Brown's "fundamental theorem" revisited

Brown's method of calculating an upper and a lower bound of the "critical s ize" for a single domain behavior is recalled, with a particular emphasis o n the case of soft ferromagnets. The upper bound for a sphere is very sligh tly improved. Any further improvement, if at all needed for isolated partic les of soft materials, should be done in the same direction. This improveme nt is used to demonstrate that this method can be extended to the case of i nteracting neighbors, but not to the study of very many grains, for which m icromagnetics is inadequate and has to be superimposed by domain theory. (C ) 2001 American Institute of Physics.