2D Landau-Lifshitz-Gilbert Vector Lattice Simulator
Explore interactive spin dynamics, magnetic skyrmion nucleation, domain wall propagation, and real-time polar hysteresis loops ($M_x$ vs $M_y$) powered by in-browser numerical differential solvers.
2D Micromagnetic Vector Field
Precession EngineLandau-Lifshitz-Gilbert Equation & Energy Functional
The dynamical evolution of continuous magnetic media is governed by the phenomenological Landau-Lifshitz-Gilbert (LLG) differential equation, describing gyromagnetic precession alongside phenomenological Gilbert damping towards local effective field minima:
Effective Field $\mathbf{H}_{\text{eff}}$
The effective magnetic field is the functional derivative of total Gibbs free energy: $\mathbf{H}_{\text{eff}} = -\frac{1}{\mu_0 M_s} \frac{\delta \mathcal{E}}{\delta \mathbf{m}}$, accounting for Heisenberg exchange, magnetocrystalline anisotropy, demagnetization dipolar tensors, and external Zeeman excitation.
Topological Skyrmion Charge
The discrete winding number $Q = \frac{1}{4\pi} \int \mathbf{m} \cdot \left( \frac{\partial \mathbf{m}}{\partial x} \times \frac{\partial \mathbf{m}}{\partial y} \right) dx dy$ characterizes protected chiral skyrmions ($Q = \pm 1$), which resist thermal destruction in high-density racetrack memory devices.
Energy Dissipation
The rate of magnetic energy loss through spin relaxation is quadratic in the cross-product torque: $\frac{d\mathcal{E}}{dt} = -\frac{\alpha \gamma_0}{1+\alpha^2} \mu_0 M_s \int |\mathbf{m} \times \mathbf{H}_{\text{eff}}|^2 dV \le 0$, driving the lattice toward energetic ground states.
OOMMF Core vs. Client-Side WebGL/Canvas Architecture
The Object-Oriented Micromagnetic Framework (developed by NIST) provides extensible C++ core classes (Oxs — OOMMF eXtensible Solver). This web implementation provides an ultra-fast in-browser playground for testing micromagnetic problem specifications before running heavy multi-GPU cluster simulations.
Oxs_EulerEvolve / RK4
Adaptive step-size Runge-Kutta Cash-Karp and Heun integrators maintain continuous normalization condition $|\mathbf{m}_i| = 1.0$ at every sub-picosecond timestep.
FFT Demagnetization
Long-range dipolar field computation is accelerated via 2D/3D Convolution theorem using discrete demagnetizing tensor kernels $N_{xx}, N_{yy}, N_{zz}$.
Zero-Allocation Loop
The in-browser JavaScript engine operates with zero heap allocations during the 60 FPS animation loop (0B GC pressure), preserving consistent sub-millisecond render frames.
Live MIF2.1 (Micromagnetic Input Format) Generator
Generate ready-to-run OOMMF batch configuration files directly from your interactive canvas parameters: