Results in Physics (Mar 2023)
Kittel’s model for ferromagnetic domains, revised and completed, including the derivation of the magnetic hysteresis
Abstract
In 1946 and 1949, Charles Kittel proposed a simple model for the size of ferromagnetic domains that is still widely used nowadays [C. Kittel, Phys. Rev. 70 (1946) 965–971 and Rev. Mod. Phys. 21 (1949) 541–583], including for other ferroic systems, such as ferroelectrics and multiferroics. Kittel’s theory is revisited in this work, with a more detailed demonstration and emphasizing the main assumptions utilized, by using SI units instead of CGS units, as in the original Kittel’s works. The validity limits of the Kittel’s scaling law where the domain width varies with the square root of the sample thickness towards low thicknesses is derived, with the possibility of evolution towards large domains for ultralow thicknesses. Further, Kittel’s model is extended to the case where the sample has a non-vanishing net magnetization and it is shown how magnetization curves at zero temperature can be obtained. This is discussed by supposing constant width of a pair of neighboring domains with opposed magnetization, or by allowing this width to vary as function on the net magnetization of the sample. Though this latter assumption seems to be more reasonable from the point of view of the evolution towards a single domain state at saturation, it seems that the model able to yield most accurate vales of the coercive field is the domain with fixed width of the pair of domains, which justifies the assumption of „domain wall pinning”. The introduction of the demagnetization factor associated with the finite size of the film yields a maximum thickness up to which the films present hysteresis curves. The validity of this theory for ferrelectric domains is also briefly discussed.
