對於磁性穿隧接合(magnetic tunnel junctions)，其磁性狀態的控 制可分別藉由外加磁場造成穿隧磁組效應(tunnel magnetoresistance)或是以自旋極化電流引發自旋傳輸矩(spin-transfer torque)調控。在穿隧磁組效應的推導中，我們藉由結合Brinkman′s model 以及Simmons′method 來計算在低電壓之下，電流對於電壓的曲線以及隧磁組效應的表達式。而在自旋傳輸矩的推導中，對於單層或是三層絕緣體的磁性穿隧接合，其中間材料可為普通絕緣體或是spin-filter 材料，我們採用tight-binding model 以及Keldysh formalism，我們分別得出 field-like spin torque以及net spin-transfer torque 所適用的general expression。經由數學推導，在spin-filter 為基底的三層磁性穿隧接合FM/I/SF/I/FM MTJ 中，我們發現其 general expression 有額外的項，而其為在三層絕緣體內部的多重反射所造成。因此藉由穿隧磁組效應和自旋傳輸矩的解析式推導來建立多層材料性質與自旋傳輸特性之間的關連，並提供簡單的方向來解釋複雜磁性穿隧接合的實驗結果。;For magnetic tunnel junctions (MTJs), where the magnetic state can be controlled either by an external magnetic field via the tunnel magnetoresistance (TMR) effect or by a spin-polarized current to induce the spin-transfer torque effect. In the derivation of TMR effect, we combine the Brinkman′s model and the Simmons′ method to calculate the current density-voltage curve and the expression of TMR at low bias. In the derivation of spin-transfer torque effect, we employ the tight-binding model with the Keldysh formalism to obtain the general expressions for field-like spin torque and spin-transfer torque, in the single- and triple-barrier-based MTJs, where the central barrier can be chosen by insulting (I) or spin-filter (SF) materials. For SF-based FM/I/SF/I/FM MTJ, the general expression of field-like spin torque has additional terms originated from the multi-reflection processes inside the triple-barrier. These analytical derivations of TMR spin-transfer torque effects reveal the relation between material properties and the spin transport properties of MTJs with multi-barriers, which provide simple guidelines to explain the experimental results in complicated MTJs.
