Write error rate in spin-transfer-torque random access memory including micromagnetic effects

Spin-transfer-torque (STT) random access memory (STTRAM) is considered to be one of the promising candidates for a non-volatile memory for improved scalability and access speed. Write error rate (WER) in an STTRAM is the probability that the free layer magnetization of the STTRAM bit does not flip when a write current is applied because of random thermal fluctuations. The WER needs to be below a certain acceptable limit for reliable write operation. Previously, WER have been studied using Fokker-Planck (FP) calculations for perpendicular bit [1] and using Landau-Lifshitz-Gilbert (LLG) simulations for the magnetization dynamics including a random thermal magnetic field and an STT term, for an in-plane bit with and without perpendicular magnetic anisotropy (PMA) [2]. These studies however assumed the free layer magnetization to be a macrospin, thereby neglecting the spatial variation in spin across the free layer (micromagnetic effects). Several important experimental observations related to WER in STTRAM have, however, been attributed to spatially varying spin-texture in the free layer magnet, for example, sub-volume excitations [3] and higher order spin wave modes related to branching of WER [4, 5].