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Tunnel magnetoresistance in magnetic tunnel junctions with embedded nanoparticles

机译：嵌入纳米粒子的磁性隧道结中的隧道磁阻

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We present a theoretical simulation to calculate the tunnel magnetoresistance (TMR) in magnetic tunnel junction with embedded nano-particles (npMTJ). The simulation is done in the range of coherent electron tunneling model through the insulating layer with embedded magnetic and non-magnetic nano-particles (NPs). We consider two conduction channels in parallel within one MTJ cell, in which one is through double barriers with NP (path I in Fig. 1) and another is through a single barrier (path II). The model allows us to reproduce the TMR dependencies at low temperatures of the experimental results for npMTJs [2-4] having in-plane magnetic anisotropy. In our model we can reproduce the anomalous bias-dependence of TMR and enhanced TMR with magnetic and non-magnetic NPs. We found that the electron transport through NPs is similar to coherent one for double barrier magnetic tunnel junction (DMTJ) [1]; therefore, we take into account all transmitting electron trajectories and the spin-dependent momentum conservation law in a similar way as for DMTJs. The formula of the conductance for parallel (P) and anti-parallel (AP) magnetic configurations is presented as following: G = Gσk /4π ∫ Cos (θ) D Sin(θ)dθdφ, where Cos(θ) is cosine of incidence angle of the electron trajectory θ, with spin index s=(↑,↓), k, is the Fermi wave-vector of the top (bottom) ferromagnetic layers; for simplicity the top and bottom ferromagnetic layers are taken as symmetric; G=2e/h and σ is area of the tunneling cell. The transmission probability D depends on diameter of NP (d), effective mass m and wave-vector of the electron k attributing to the quantum state on NP (corresponding to th- k-vector of the middle layer in DMTJs [1], and which is affected by applied bias V). Furthermore D) depends on Cos(θ), k, barriers heights U and widths L, respectively. The exact quantum mechanical solution for symmetric DMTJ was found in Ref.[1]. Here we employ parallel circuit connection of the tunneling unit cells, where each cell contains one NP with the average d less than 3 nm per unit cell's area (σ =20 nm), while tunnel junction itself has surface area S and consists of N cells (N=S/σ). The total conductance of the junction is G = Nx (G+G↑+G+G↓), where G is dominant conductance with the NP (path I), G is conductance of the direct tunneling through the single barrier (path II), and TMR=(G-G)/G ×100%.
机译：我们提出了一种理论模拟，以计算具有嵌入式纳米粒子（npMTJ）的磁性隧道结中的隧道磁阻（TMR）。在相干电子隧穿模型的范围内，通过具有嵌入的磁性和非磁性纳米粒子（NPs）的绝缘层进行了仿真。我们考虑在一个MTJ单元中并联的两个传导通道，其中一个通过带有NP的双重势垒（图1中的路径I），另一个通过单个势垒（路径II）。该模型使我们能够再现具有平面内磁各向异性的npMTJ [2-4]的实验结果在低温下的TMR依赖性。在我们的模型中，我们可以使用磁性和非磁性NP再现TMR和增强型TMR的异常偏差依赖性。我们发现，通过NP的电子传输类似于双势垒磁性隧道结（DMTJ）的相干电子[1]。因此，我们以与DMTJ相似的方式考虑所有传输电子轨迹和自旋相关的动量守恒定律。平行（P）和反平行（AP）磁结构的电导公式表示如下：G =Gσk/4π∫Cos（θ）D Sin（θ）dθdφ，其中Cos（θ）是入射余弦自旋指数s =（↑，↓），k的电子轨迹的角度θ是顶部（底部）铁磁层的费米波矢量；为简单起见，将顶部和底部铁磁层视为对称； G = 2e / h，σ是隧道单元的面积。传输概率D取决于NP（d）的直径，有效质量m和归因于NP上的量子态的电子k的波矢量（对应于DMTJs中层的th-k矢量）[1]，并且这受施加的偏压V）的影响。此外，D）分别取决​​于Cos（θ），k，势垒高度U和宽度L。参考文献[1]中找到了对称DMTJ的精确量子力学解。在这里，我们采用隧道单元的并联电路连接，其中每个单元包含一个NP，每个d的平均d小于每个单元单元的面积（σ= 20 nm）小于3 nm，而隧道结本身具有表面积S，由N个单元组成（N ＝ S /σ）。结的总电导为G = Nx（G + G↑+ G + G↓），其中G是NP的主要电导（路径I），G是通过单个势垒的直接隧穿的电导（路径II）。 ，并且TMR =（GG）/ G×100％。

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