What is the critical size of magnetic nanoparticle to be superparamanetic and how can I determine its domain?
And what is the range of squareness ratio (M r/M s) for superparamanetic nanoparticle?
The domain theory applies only to solid nanoparticles. We observed superparamagnetic properties in solutions of surfactant micelles with gadolinium ions on their surface. Superparamagnetism of solid particles assumes the existence of a single domain. See also A. P. Kuz’menko ,P.V. Abakumov ,M.B. Dobromyslov , N.I. Shumakova. Justification of Visualization Technique of Domain Structure with Raman Scattering. Article Jul 2013 Journal of Nano- and Electronic Physics
Dear Naghmeh,
As Yuri said, in superparamagnetism it is assumed that the particles are single domain and there is coherent rotation with them for the magnetic moments. You also asked about the critical sizes for having superparamagnetism. This question is not easy to answer because it depends of several variables. One of them is the form which is very important for the magnetostac energy associated to the particles, the easy to consider is the spheric. The other is the exchange stiffness which measures the force to keep the nearest neigbours spins parallels. This is function of the number of atoms per unit cell, lattice constant, magnetic moments associated to the spins and their exchange integrals. In the practice this is quite difficult to calculate noticing that there are details as the surface atoms are with very different values than the ones of the bulk and so on.
Let us give an example of spheric iron particles. The stiffness constant goes from 0.3 to 2 per 10-6 erg/cm, this gives an sphere of approximate diameter of 17nm. This is a critical size,i.e. below it you have always superparamagnetic single domain nanoparticles while to higher values you haven't superparamagnetism because magnetic walls appear.
Hi Naghmeh
In "Principles of Nanomagnetism (Chapter 3. Equation 3.17 and Equation 3.18)" of Alberto P. Guimarães, you can view an analytical expressions for the critical size of magnetic nanoparticle (superparamagnetism).
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