在此篇論文中，我主要是研究在鐵磁/稀磁性半導體/鐵磁的三層接面結構內的磁性反應，然後利用線性反應理論來計算此結購中磁化率張量，因為稀磁性半導體內的磁化量會對內部的載子施加一個內在磁場，使得磁化率張量產生非零的非對角線元素，其不為零的原因可理解為載子自旋會在均勻磁場下做precession，而稀磁性半導體內載子所形成的費米氣體本身在磁化率張量的對角線上就不為零，這就是過去已被知道的RKKY交換，所以我會將非對角線上的元素稱為螺旋交換，而RKKY交換和螺旋交換分別來自於各自不同的物理機制，且在我們的系統內能同時共存。因為有磁性反應的緣故，兩層鐵磁層的磁矩之間會產生一個角度，稱之為螺旋角，其由上述兩種交換間的相對強度來決定，我的論文則會著重在討論螺旋角如何隨著稀磁性半導體內的磁化量、載子自旋生命期和稀磁性半導體層的寬度而改變，然後我們提出當稀磁性半導體內的載子只被部份自旋極化且自旋鬆弛率夠大下，較可能從實驗上觀察到這樣的螺旋交換。

In this thesis, I study the magnetic response of a ferromagnet/DMS/ferromagnet junction. Linear response theory is used to calculate the magnetic susceptibility tensor. Because there is an internal magnetic ‾eld, namely magnetization, inside the DMS layer, it causes the tensor to have non-diagonal matrix elements. I attribute the non-diagonal elements to carrier spin precession under a uniform magnetic field. However, the Fermi gas owns an intrinsic magnetic response, RKKY exchange, so we call the non-diagonal elements spiral exchange. These two exchange mechanisms originate from each one's physical reason but interplay with each other in our system. The angle be-
tween the two ferromagnetic layer moments, called the spiral angle, depends on the relative magnitude of the two exchange. This thesis emphasizes on studying how the sprial angle changes with magnetization, carrier spin lifetime, and width of the DMS layer. I will suggest that the spiral exchange can be possibly observed experimentally in the regime where carriers are partially polarized and have enough large spin relaxation rate.

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