We have acquired FMR curves dI/dH=f(H) for Fe3O4 superparamagnetic nanoparticles. I need to calculate their effective magnetic anisotropy Keff. How is this possible? Thanks in advance
You may want to look into the papers of the two colleagues linked below for a detailed answer to your question.
Unless your specimens contain oriented particles, they will (essentially) look homogeneous to the FMR experiment as long as they are non-interacting. So, at first glance it would seem as there was not so much you could do.
Dipolar interactions between particles will show up in thin films or stripes (generated e.g. by drying particle solutions in magnetic field) will show up as directional dependencies of the FM resonance frequency. FMR is indeed one of the most sensitive probes of such small anisotropy energy scales.
But what is maybe (I'm not the expert here) the most interesting part for you is to look into the width of the resonance, because the anisotropy energy will show up here. Of course, if the anisotropy energy density terms has an inhomogeneous broadning in the particle ensemble (which many particle specimens have) then the information at the particle level may be overwhelmed by that. I add the link to a paper where we measured such a broadening (unexpected to us, at the time) by other means.
https://www.researchgate.net/profile/Michael_Farle
https://www.researchgate.net/profile/Marina_Spasova
Article Magnetic properties of Fe nanoclusters on Cu(111) studied wi...
Using field cooled and zero field measurements you can calculate effective anisotropy constant. Detaileds are given in our papers on ESR available on RG.
If you are interested in calculating the effective magnetic anisotropy of an assembly of magnetic nanoparticles, angular FMR studies are a good way of doing this. In effect the dipolar interactions between the nanoparticle can give rise to an overall magnetic anisotropy of the assembly. For example in deposits of nanoparticles on a substrate you would expect a uniaxial anisotropy, which is much like that for a thin film. See our following papers for some examples:
D. S. Schmool, « Ferromagnetic resonance in nanometric magnetic systems. », Reference Module in Materials Science and Materials Engineering, S. Hashmi (Ed.), Elsevier, (2016). (19 pages)
D. S. Schmool, « Recent studies of spin dynamic studies in ferromagnetic nanoparticles. », in Advanced Nanomaterials: Synthesis, Properties and Applications, S . Thomas, N. Kalarikkal, A. Manuel Stephan, B. Raneesh, and A. K. Haghi (Editors), Apple Academic Press (CRC), Chapter 1, pp 1 - 24, (2014)
D. S. Schmool and M. Schmalzl, (Invited) «Ferromagnetic resonance in magnetic nanoparticle assemblies. », Journal of Non-Crystalline Solids, 353, 738, (2007).
D. S. Schmool, R. Rocha, J. B. Sousa, J. A. M. Santos, G. Kakazei, J. S. Garitaonandia and L. Lezama, « The role of dipolar interactions in magnetic nanoparticles: ferromagnetic resonance in discontinuous multilayers. », Journal of Applied Physics, 101, 103907, (2007).
Dear Mr. Costas Papadopoulos
The FMR is dM/dt = gamma * ( M x H eff )
in H eff you have all magnetic internal and external fields, like the internal anisotropic field proportinal K1 .
So you have a great complex calculation. Look please at the literature:
Michalowsky. L " Magnettechnik " fachbuchverlag Leipzig 1995 .
All the best
F. Gräbner
@ Rasbindu V. Mehta can you please share the paper/method for calculating the effective anisotropy constant using field cooled and zero field measurements.
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