Rayleigh's Law of Magnetization

the dependence, established by Lord Rayleigh in 1887, of the magnetization J (or magnetic induction B) of ferromagnetics on magnetic field strength H in weak fields—that is, where the strength of the field acting on the specimen is much smaller than the coercive force H_C

Rayleigh’s law of magnetization can be expressed by the following two equations: (1) for the curve of initial magnetization, J = K_REVH ± RH² (SEEMAGNETIZATION CURVE), where K_rev is the reversible magnetic susceptibility, which characterizes the reversible linear part of the process, and R is Rayleigh’s constant, which characterizes irreversible nonlinear magnetization processes; (2) for the ascending and descending branches of the hysteresis loops, ǀΔJǀ = K_REVǀΔHǀ + RǀΔHǀ²/2, where ǀΔJǀ and ǀΔHǀ are the absolute values of the increments to J and H.

Rayleigh’s law is satisfied not only near the demagnetized state (J = 0, H = 0), but also for other initial values of J or B, as long as the value of H and the variation AH in this value are small compared with H_C (H, AH ≪ H_C). The parameters K_REV and R may, of course, vary. Near the demagnetized state, K_REV coincides with the reversible initial magnetic susceptibility κ_a and is due to reversible shifts in the domain boundaries (see MAGNETIZATION). If initial J ≠ 0 and H ≠ 0, then K_revΦ κa. Even in this case, however, K_REV is determined by reversible processes of the displacement of domain boundaries. The parameter R characterizes irreversible shifts of domain boundaries. The range of applicability of Rayleigh’s law for different ferromagnetics may vary from a few millioersteds (ferrites) to a few oersteds (perminvars).