Diamagnetism, ferromagnetism and ferrimagnetism

Magnetic behaviour depends on whether atoms carry a permanent magnetic moment and on how the magnetization vectors of neighbouring atoms are arranged. Magnetization $M = \chi H$ is the net moment per unit volume.

 Diamagnetic:   no moments; induced m opposes H
                H ->    m <-  m <-  m <-
 Ferromagnetic: ^  ^  ^  ^   parallel
 Ferrimagnetic: ^  v  ^  v   antiparallel, unequal
               (long ^, short v)

Diamagnetism

• Atoms have no permanent magnetic moment (all electron orbits and spins paired).
• An applied field changes the orbital motion of electrons; by Lenz's law, the induced magnetization vector points opposite to $H$.
• $\chi$ is small and negative ($\approx -10^{-5}$), $\mu_r$ slightly below 1, and independent of temperature.
• Field lines are pushed out; the material is repelled from strong-field regions.
• Examples: Cu, Bi, Ag, Au, water, graphite. A superconductor is a perfect diamagnet, $\chi = -1$ (Meissner effect).

Ferromagnetism

• Atoms have permanent moments (unpaired 3d electrons in Fe, Co, Ni).
• Strong positive exchange interaction aligns neighbouring magnetization vectors parallel, giving spontaneous magnetization in domains.
• A small $H$ grows favourable domains and rotates others, so $M$ becomes very large: $\chi \approx 10^2$–$10^5$.
• Shows hysteresis, saturation, remanence. Above the Curie temperature $T_C$ (Fe 770 °C) it becomes paramagnetic: $\chi = C/(T - T_C)$.
• Examples: Fe, Co, Ni, Gd and their alloys.

Ferrimagnetism

• The crystal has two sublattices (A and B sites) whose magnetization vectors are antiparallel but unequal.
• Net spontaneous magnetization $M = M_B - M_A \ne 0$; domains and hysteresis exist, but saturation is lower than in ferromagnets.
• In magnetite Fe₃O₄, Fe³⁺ ions on A and B sites cancel and the Fe²⁺ moments give the net magnetization.
• Ferrites are ceramic oxides with very high resistivity, so eddy-current loss is small; ideal at high frequency.
• Above the Curie (Néel) temperature they become paramagnetic.
• Examples: Fe₃O₄, MnZn and NiZn ferrites, barium ferrite, YIG.