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 B B , the exchange field B EX , and the number of monolayers N in the soft magnetic layer. For bilayers B B / B EX = (π/2 N ) 2 , whereas for multilayers B B / B EX = (π/ N ) 2 . In addition, it is shown that Jacobi elliptic functions, originally used by Goto et 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 B B .