Hard magnets and soft high-frequency materials

The choice depends on the shape of the B–H (hysteresis) loop.

       B   soft (narrow)         B   hard (wide)
       ^   __                    ^   ______
       |  / /                    |  /     /
  -----+-/-/-----> H     --------+-/-----/----> H
      -/-/ |               -Hc  / |    / +Hc
      /_/  |                   /__|___/
   small Hc, small area       large Br, Hc, area

Hard magnetic material for permanent magnets

A permanent magnet must keep strong magnetism indefinitely without a supply and resist demagnetization.

• High retentivity $B_r$: a large flux density remains after the magnetizing field is removed, so the magnet is strong.
• High coercivity $H_c$: a large reverse field is needed to destroy the magnetism; stray fields, vibration, shocks and temperature changes cannot easily demagnetize it.
• Large $(BH)_{max}$ (area of the second-quadrant curve): more magnetic energy stored per unit volume, so a smaller magnet is enough.
• The wide loop (large hysteresis loss) does not matter because the magnet is magnetized only once.
• Examples: Alnico, NdFeB, SmCo, barium/strontium ferrite; used in loudspeakers, PMDC motors, meters.

Soft magnetic material for high-frequency applications

In transformers, inductors and chokes at high frequency, the flux reverses thousands to millions of times per second.

• Narrow loop, low $H_c$: hysteresis loss per cycle (loop area) is small. Since $P_h = \eta B_{max}^{1.6} f V$ is proportional to $f$, a small loop area is essential at high $f$.
• High permeability: little magnetizing current is needed and the material follows the rapidly changing field.
• Low remanence: no residual magnetism to oppose the next half-cycle.
• High resistivity (soft ferrites, MnZn and NiZn): eddy-current loss $P_e \propto f^2$ is kept small, which is critical at high frequency.
• Examples: soft ferrites in SMPS transformers, RF coils, antenna rods; permalloy and amorphous alloys in pulse transformers.