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

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. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.