Discrete exchange-springs in magnetic multilayer samples

The properties of soft magnetic exchange-springs in both bilayer and multilayer samples are investigated, with particular emphasis on the discrete nature of the spring. it is shown that, in a mean-field model, a very simple relationship exists between the bending field Bg, the exchange field B-EX and the number of monolayers N in the soft magnetic layer. For bilayers B-B/B-EX = (pi /2N)(2), whereas for multilayers B-B/B-EX = (pi /N)(2) In addition, it is shown that Jacobi elliptic functions, originally used by Goto at al for continuous bilayer springs, provide a surprisingly robust description of discrete bilayer and symmetric multilayer exchange-springs. Finally, the problem of soft exchange-spring penetration into neighbouring hard magnetic layers is discussed. Calculations show that this is an important effect, which leads to a reduction in the bending field Bs.