File:Spin wave.gif
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Summary
| Description |
English: Spin waves are an intrinsically quantum phenomenon, so they are hard to visualize. But if we think in term of magnetization we can get a general picture of what it is going on, and how a point excitation propagates in the medium.
Obtained integrating the Landau–Lifshitz equation on a square grid, where each "spin" feels an effective magnetic field proportional to the sum of its scalar products with its 4 nearest neighbours. It's a toy model, but it gives the general idea. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1372550090083155970 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
\[Gamma] = 1; \[Lambda] = 0.05; dt = 0.05; J = 0.2;
steps = 500;
nx = 21; ny = 21; n = nx*ny;
adjacency = Normal@AdjacencyMatrix[GridGraph[{nx, ny}] ];
M0 = Table[{0, 0, 1}, {n}];
M = M0; M[[Floor[nx/2]*ny + Floor[ny/2] + 1]] = {1, 1, 0};
Graphics3D[{
Flatten@Table[Line[{{Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0}, {Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0} + M[[j]]} ], {j, 1, n}] }, PlotRange -> {{Sqrt[n]/4, 3/4 Sqrt[n] + 1}, {Sqrt[n]/4, 3/4 Sqrt[n] + 1}, {-0.25, 1}}]
evo = Reap[Do[
M = (#/Norm[#] &) /@ M;
Hext = J*adjacency . M;
M = Table[ M[[j]] + dt*(-\[Gamma] Cross[M[[j]], Hext[[j]] ] - \[Lambda] Cross[ M[[j]], Cross[M[[j]], Hext[[j]] ]]), {j, 1, n}];
Sow[M];
, {steps}]][[2, 1]];
\[Alpha] = 1;
frames = Table[Graphics3D[{
Black,
Table[ Sphere[{Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0}, 0.08], {j, 1, n}],
Table[ Sphere[{Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0} + \[Alpha]*evo[[k, j]], 0.05], {j, 1, n}],
Thick,
Flatten@Table[ Line[{{Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0}, {Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0} + \[Alpha]*evo[[k, j]]} ], {j, 1, n}],
Red,
Table[ Line[({Mod[j, Sqrt[n], 1], Quotient[j, Sqrt[n], 1] + 1, 0} + # &) /@ (\[Alpha]*evo[[Max[1, k - 50] ;; k, j]]) ], {j, 1, n}],
Gray,
Cuboid[{Sqrt[n]/4, Sqrt[n]/4, 0}, {3 Sqrt[n]/4 + 1, 3 Sqrt[n]/4 + 1, -0.2}]
}, PlotRange -> {{Sqrt[n]/4, 3/4 Sqrt[n] + 1}, {Sqrt[n]/4, 3/4 Sqrt[n] + 1}, {-0.25, \[Alpha] + 0.1}}, ImageSize -> 500,
Lighting -> "Neutral", Boxed -> False]
, {k, 2, steps/1, 4}];
ListAnimate[frames]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:54, 22 March 2021 | | 667 × 446 (4.57 MB) | Berto | Uploaded own work with UploadWizard |
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