# Mémoire sur Piste à Skyrmions Magnétiques

Spintronique topologique interactive : des skyrmions de Dzyaloshinskii-Moriya poussés par des impulsions de ultrafaible courant le long d'une nanopiste — écriture, décalage et lecture de bits avec effet Hall du skyrmion et diagnostic d'épinglage.

> Page canonique: https://elysiatools.com/fr/visualizations/skyrmion-racetrack-memory

- **Catégorie:** Physics

## Présentation

Interactive topological spintronics — distinct from the existing spin-ice-magnetic-monopole-walk (spin-ice emergent monopoles, a lattice-frustration case) and topological-quantum-walks (quantum walk algorithm, a quantum-computation case); this is the only case treating real 2D topological spin textures in chiral magnets and their flagship device application. The model implements the full ultrathin-film micromagnetics of Rohart & Thiaville (PRB 88, 184412): K_eff = K_u − μ0M_s²/2, domain-wall width Δ = √(A/K_eff), critical DMI D_c = 4√(A·K_eff)/π where the wall energy σ = 4√(A·K_eff) − πD vanishes, and the helical period L_D = 4πA/D. The skyrmion is the circular 360°-domain-wall ansatz θ(r) = θc·atan(exp((R−r)/w))/(π/2) whose energy (exchange + curvature + DMI + anisotropy + Zeeman) is numerically integrated; the metastable radius R comes from a two-parameter (R, w) variational minimization — R grows toward D_c, shrinks under field, and the ansatz topological charge Q = (1/4π)∫m·(∂ₓm×∂ᵧm)dxdy = −1 is verified on a grid (96–360 points adaptively resolved to the wall width). The field window uses the bubble-collapse saturation scale B_sat = 2.5·κ²·K_eff/M_s, placing MnSi-like and FeGe-like parameters at their measured ~0.3 T collapse fields. Current drive follows Sampaio et al. via the spin-drift velocity u = P·μ_B·j/(2e·M_s) (u in m/s is numerically nm/ns), and every on-track skyrmion obeys the rigid Thiele equation G ẑ×(v−u) + D̃(v−βu) = F with gyrovector G = 4πQ (skyrmion Hall effect), solved as a 2×2 linear system per substep over forces: stiff edge confinement (rails), Gaussian pinning wells (disorder), and short-range skyrmion–skyrmion repulsion (packing). Four visualization panels: (1) The nanotrack top view with per-pixel spin-texture rendering (ImageData) — hue = in-plane spin angle (the radial Néel colour wheel), lightness = m_z (dark core −1), with write (green) / read (gold) gates, pinning-site dots, fading trajectory trails that show the Hall deflection and edge sliding, and animated current chevrons during pulses. (2) Drift-velocity-vs-current plot: the strictly linear no-threshold Thiele response (the ~10⁶ A/m² ultralow-current advantage over domain walls) with the pinned window below j_c shaded when disorder is present. (3) B–D/D_c phase diagram with the saturation curve, the κ=1 stripe boundary, skyrmion/stripe/saturated regions shaded, and the live operating point. (4) TMR read-head signal strip: a spike for every skyrmion passing the read gate — the serial bit stream. Full device operations: Write bit (nucleation at the gate with spacing enforcement), Shift pulse (timed current pulse), Auto stream (random bit stream), Clear; skyrmions annihilate at the end gate after being read. Four material presets (Pt/Co/Ta, Co/Pt high-D, FeGe plate, MnSi) and three scenarios (clean track, disordered — pinning until j > j_c then topologically protected escape, bit stream). Adjustable parameters: field B (0–3 T), current density j (10⁶–10¹² A/m², log), DMI ratio D/D_c (0.3–1.05), disorder density (0–100%), pin strength. Real-time diagnostics: regime badge (isolated/stripe/saturated), radius R, topological charge, wall width, helical period, B_sat, skyrmion count, drift speed, skyrmion Hall angle, depinning threshold j_c, sim clock, and the read bit register. Educational content covers the Néel texture and DMI chirality locking, the micromagnetic length scales, the topological charge, the Thiele equation and skyrmion Hall effect with edge-guided motion, the racetrack write/shift/read/delete architecture and density/energy arguments, and topological protection vs pinning (the deformation-around-defects picture and edge annihilation). Multi-language support (zh, en, es, fr, de, ru, pt).

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