半填滿的S能帶的鐵磁不穩定性研究

Ferromagnetic Instability in an Almost Hall-filled s-band

郭良吉(Liang-Chi Kuo)

指導教授 ： 黃偉能

中原大學/理學院/應用物理研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200510

摘要

摘要

　　當單一電洞的鐵磁態(ferromagnetic state)系統為基態被證實後，學者便朝兩個電洞的鐵磁態系統前進。由於兩個電洞的鐵磁態系統能量是否為最低的問題，直至現今仍爭議不斷，而眾多學者持續為自己所支持的論點提出研究的成果，不同的計算方式以及近似方法也相繼成現在世人面前，但始終無一結果可讓兩方的支持者同時接受。
本文利用在1963年被提出的哈柏模型(Hubbard model)進行計算，此模型將個電子的能帶緊縮，使之不與鄰近的電子有交互作用，此方式即稱為能帶緊束法(Tight binding method for energy bands)﹔整個模型則是電子移動後所獲得的能量t(t<0 )與庫倫位能U這兩項的影響與限制，且電子只能移動到最鄰近的位置上，而計算的時所考慮的限制條件則是電子移動時不可能發生的情況。
最後，我們得到兩個電洞的單重態(singlet state)能量低於鐵磁態，而這就表示兩個電洞的鐵磁態能量並不是最低，也就是說兩個電洞的鐵磁態並不穩定。

關鍵字

單重態 ； 哈柏模型 ； 鐵磁態

並列摘要

Abstract

After the fact that the ferromagnetic state with one hole in a narrow band is ground state has been verified, next comes the question whether the ferromagnetic state with two holes is still the ground state. Researchers have presented diverse ways of taking approximations and doing calculation, but there is no rigorous proof for two holes, and the stability of the ferromagnetic state is still an unsolved problem.

In this thesis, we use Hubbard model, which is presented in 1963 and tight binding method for energy bands to study the problem. The model is determined by a nearest-neighbor transfer matrix t and on-site repulsion U. We take further limit U= to simplify the consideration.

In conclusion, for two holes, we are able to obtain a singlet state with lower energy than that of ferromagnetic state. The ferromagnetic state is no longer the ground state as soon as two holes are present.

並列關鍵字

ferromagnetic state ； Hubbard model ； singlet state

參考文獻

1. Electron correlations in narrow energy bands

2. On the instability of the ferromagnetic state in the

limit of the Hubbard model

by B.Doucot and R. Rammal, Int. J. Mod. Phys. B3, 12(1989).

3. Electron correlation and ferromagnetism of transition metals