# User:Brian P. Josey/Notebook/2010/01/25

Project name Main project page
Previous entry      Next entry

Just some ideas and notes.

### Superparamagnetism

SJK 22:50, 25 January 2010 (EST)
22:50, 25 January 2010 (EST)
This is great that you're learning this information so early! As a major coincidence (or perhaps not so coincidental, since superparamagnetic ionorganic nanocrystals (SPIONs) are a rapidly growing biotech area) I was a talk today where the speaker was explaining these same issues to the audience. She used the term "Neelian" pronounced somthing like "nail-ean," which I'd not heard before for "Neelian relaxation time." I'd heard "Neel time," so I guess that reinforces that it's pronounced "Nail."

Also, I'll note that the equation you show for relaxation time is exactly the same as used in Arrhenius rates, for Kramers' reaction rate theory, etc.

Brian P. Josey 10:28, 27 January 2010 (EST) I'm actually enjoying this material a lot. But I could have sworn that Neel was pronounced like kneel.As for the equation, I had to look it up again, but it seams to be used by chemists all the time.

When you take a magnetic material, and decrease its size, you eventually come to a point where it has only one domain, a single domain (SD) sample. There is another point, where as you decrease the size of the sample the remanence and coercivity go to zero. Remanence being the amount of magnetization left when a field is removed, and coercivity is how strong the applied magnetic field is needed to remove the magnetization. When this happens to a ferromagnetic material, it becomes superparamagnetic.

When superparamagnetic materials are sitting by themselves, without an external field and at temperatures above 0K, they have an average zero magnetic moment. When there is an applied field, there is a statistical alignment of the magnetic moments. This is like paramagnetism, except on a larger scale, going from a single atom to 105 atoms. The size needed for this is on the scale of 3-50 nm, depending on the material.

For a superparamagnetic material, there is a chance that the domain will flip direction, due to heat. The mean time between two flips is called the Neel relaxation time, and is given by:

$\displaystyle \tau_N = \tau_0 ~ \exp(K V/(k_B T))$ , where:

• $\displaystyle \tau_N$ is thus the average length of time that it takes for the nanoparticle magnetization to randomly flip as a result of thermal fluctuations.
• $\displaystyle \tau_0$ is a length of time, characteristic of the material, called the attempt time or attempt period (its reciprocal is called the attempt frequency); its typical value is 10-9-10-10 second.
• K is the nanoparticle magnetic anisotropy and V its volume. KV can be thought of as the energy barrier associated with the magnetization moving from its initial "easy axis" direction, through a "hard axis", ending at another easy axis.
• kB is the Boltzmann constant.
• T is the temperature.

Taken from Wikipedia.

When you look at a superparamagetic material, how long you take the measurement of the magnitization will tell you if it is superparamagnetic, or ferromagnetic. If the measurement time is much less than the Neel relaxation time, there wouldn't be any flips in the direction of the magnetic moments, appearing to be ferromagnetic. If the measurement time is much larger than the Neel relaxation time, then there will be several, and the magnetization measured would be zero, appearing to be superparamagnetic. This was just interesting, and I included it, just in case it came up later.

### Notes on Paper

I also read a short paper today on magnetoferritin. It is "Magnetoferritin: In Vitro Synthesis of a Novel Magnetic Protein" by Meldrum, Heywood and Mann.