Rayleigh relation and scaling power laws in minor hysteresis loops

Abstract

Seven scaling power-law relations were discovered in the minor hysteresis loops of ferromagnetic materials several years ago. These relations include universal constants that are independent of the type of material and temperature, along with coefficients that provide information about the material and lattice defects. Four universal constants and four coefficients are explained in connection with the Rayleigh relation, which is caused by two scaling laws for l(H) and p(H), where l(H) is the pinning and unpinning length in the domain wall displacement, H is the magnetic field, and p(H) is the number of domain walls involved. The dependence of the coefficients on the dislocation density, ρ, is explained to increase in proportion to the square root of ρ. This result agrees with experimental results. The force profile of the domain walls has similar structures at every point.

Keywords:

• minor hysteresis loop
• scaling rule
• Rayleigh law
• iron
• dislocation

Acknowledgements

The authors would like to thank Dr Yoshiki Kuramoto (Professor Emeritus, Kyoto University) and Prof. Mitugu Matsushita (Faculty of Science and Engineering, Chuo University) for the helpful discussion and critical reading of the manuscript. This research was partly supported by a Grant-in-Aid for Scientific Research (S), Grant No. 14102034, from the Ministry of Education, Culture, Sports, Science and Technology of Japan.