Domains, domain walls and magnetic losses

Magnetic domain

A magnetic domain is a small region (about $10^{-6}$–$10^{-3}$ m) inside a ferromagnetic material in which all atomic magnetic moments are aligned in the same direction by the exchange interaction, so the region is magnetized to saturation.

Domain wall

A domain wall (Bloch wall) is the transition layer, a few hundred atoms thick, separating two adjacent domains. Across it the direction of the moments rotates gradually from that of one domain to the other.

 domain 1  | wall          | domain 2
 ^ ^ ^ ^   | ^ / -> \ v    | v v v v

Losses in magnetic materials

When a magnetic core carries alternating flux, part of the input energy is turned into heat. These core (iron) losses are:

1. Hysteresis loss

   • Energy spent in moving domain walls and rotating domains back and forth each cycle; equals the area of the B–H loop per cycle per m³.
   • Steinmetz formula: $P_h = \eta\,B_{max}^{1.6}\,f\,V$
   • Reduced by soft materials with a narrow loop (silicon steel, CRGO).

2. Eddy-current loss

   • Alternating flux induces emfs and circulating currents in the conducting core, causing $I^2R$ heating.
   • $P_e = K_e\,B_{max}^2\,f^2\,t^2\,V$ (t = lamination thickness)
   • Reduced by thin insulated laminations, adding silicon to raise resistivity, or using ferrites/powder cores.

3. Anomalous (excess/residual) loss

   • Extra eddy loss from local, jerky domain wall motion (Barkhausen jumps); becomes important at high frequency.

Total core loss $P_c = P_h + P_e (+ P_{anom})$; it appears as heat and lowers efficiency of transformers and machines.