Explore ferromagnetic domain alignment and M-H hysteresis loops with a simplified Jiles-Atherton-inspired model
When a ferromagnetic material is exposed to an external magnetic field H, its internal magnetization M does not follow H linearly. Instead, M lags behind H due to domain wall pinning at crystal defects and grain boundaries. When H returns to zero, M retains a nonzero value called remanence (Mr). To reduce M to zero, a reverse field called the coercivity (Hc) must be applied. Tracing H through a full cycle produces the characteristic hysteresis loop. The area enclosed by the loop represents the energy dissipated as heat per magnetization cycle — a critical factor in transformer and motor design.
This visualization uses a compact Jiles-Atherton-inspired update rather than a calibrated materials model. The effective field He = H + αM shifts the anhysteretic magnetization Man = Ms·L(He/a), where L(x) = coth(x) − 1/x. Parameter k controls pinning strength and loop width, while c blends reversible response with an irreversible magnetization state. The result is useful for seeing qualitative hysteresis, coercivity, remanence, and phase lag, but the numeric values are normalized teaching values rather than measured material constants.
Transformers use soft magnetic cores (low Hc, narrow loop) to minimize energy loss during AC operation. Permanent magnets (hard magnetic materials, high Hc, wide loop) maintain magnetization for motors, speakers, and MRI machines. Magnetic storage devices exploit hysteresis — binary data is encoded as remanent magnetization directions on disk platters. Electric motors and generators rely on cyclic magnetization of their stator and rotor cores, where minimizing hysteresis loss is crucial for efficiency.
Drag the H slider to manually apply a magnetic field and watch the M-H curve trace in real time. Click 'Auto Sweep' to sinusoidally cycle H and observe the loop forming. Switch between materials (Soft Iron, Hard Ferrite, Steel, Permalloy) to compare their loop shapes, coercivity, and remanence. Adjust Ms, a, and k to create custom qualitative materials. The domain panel shows arrow orientations relaxing toward the current magnetization and highlights sharp orientation changes as domain-wall-like boundaries.