Skyrmion
In theoretical physics, the Skyrmion (after Tony Skyrme ) is a model of topologically stable solitons - vortices in fields . These eddies behave like particles or quasiparticles of finite mass.
Skyrmions were used as a model from 1958 in attempts to explain the previously puzzling strong interaction . Protons, neutrons and pions are particularly subject to it. Tony Skyrme wanted to explain the strong interaction by saying that protons and neutrons were eddies in pion fields. The stable eddies were called "skyrmions". Around 1965 it became clear that protons, neutrons, and pions are made up of quarks. This meant that in nuclear physics there was no longer any need for skyrmions as an explanatory model.
From the 1980s the term model was adopted in solid state physics . It became popular in particle physics with the work of Edward Witten and various bag models (see also Kenneth A. Johnson ) and u. a. discussed for the quantum Hall effect in two-dimensional electron gases. Skyrmions are currently also being investigated at the surfaces and interfaces of magnetic systems.
In early 2009 was at the Technical University of Munich from Sebastian Mühlbauer , Christian Pfleiderer , Peter Böni , the theorist Achim Rosch ( University of Cologne ) and other first time skyrmion lattice in a magnetic solids ( manganese silicon at -245 ° C and in a magnetic field of 0.2 Tesla ) can be detected directly. A publication submitted in September 2010 and published in July 2011 by a research group at the Universities of Kiel and Hamburg and the Jülich Research Center describes the first evidence of skyrmions without an external magnetic field. In 2013, the University of Hamburg succeeded in creating and deleting skyrmions in a targeted manner on surfaces. Since stable skyrmions have also been demonstrated at room temperature, their use in fast information storage devices appears possible in the future. A distinction is made in crystals between Néel and Bloch skyrmions and anti-skyrmions as a mixture of Néel and Bloch states. In 2019, the three-dimensional resolution of the magnetic structure of skyrmions was achieved, whereby the approximately 100 nm large skyrmions were investigated in multiple layers of Ta / CoFeB / MgO. The dipole-dipole interaction together with the interaction with the external magnetic field turned out to be particularly important for stabilization.
Simulation in FDTD (2D)
A 2D skyrmion results from the rotation of the soliton of the Sinus Gordon equation around the center. It can be modeled in an FDTD simulation medium, which in 2D resembles a grid of math boxes. In each box there is a 3D vector arrow with the unit length 1 on the 2D surface. The third coordinate axis enables the arrow to point in one of the two neutral directions (e.g. Down) at a location without particles. Often the skyrmion is shown as a hedgehog unwound on the surface. The hedgehog can also be made in such a way that the arrows are arranged in boxes. Most of the arrows pointing down have been omitted in the diagram.
FDTD means that e.g. B. a small world with 360 × 240 pixels is created. The few formulas used in the simulation are world formulas in this world. The author of the simulation can determine what will happen during runtime by initializing the medium (main memory). The special feature of the Sinus-Gordon equation is that, as a universal formula, it enables particles to be at rest.
A double buffer algorithm is used in the simulation videos shown. In cycle 1, differences between the values stored in the pixels are created (1st derivative). After that, a step that usually does not occur in the double buffer forms the mean value of one pixel and its eight neighboring pixels. As a second step, the Sinus Gordon equation and a wave algorithm are used, which are superimposed. The calculation does not require an explicit call to the sin () function; it is reproduced by simulation. Simply put, each pixel is only dependent on its close environment from the previous image. It is not calculated depending on any time. As a limitation, there is the need to normalize the unit length of the 3D vectors at each step by approximation because of step deviations. The square root is necessary for this. The simulation also contains a damping term. Edges have not yet been terminated (see probe termination). The formation of the neighborhood difference results in an odd grid. Pixels from step one and step two overlap. To optimize computing time, the x-axis points 45 ° from top left to bottom right. The y-axis shows 45 ° from bottom left to top right. The simulation only renders every second image into the video in time-lapse.
The variables
// Alle Pixel.
p->* ... Pixel(x, y) bestehend aus den folgenden Mitgliedern:
l ... Links
r ... Rechts
d ... Unten
u ... Oben
ld ... Links unten
lu ... Links oben
rd ... Rechts unten
ru ... Rechts oben
// Elektrisches Potential
p ... elektrisches Potential ### Grüne Linie im Video.
px ... Differenz zwischen zwei Nachbarn, Gradient.x
py ... Differenz zwischen zwei Nachbarn, Gradient.y
pxxyy ... Differenz, Divergenz des obigen Gradienten, Quellfeld
pt ... Änderung von p bei jedem Bild-Fortschritt
// Partikel
// Winkel als Kreuzprodukt
// Drehen durch aufaddieren eines kleinen Winkels (Kreuzprodukt) und normieren
Q ... Datenstruktur eines Vektors(x, y, z) mit definiertem Kreuzprodukt.
q ... Vektor(x, y, z) der Länge 1.
qx ... Winkel zwischen q_links_oben und q_rechts_unten ### Als Grautöne im Video gezeigt.
qy ... Winkel zwischen q_links_unten und q_rechts_oben
qdiv ... Divergenz durch Summe aus qx und qy
qxxyy ... Summe aus Divergenzen, durch probieren ermittelt
qcorpus ... Sinus-Äquivalent zur Sinus-Gordon-Gleichung
qt ... Änderung von q bei jedem Bildfortschritt
Step 1 (for each pixel in each frame of the video)
// Pixel von Schritt 1 und 2 sind schräg um einen 1/2 verschoben.
Pixel *p = space[i], *lu = p, *ld = p->d, *ru = p->r, *rd = p->r->d;
p->px = lu->p - rd->p; // Ableiten durch Differenz.
p->py = ld->p - ru->p; // Es erfolgt kein Aufaddieren.
p->qx = lu->q < rd->q; // Ableiten, Winkelzeichen definiert als Kreuzprodukt.
p->qy = ld->q < ru->q; // Es erfolgt kein aufaddieren.
p->qdiv = p->qx.y - p->qy.x; // Flächensinn (Divergenz) ermitteln.
Step 2 (for each pixel in each frame of the video)
// Pixel von Schritt 1 und 2 sind schräg um einen 1/2 verschoben.
Pixel *p = space[i], *lu = p->l->u, *ld = p->l, *ru = p->u, *rd = p;
// Durch Summenbildung erfolgt eine Mittelung der Werte benachbarter Pixel.
double
px = +lu->px +ld->px +ru->px +rd->px,
py = +lu->py +ld->py +ru->py +rd->py,
qdiv = +lu->qdiv +ld->qdiv +ru->qdiv +rd->qdiv
;
// Winkeldifferenz des aktuellen q zur neutralen Vektor-Richtung (=Down).
p->qcorpus = Q::Down < p->q;
// Zweite Ableitung der Winkelunterschiede zwischen den q-Vektoren.
p->qxxyy =
Q(
-ld->qdiv +ru->qdiv, // Winkel um x-Achse.
+lu->qdiv -rd->qdiv, // Winkel um y-Achse.
// Winkel um Hochachse, Ableiten von Torsion, da sonst instabil.
+lu->qx.z -rd->qx.z +ld->qy.z -ru->qy.z
);
// Ermitteln der Bewegung der einzelnen Vektoren.
p->qt = 0.99 * p->qt // Aufaddieren mit Dämpfung.
+1e-1 * p->qxxyy // Zweite Ableitung.
+2.0e-2 * p->qcorpus // Corpus, Partikeleigenschaft.
// Implementieren der Kraftwirkung.
+1e-2 * Q(-py, px, 0.0); // Einkoppeln des elektr. Pot., nur im 2. Video.
// Drehen des aktuellen q-Vektors mit der vorher ermittelten Geschwindigkeit.
p->q = p->q >> p->qt;
// Ermitteln der zweiten Ableitung des elektr. Pot. (Divergenz).
p->pxxyy = +lu->px -rd->px +ld->py -ru->py;
// Zeitliche Änderung des elektr. Pot. (Ausbreitung).
p->pt = 0.99 * p->pt // Aufaddieren mit Dämpfung.
+1e-1 * p->pxxyy // Zweite Ableitung.
// Potential innerhalb des Partikels biegen.
+1e-3 * qdiv; // Partikel einkoppeln, nur im 2. Video.
// Ändern des Feldes um die ermittelte Differenz.
p->p = p->p + p->pt;
Web links
- Uni-Regensburg: Ultra-fast exciton dynamics on the quantum Hall ferromagnet . ( Memento from June 10, 2007 in the Internet Archive )
- Pro-Physics: Skyrmions in the Spin Lattice
- FDTD Skyrmion simulation in calculating pixel space
References and footnotes
- ↑ Spectrum of Science April 2009, p. 11, field nodes as particles
- ^ Tony Skyrme: A non linear theory of strong interactions . In: Proc.Roy.Soc. . A 247, 1958, p. 260. doi : 10.1098 / rspa.1958.0183 .
- ↑ Tony Skyrme: A unified model of K and Pi-Mesons , Proc. Roy. Soc. A 252, 1959, p. 236
- ↑ Tony Skyrme: A nonlinear field theory , Proc. Royal Society A 260, 1961, pp. 127-138
- ↑ Tony Skyrme: Particle states in a quantized meson field , Proc. Roy. Soc. A 262, 1961, p. 237
- ↑ Colloquium announcement at the University of Regensburg, "PDF" ( Memento from October 14, 2013 in the Internet Archive ).
- ↑ Christian Pfleiderer: Magnetismus mit Drehsinn , Physik Journal 11 (2010), p. 25, and: Wirbel um Spinwirbel , ditto 20 (2013), booklet (10), pp. 20-21
- ↑ TU Munich: Magnetic vortex filaments in the electron soup
- ↑ German researchers discover new "skyrmions" , message from July 31, 2011 on heise.de; Retrieved July 31, 2011
- ↑ Electricity moves skyrmions , Pro Physik 2010
- ↑ Magnetic Nano-Nodes as Data Storage - First Step Successful: Researchers create and delete skyrmions on a surface . Original from Science , 2013. doi : 10.1126 / science.1240573 . Retrieved August 9, 2013.
- ↑ Anti-magnetic vortex in an exotic alloy . Original from Nature , 2017. doi : 10.1038 / nature23466 . Retrieved December 26, 2017.
- ↑ Wenjing Li, Gisela Schütz et al: Anatomy of Skyrmionic Textures in Magnetic Multilayers , Advanced Materials, Volume 31, 2019, Issue 14
- ↑ Gisela Schütz, Joachim Gräfe, Linda Behringer: 3D structure of skyrmions becomes visible for the first time , Max Planck Institute for Intelligent Systems, March 1, 2019