About field-cooled / zero-field-cooled curves of superparamagnetic particles?

[jeebs]

Say we had a material which contains nanoparticles with uniaxial magnetic anisotropy - single domain "Stoner-Wohlfarth" particles. If you know what I'm talking about then you might be familiar with "field-cooled" and "zero field-cooled" curves, where the material has its magnetization plotted as a function of temperature, as it is cooled down from high temperature. The cooling is done both in the absence and presence of a magnetic field.

a typical set of results would look like this:
http://www.rsc.org/ejga/DT/2008/b807603k-ga.gif
where the black line is for the cooling with the field applied, and the red line is when there is no field.

I understand what is going on with the field-cooled curve. That's straightforward enough - as the temperature drops, the individual magnetic moments associated with each particle go from a totally disordered state, cancelling each other out over the whole sample, to being aligned in a common direction (parallel to the field).

However, I cannot get my head around the zero-field cooled curve. It has a peak at a temperature known as the "blocking temperature" of the particle (which is dependent on the particles' size and composition), then drops to zero as the temperature falls to zero.

Can anyone explain why the ZFC curve takes the shape that it does?
Thanks.

 

[diffractal]

Hi jeebs,


I'm sure this is far too late to be of help for you, but I'll give it a shot anyway, since this ZFC/FC stuff confused me at first.

I think the key point you are missing, at least the key point I missed initially, is that to measure these types of curves we need to apply an external field. Therefore, regardless of ZFC or FC initial conditions, when we raise the temperature from below 1K to do the measurement, a small field is applied in both cases.

It's easiest for me to imagine starting from low temp. So, we take our sample of magnetic nanoparticles and cool it to low temp with no applied field for a ZFC measurement. We end up with no net magnetization, since all the macrospins began in random alignment. As we begin to heat the sample, we approach the blocking temperature, which is the temperature for which there is sufficient thermal energy to overcome the energy barrier between parallel and antiparallel alignment of the macrospin with respect to the anisotropy axis (of couse all of this is in 3D, but ignore that for the moment). If you are unclear on magnetic anisotropy, blocking and/or superparamagnetism, read up on that stuff first and everything will become much more clear.

So when the increasing temperature reaches the blocking temperature, we see an abrupt but continuous increase of the magnetization. For an assortment of particle sizes (i.e. not all the nanoparticles are exactly 3 nm), this abrupt change is smoothed out. So, as temperature increases, more and more particles go from 'blocked' to 'superparamagnetic' and are able to align with the small external field we apply. As temperature is further increased, the random fluctuations from thermal energy begin to dominate and the macrospins become randomly oriented once again, producing the 1/T exponential decrease of the magnetization that we see at higher temperatures.


I hope I've explained this fairly well, but for the real version with good pictures and formulas and all that jazz (my source in fact), see Coey's Magnetism and Magnetic Materials, particularly if you are confused about the blocking vs. superparamagnetism stuff. I'm sure a skilled google search will provide you with what you need.


And if you needed to know five months ago, well, I hope you're still interested in the response.

cheers