Computer simulation study of rare events in magnetic nanosystems: error rates and energy barriers in STT-MRAM cells

• Applicant: Privatdozent Dr. Dmitry Berkov
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 389034432

• Final Report Year: 2021

Final Report Abstract

The following results have been obtained during the project processing: • A tool for simultaneous simulations of magnetization dynamics in a collection of small non­ interacting nanoelements, which uses the whole performance of modern GPUs (normally available only for large systems) has been created. Corresponding simulations of magnetization reversal in such nanoelements have revealed a decisive role of internal dynamic modes in the current­driven magnetization reversal. • The Rare­Event­Enhancement (REE) method for simulation of write error rates (WER) in MRAM cells has been implemented and strongly optimized. Simulations of WER in nanoelements with both in­plane and out­of­plane anisotropy in the macrospin approximation and in the micromagnetic approach have been carried out. • A new formalism for predicting the space and time dependencies of a magnetic field pulse which would ensure the magnetization reversal of a nanoelement with minimal energy consumption has been developed. Results for a uniaxial and biaxial macrospins have shown a highly non­trivial dependence of such a field pulse and the minimal required energy on the nanoelement parameters. • To study the read error rates (RER), long­time micromagnetic simulations on a large collection of magnetic nanoelements for different read currents have been performed. Qualitative changes of the life time distribution of the stored information have been found with increasing current. Obtained results show the possibility to compute arbitrarily small RER by analyzing the corresponding life time distribution. • A comprehensive comparative analysis of two analytical and four numerical method ­ accompanied by a strong optimization of the latter ones ­ for computing the switching rate over high energy barriers in magnetic systems have been conducted. We have shown that among all existing classes of numerical methods only the forward flux sampling (FFS), which we have crucially optimized by suggesting a new paradigm for placing FFS interfaces, can provide self­consistent and sufficiently accurate results. • We have created a completely new class of methods for computing the switching rate over arbitrarily high energy barriers via single­stage Langevin dynamics simulations basing on the concept of an energy­dependent effective temperature. Computer time for evaluation of the switching rate with these methods does not increase with the energy barrier height, what provides a very large speedup compared to the traditional ’climbing’ methods like FFS.

Publications

• Injection Locking at Fractional Frequencies of Magnetic­ Tunnel­Junction­Based Read Sensors’ Ferromagnetic Resonance Modes, Phys. Rev. Appl. 12 (2019) 054022
  E. Auerbach, D. Berkov et al.
  
• Magnetization switching in nanoelements induced by the spin­transfer torque: Study by massively parallel micromagnetic simulations, AIP Advances 9 (2019) 055307
  E.K. Semenova and D.V. Berkov
  
• Evaluation of the switching rate for magnetic nanoparticles: Analysis, optimization, and comparison of various numerical simulation algorithms, Phys. Rev. B 102 (2020) 144419
  E.K. Semenova, D.V. Berkov, and N.L. Gorn
  
• Optimal Control of Magnetization Reversal in a Monodomain Particle by Means of Applied Magnetic Field, Phys. Rev. Lett 126 (2021) 177206
  G.J. Kwiatkowski, M.H.A. Badarneh, D.V. Berkov, and P.F. Bessarab
  
• Single­stage direct Langevin dynamics simu­ lations of transitions over arbitrary high energy barriers: Concept of the energy­dependent temperature
  D. Berkov, E.K. Semenova, and N.L. Gorn