Journal of Magnetism and Magnetic Materials 217 (2000) L1}L4 Letter to the editor Estimation of exchange constant A and g factor for Co  Ni  microspheres from size-dependent ferromagnetic resonance modes P.A. Voltairas, D.I. Fotiadis, C.V. Massalas* Department of Computer Science, University of Ioannina, Ioannina GR 451 10, Greece Department of Mathematics, Division of Applied Mathematics and Mechanics, Rector'sOzce, University of Iaonnina, P.O. Box 1186, Ioannina GR 451 10, Greece Received 26 January 2000 Abstract The exchange constants A and the g factors for Co  Ni  microspheres are estimated by comparing theoretical calculations of size-dependent resonance modes with the experimental data of spherical monodisperse Co}Ni particles. Only cylindrically symmetric modes are studied. The deviation from previously reported values is presented.  2000 Elsevier Science B.V. All rights reserved. PACS: 76.50.#g; 75.50.Tt; 75.30.Et; 75.50.!y Keywords: Ferromagnetic resonance; Magnetic microspheres; Magnetostatic modes; Exchange resonance modes; Mode mixing 1. Introduction The internal structure, the properties and the response of nano and microscale ferromagnetic particles to: external magnetic "elds, applied mech- anical stresses or change in temperature, are of great importance due to a variety of applications in diverse "elds. Chains of magnetic nanoparticles (called magnetosomes), help magnetotactic bac- teria, birds, "sh and bees to navigate in the earth's magnetic "led [1,2]. The detection of ferromagnetic nanoparticles in the human brain and other human * Corresponding author. Tel.: #30-651-41800; fax: #30- 651-42215. E-mail address: cmasalas@cc.uoi.gr (C.V. Massalas). tissues raise questions of whether weak electromag- netic "elds might have biological e!ects, including cancer [3]. Among the methods used to destroy cancer tumors, is the use of vesicles that contain magnetic microspheres and can target drugs to speci"c location inside the human body via ex- ternally applied magnetic "elds [4]. Moreover, col- loidal suspensions of ferromagnetic nanoparticles in a liquid carrier, well known as ferro#uids [5], "nd many technological [6] and medical applica- tions [7]. A phenomenological approach to de- scribe such coupled phenomena in ferromagnetic solids is the continuum theory of micromagnetics [8,9]. For particles with diameters above 1 mm, mag- netostatic forces dominate over exchange interac- tions. In the size range the resonance spectrum was LETTER TO THE EDITOR 0304-8853/00/$-see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 0 4 4 - 5