For problem part (a) the applied field is µ0H = (-24.6 mT, 4.3 mT, 0.0 mT), where the first (x) coordinate is the long (500 nm) axis of the part and the last (z) coordinate is the short (3 nm) axis. This field is in the xy-plane with of a magnitude of approximately 25 mT directed 170° from the positive x-axis. The reversal proceeds relatively smoothly with the magnetization as a whole rotating counterclockwise towards the reversed direction. The reversal overshoots before gradually settling down into the reversed (non-zero field) equilibrium state.
In problem part (b) the applied field is µ0H = (-35.5 mT, -6.3 mT, 0.0 mT), which has magnitude of approximately 36 mT directed 190° from the x-axis in the xy-plane. The reversal in this case is more complicated. The end regions initially rotated counterclockwise while the middle section rotates clockwise, with the result that 360° domain walls form between the middle and end domains. The 360° domain walls gradually move out from the center and dissipate at either end of the part.
Parameter, but for simplicity of presentation that has not been done here.
The discretization cell size in these simulations is set at 1 nm × 1 nm × 1 nm , so the the number of cells in the simulation is 500 × 125 × 3 = 187500 cells. This mesh is sufficiently small to keep the maximum angle between neighboring cells below about 6° in part (a) and 18° in part (b). These files are loaded into Oxsii; in the dynamic simulations the magnetization state was written to disk at the end of each stage, i.e., every 4 picoseconds of simulation time. These simulations each run 2 ns, so including the initial state 501 magnetization files are saved for each simulation.
Here are plots showing how the magnetization components,
averaged across the entire volume, vary with time:
(The backslash character at the end of the first two lines is a command line continuation character. On Windows these would be caret characters, ^, instead—or just type it all out on one long line.) The avf2ppm configuration file stdprob4-div.config determines the scaling and coloring of the output images. In this case the arrows are colored based on their z-component and the pixels are shaded by the pointwise divergence. The configuration file is created by first viewing a sample .omf file in mmDisp and adjusting the controls to get an acceptable image. The configuration is saved via the
tclsh oommf.tcl avf2ppm stdprob4*omf -config stdprob4-div.config \
-opatexp "Oxs_TimeDriver-Magnetization-([0-9]+)-.*.omf" \
-opatsub "\1.png" -filter pnmtopng
File|Write config…dialog box in mmDisp, and then additional edits are made with a plain text editor. In particular, the configuration options
enable anti-aliasing for the arrows, and set the image width and height to 1200×360 pixels, dimensions that are compatible with the video codecs used below.
-opatsub expressions shorten
the output filenames and change the extensions to .png, e.g.,
stdprob4a-Oxs_TimeDriver-Magnetization-0000013-0000977.omf → stdprob4a-0000013.pngIn particular, this retains the stage number (here 13) and drops the iteration number (977).
-filter pnmtopng option sends the PPM bitmap output
from avf2ppm through
command line program pnmtopng, which converts the output to PNG format.
The movie making software FFmpeg can read PPM files directly, so this
step is optional. However, the (compressed) PNG files are much smaller
than the (uncompressed) PPM files, so this step reduces intermediate disk
Once the bitmap files are created, the FFmpeg tool can be used to create movies in any of a wide variety of formats. For this page movies are made in three formats: MP4, WebM, and Ogg. (FFmpeg can also be used to create animated GIFs. However, they can be rather large, so for performance reasons the instructions for building animated GIFs are on a separate page.)
The commands for creating the Standard Problem 4a movies are
The quality settings above (
ffmpeg -start_number 0 -i stdprob4a-%07d.png -r 25 -c:v libx264 \
-pix_fmt yuv420p -qmin 0 -qmax 32 -an stdprob4a-div.mp4
ffmpeg -start_number 0 -i stdprob4a-%07d.png -r 25 -c:v libvpx \
-qmin 0 -qmax 32 -an stdprob4a-div.webm
ffmpeg -start_number 0 -i stdprob4a-%07d.png -r 25 -c:v libtheora \
-qscale:v 5 -an stdprob4a-div.ogv
-qscale) produce movies of similar quality, although the file size for the last is a considerably bigger (18 MB) than the first two (9 MB and 6 MB, respectively). The same options are used for the Standard Problem 4b movies; in that case the resulting movie files are sized 11 MB, 8 MB, and 21 MB respectively.
The movies are 501 frames long and run at 25 frames per second, so the viewing duration is 20 seconds. The simulation time is 2 ns, so each second of viewing time corresponds to 100 ps of simulation.
Download Video: "MP4" "WebM" "Ogg"
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Date created: Sep 18, 2014 | Last updated: Sep 25, 2014 Contact: Webmaster