Magnetic materials

Goal. Resolve magnetization switching inside polycrystalline magnetic materials, where each grain has its own easy axes.

Significance. The response of sensors, actuators and transformer cores depends on this switching. The LLG micromagnetics module of the μ-Pro phase-field package, developed by R. Wang, resolves magnetic domains grain by grain with exchange, anisotropy, stray-field and magnetoelastic energies.

Switching and hysteresis in a polycrystalin preparation

In a polycrystal, each grain pulls the magnetization toward its own easy axes, and the stray field couples the grains. This example sweeps an applied field across a polycrystalline disk and records the hysteresis loop together with the domain pattern at each stage.

A 600 nm, 5 nm-thick polycrystalline disk (about 39 grains) under a field swept +40 → −40 → +40 kA/m. Left: magnetization (blue = up, red = down, arrows = direction, lines = grain boundaries). Right: the hysteresis loop as it is traced.

Hysteresis loop with states A to D — The loop with four states marked: A saturated, B remanence at zero field, C reversed, D partway through switching.

Four magnetization snapshots — The disk at states A–D. Reversal starts at the edges and sweeps inward, passing through a non-uniform state (D).

Grains colored with magnetization arrows — Grain structure (colors) with magnetization arrows at remanence.

μ-Pro: team code. Magnetic (LLG) module, simulation setup and analysis: R. Wang.