Switching thresholds in MTJ using SPICE model – Effects of spin and Ampere torques

Abstract

Spin torque due to spin polarized tunneling current can be used to switch the free layer in a magnetic tunnel junction (MTJ). This current also gives rise to an Ampere torque, which influences the switching threshold of the MTJ. We modified the Landau–Lifschitz–Gilbert equation (LLGE) to include an Ampere torque term and solved for the magnetization dynamics under the single domain approximation using a linear solver in SPICE. We also extend the model to a square array of MTJs to study the effect of nearest neighbour interactions in addition to effects like demagnetization and magnetostatic interactions with the pinned layer. The interlayer exchange field between the free and pinned layers of a MTJ and the spin torque are competing factors that decide the threshold current density for switching the MTJ. We used a two current model to study the effects of barrier height and barrier thickness on spin torque and exchange energy. We observe that both the spin torque and exchange energy decrease with an increase in barrier height (for ferromagnetic coupling) and barrier thickness. We find that the inclusion of Ampere torque causes a reduction in the switching current. Varying the thickness of MgO and Al2O3 barriers allows us to minimize the switching threshold voltage. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Advanced Macro-Model with Pulse-Width Dependent Switching Characteristic for Spin Transfer Torque Based Magnetic-Tunnel-Junction Elements

“…There have been several works to model basic characteristics of conventional or STTbased MTJ. [2][3][4][5][6] The prior models of an STT-based MTJ focused on the modeling of asymmetrical tunneling magneto resistance (TMR). 3) These models, however, do not fully represent the behavior that the minimum current density for switching depends on the pulse-width of applied current.…”

“…There are other works which focused on the compact modeling of a MTJ, 5) and switching threshold in MTJ using SPICE model. 6) In these woks, the resistance of MTJ and switching behavior are determined either by magnitude of the current or Ampere torque induced by the current. By reflecting relation between switching current and pulsewidth of the current to the model, more accurate prediction is possible in circuits with STT-MTJ elements.…”