Proposal for a Standard Problem for Micromagnetic Simulations Including Spin-Transfer Torque
Massoud Najafi, Benjamin Kruger, Stellan Bohlens, Matteo Franchin, Hans Fangohr, Antoine Vanhaverbeke, Rolf Allenspach, Markus Bolte, Ulrich Merkt, Daniela Pfannkuche, Dietmar P. F. Moller, and Guido Meier
University of Hamburg, IBM Zuerich, University of Southampton
Online: journal, local postprint pdf, eprints.soton.ac.uk
Table of contents (this web page)
- The micromagnetic standard problems allow to compare
the simulation results of different simulation tools and help
finding bugs and errors.
- Here we propose a new standard problem that adds a spin-torque
transfer term to the micromagnetic model.
We propose a micromagnetic standard problem including the spin-transfer torque that can be used for the validation and falsification of micromagnetic simulation tools.
The work is based on the micromagnetic model extended by the spin-transfer torque in continuously varying magnetizations as proposed by Zhang and Li.
The standard problem geometry is a permalloy cuboid of 100 nm edge
length and 10 nm thickness, which contains a Landau pattern with a
vortex in the center of the structure
Plot of the relaxed state in the absence of a spin-torque transfer torque. The colours represent the out-of-plane component of the magnetisation. Ms is 80k A/m.
A spin-polarized dc current density of 1012 A/m2 flows laterally through the cuboid and moves the vortex core to a new steady-state position.
We show that the new vortex-core position is a sensitive measure for the correctness of micromagnetic simulators that include the spin-transfer torque.
We compute, show and compare numerical results from four different
finite-difference and finite-element-based simulation tools. We also
show the solution of an approximate but analytical model.
A comparison of the spatially averaged x-component of the system after
application of a spin-polarised current at time t=0, computed
repeatedly using different methods.
- The mesh and two simulation files are available in the Nmag manual together with a detailed description. We provide them for completeness again:
- pyfilm.nmesh.h5 -- the mesh (this is a somewhat coarser mesh than used in the publication to allow faster computation)
- relaxation.py -- the script to compute the ground state (without the spin-torque-transfer current)
- stt.py -- the script to compute the time development with the applied spin-polarised current.
