Operating conditions and stability of spin torque majority gates: Analytical understanding and numerical evidence

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Abstract
The functionality of a cross-shaped Spin Torque Majority Gate (STMG) is primarily limited by the pinning of a domain wall (DW) at the center of the device. Here, an analytical model is built to calculate the conditions for such a pinning and to deduce the operating range. The assumptions of the model and the conclusions are validated by micromagnetic simulations. The total magnetic energy of the DW state is derived. By minimizing this energy with respect to two degrees of freedom, the DW stability condition is obtained. We find that the lateral length of the STMG is the critical dimension: it must be smaller than about five times the DW width. This result is confirmed by micromagnetic simulations with a high accuracy. In process, we solved a more fundamental problem: the macrospin limit of a finite ferromagnet containing one pinning site. We found the correction of the usual DW width expression due to finite length of wires.

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