The magnetic properties, including the Ms, Mr, and Hc, of Fe3O4 NPs are highly influenced by the particle size and domain structure. Te Ms increases with increasing particle size, regardless of the crystal structure and particle shape. Afer exceeding the superparamagnetic limit, the Hc and Mr values increase with increasing particle size up to a maximum value of about 190Oe and 13 emu/g, respectively, at the critical size of 76nm. Above this critical size, the Hc and Mr values decrease with further increases in the particle size, and the cube-like Fe3O4 NPs change from a single- to multi-domain structure. Te multiple orientations of the crystallites within the multi-domain-structured NPs lead to the decrease in the Hc value. Tese fndings suggest that considerable attention should be given to the particle size and crystalline properties of Fe3O4 NPs, which have potential biomedical and industrial applications. Tese applications require that magnetic particles are sized appropriately to achieve a good balance between efective surface area and satisfactory magnetic performance.
Ref .https://www.nature.com/articles/s41598-017-09897-5.pdf
read the attached articles for detail information.
Depending on the single ion anisotropy in case of materials like ferrites, the size and shape of the particle, composition; magnetization and coercivity changes.
If you can study about the length scales for various properties like exchange length in case of magnetization etc, you will better understand about the influence of size and shape on the properties of magnetic nanoparticles.
http://iopscience.iop.org/article/10.1088/0022-3727/39/21/R02/meta
http://iopscience.iop.org/article/10.1088/0953-8984/14/49/201/meta
https://www.researchgate.net/publication/50395476_Magnetic_Surface_Nanostructures/figures?lo=1
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