichroism spectrum at the U 3d→5f x-ray absorption is also calculated and agrees with the recent experiment. It is shown that the exact exchange potential, gained by HFA, can mix the spin up and down states and enhance the effect of the spin-orbit interaction. This feature is not seen in the LDA potential, and the problems of LDA in the estimation of the orbital moments are discussed.

Electrical engineering [ 540 ]

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広島大学