## Abstract

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_{s}^{P(AP)} = G_{0}σk _{F, s}^{2}/4π ∫ Cos (θ_{s}) D_{s}^{P(AP)} Sin(θ)dθ_{s}d, where Cos(θ_{s}) is cosine of incidence angle of the electron trajectory θ_{s}, with spin index s=(↑,↓), k_{F, s}, is the Fermi wave-vector of the top (bottom) ferromagnetic layers; for simplicity the top and bottom ferromagnetic layers are taken as symmetric; G_{0}=2e^{2}/h and σ is area of the tunneling cell. The transmission probability D_{s}^{P(AP)} depends on diameter of NP (d), effective mass m and wave-vector of the electron k_{NP} attributing to the quantum state on NP (corresponding to the k-vector of the middle layer in DMTJs [1], and which is affected by applied bias V). Furthermore D_{s}^{P(AP}) depends on Cos(θ_{s}), k_{F, s}, barriers heights U_{1,2} and widths L_{1,2}, 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^{2}), 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_{1↑}+G_{2}↑+G_{1↓}+G_{2}↓), where G_{1, s} is dominant conductance with the NP (path I), G_{2, s} is conductance of the direct tunneling through the single barrier (path II), and TMR=(G^{P}-G^{AP})/G^{AP} ×100%.

Original language | English |
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Title of host publication | 2015 IEEE International Magnetics Conference, INTERMAG 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781479973224 |

DOIs | |

State | Published - 14 Jul 2015 |

Event | 2015 IEEE International Magnetics Conference, INTERMAG 2015 - Beijing, China Duration: 11 May 2015 → 15 May 2015 |

### Publication series

Name | 2015 IEEE International Magnetics Conference, INTERMAG 2015 |
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### Conference

Conference | 2015 IEEE International Magnetics Conference, INTERMAG 2015 |
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Country/Territory | China |

City | Beijing |

Period | 11/05/15 → 15/05/15 |