What does the area of a hysteresis loop mean?

The loop area ∮H dB is the energy per cubic metre turned into heat in each magnetization cycle (J/m³). Multiply by the frequency and you get the hysteresis loss power density. Transformer and motor cores need thin-loop soft materials such as silicon steel to keep losses low; permanent magnets need fat loops with high coercivity so they are hard to demagnetize.

What are remanence and coercivity?

Remanence B_r is the flux density left in the material after the applied field is brought back to zero. Coercivity H_c is the reverse field needed to bring B back to zero. Soft magnetic materials have H_c of a few to a few tens of A/m; hard (permanent) magnets reach 10⁵–10⁶ A/m. NdFeB has B_r about 1.3 T, H_c about 900 kA/m and a maximum energy product of about 300–400 kJ/m³.

What is the Barkhausen effect?

A ferromagnet is made of many domains. As the field rises slowly, domain walls do not glide smoothly: impurities and defects pin them until they break free suddenly and a whole region flips at once. Wired to a coil and a speaker these jumps sound like clicks, the Barkhausen noise, showing that magnetization proceeds by many small discontinuous avalanches.

What is the Curie temperature?

Above its Curie temperature a ferromagnet loses its spontaneous magnetization and becomes paramagnetic: iron at 1043 K (770 °C), cobalt 1388 K, nickel 627 K and gadolinium only 292 K (about 19 °C). Above the Curie point the susceptibility follows the Curie–Weiss law χ = C/(T − T_c). Heat a magnet above its Curie point and cool it again and it loses its original magnetization.

Can a frog really be levitated by a magnet?

Yes. Water and living tissue are diamagnetic (χ ≈ −9×10⁻⁶) and are pushed away from strong fields in a non-uniform field. The condition is B·dB/dz = μ₀ρg/|χ| ≈ 1400 T²/m, roughly a field of over ten tesla changing a lot over ten centimetres. In 1997 Andre Geim levitated a frog in a magnet of about 16 T, which earned him an Ig Nobel Prize.

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🧲Hysteresis Loop Simulator - Soft & Hard Magnets, Domains, Curie Point

Pick a material, drive it with a sinusoidal field and watch the B–H loop being traced. Read off the remanence, coercivity and peak flux density, the loop area (hysteresis loss per cycle) and the loss power at the operating frequency; permanent magnets also show the maximum energy product. The domains tab uses the random-field Ising model to show magnetization advancing in avalanches (Barkhausen noise). There is also a susceptibility table, Curie temperatures with mean-field magnetization curves, the field gradient needed to levitate a frog, and the on-axis field and pull force of cylinder magnets.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Magnetic Materials & Hysteresis

1On Hysteresis loop, choose a material and drive (major loop, minor loop or AC demagnetization), set amplitude and frequency, and play
2Read B_r, H_c, loop area and loss power; for permanent magnets look at the second quadrant and (BH)max
3On Domains & Barkhausen, change the disorder R and watch domains flip, the M–H loop and the noise
4Use the other two tabs for susceptibilities, Curie points and levitation, or enter magnet size and grade for field and pull force

FAQ

What does the area of a hysteresis loop mean?: The loop area ∮H dB is the energy per cubic metre turned into heat in each magnetization cycle (J/m³). Multiply by the frequency and you get the hysteresis loss power density. Transformer and motor cores need thin-loop soft materials such as silicon steel to keep losses low; permanent magnets need fat loops with high coercivity so they are hard to demagnetize.
What are remanence and coercivity?: Remanence B_r is the flux density left in the material after the applied field is brought back to zero. Coercivity H_c is the reverse field needed to bring B back to zero. Soft magnetic materials have H_c of a few to a few tens of A/m; hard (permanent) magnets reach 10⁵–10⁶ A/m. NdFeB has B_r about 1.3 T, H_c about 900 kA/m and a maximum energy product of about 300–400 kJ/m³.
What is the Barkhausen effect?: A ferromagnet is made of many domains. As the field rises slowly, domain walls do not glide smoothly: impurities and defects pin them until they break free suddenly and a whole region flips at once. Wired to a coil and a speaker these jumps sound like clicks, the Barkhausen noise, showing that magnetization proceeds by many small discontinuous avalanches.
What is the Curie temperature?: Above its Curie temperature a ferromagnet loses its spontaneous magnetization and becomes paramagnetic: iron at 1043 K (770 °C), cobalt 1388 K, nickel 627 K and gadolinium only 292 K (about 19 °C). Above the Curie point the susceptibility follows the Curie–Weiss law χ = C/(T − T_c). Heat a magnet above its Curie point and cool it again and it loses its original magnetization.
Can a frog really be levitated by a magnet?: Yes. Water and living tissue are diamagnetic (χ ≈ −9×10⁻⁶) and are pushed away from strong fields in a non-uniform field. The condition is B·dB/dz = μ₀ρg/|χ| ≈ 1400 T²/m, roughly a field of over ten tesla changing a lot over ten centimetres. In 1997 Andre Geim levitated a frog in a magnet of about 16 T, which earned him an Ig Nobel Prize.

Features

Preisach hysteresis model with a reversible Langevin term: minor loops and memory come out naturally
Presets for iron, silicon steel, MnZn ferrite, NdFeB and AlNiCo, with animated loops and H(t), B(t) traces
Remanence, coercivity, loop area, hysteresis loss power and maximum energy product
Random-field Ising model of domain avalanches and Barkhausen noise
Susceptibility table, Brillouin mean-field M(T), Curie–Weiss law and the levitation condition
Exact on-axis field of a cylinder magnet and pull-force estimates on a steel plate and between two magnets

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