1 / 13

Check LLG Solution and Approximation

This study evaluates the accuracy of the Japanese, Sun's, and our own approximations in integrating Huanlong equations from the Landau-Lifshitz-Gilbert (LLG) model. Results show that the Japanese approximation is superior for small initial angles, while ours is better for larger overdrives. Comparisons reveal that Sun's method yields a larger switching time due to overlooking the second term and modifying the tangent function. Experimental conditions favor Sun's approximation due to consistent performance regardless of initial angles.

francis-alvarez
Télécharger la présentation

Check LLG Solution and Approximation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Check LLG Solution and Approximation Huanlong

  2. Equations Integration LLG: Exact solution: Our Approximation : Sun Approximate : Japanese Approximation :

  3. Results I: integration from LLG E: Exact solution A1: Our approximate solution A2: Japanese approximation AS: J. Sun’s approximation

  4. Results

  5. Results

  6. Conclusion • Exact solution is the same as numerical integration of LLG equation. • Japanese approximation is always better(almost the same as the exact solution for these small initial angles) than our approximation, since it keeps more terms. • Compare J. Sun’s approximation with ours.

  7. J. Sun’s approximation vs. ours • Both approximations ignore the second term, which yields a largerτ. • Sun’s approximation also change tan(θ/2) to θ/2 • tan(x) < x for all 0 < x < π / 2 • the difference between tan(x) and x increases as x increases. Which will reduce the value of τ. • Need to compare the increase of τ(both) with the decrease of τ(Sun). τ Ours tan(x) –>x Sun’s no 2nd term Exact solution Approximations tan(x) –>x Sun’s

  8. Compare Approximations Time(time difference between the exact solution and approximations) to reach the equator as a function of initial angles Small overdrive: Sun’s is better than ours

  9. Compare Approximations Time(time difference between the exact solution and approximations) to reach the equator as a function of initial angles large overdrive: Ours is better than Sun’s

  10. Compare Approximations • τE: switching time from the exact solution. • τO: switching time from our approximation. • τS: switching time from Sun’s approximation. • Sun’s approximation is better for i < 6 • Ours approximation is better for i > 6. • In experimental condition, Sun’s approximation is better. Doesn’t change much with initial angles Sun’s is better Ours is better

  11. Results

  12. Results

  13. Results

More Related