If the applied field is pinning the particles then their relaxation should be slow and thus the blocking temperature should increase. But I guess this is not the correct way to look at it as this gives a complete contradictory picture to the established one.
This may due to which is dominant-Zeeman energy or thermal energy. At low magnetic field, the Zeeman energy is much smaller than the thermal energy. The temperature induced net moment increase of newly relaxed larger particles, which can overcome the decrease of the superparamagnetic particles (M−1/T). At higher magnetic field, however, M(T) decreased much slower than 1/T dependence as the larger Zeeman energy resulting large magnetic moment of the magnetic particles.
Can you specify the measurement protocol more precisely? What does AC field mean?
An AC magnetic field,H=H0sinwt where Ho is some small magnetic field is the amplitude(usually few Oe).The frequency of the signal can vary from 10 Hz to 1000 Hz or even more.With fixing one frequency, if you apply extra DC magnetic field and change its value from 0 to say,4 T,then with the increasing DC field,the blocking temperature decreases.This behavior with some variation is observed in almost all superparamagnets.But I am not clear why this happens.
If you are talking about superimposing a static field simultaneously to the AC susceptibility measurement, if the applied field is high enough, the energy barrier for magnetization reversal is decreased with increasing field. This can be qualitatively understood within the Stoner-Wohlfarth model, see for example
http://iopscience.iop.org/0143-0807/29/3/008
The decrease in the energy barrier would translate in a lowering of the blocking temperature.
Ok, thanks, Prachi Telnag.
What then do you consider as a blocking temperature? Some singularity on the measured susceptibility, I guess?
If this is the case, then the explanation could be as following.
Let's talk about an ensemble of nanoparticles each having a uniaxial anisotropy directed along the external magnetic field. Suppose that such ensemble is blocked and initially prepared in the ZFC regime. Then, in an infinitely small magnetic field the net magnetic moment of the ensemble will be zero because half of magnetic moments will be directed parallel to the external field and the second half is anti-parallel. Increasing the external magnetic field one will decrease the anisotropy barrier for the particles belonging to the second half (also it will change the equilibrium population in these two sub-ensembles). When the barrier height will be lower than some critical value (determined mainly by the temperature and the effective measurement time), magnetic moments of the second half will be able to overcome the energetic barrier and the relaxation in the ensemble's magnetization start going; this will be observable as an increase of the susceptibility in the measurement protocol you specified. For other types of ensembles the situation will have some additional features.
So, the answer in short is: the applied external magnetic field disbalances the equilibrium and at T=Tb a nonequlibrium part of the magnetization is start relaxing. The higher the field, the stronger the disbalance, the lower the barrier and, consequently, the lower the blocking temperature.
Thanks.That does help in getting a clear picture about the Tb dependence on the field.
What Irene has said is true with respect to the height of the barrier of the potential associated to the supermomentum of the particle under a reversal magnetic field, but there are more subtleties besides the magnetic field that we have tried to study in a simple form in the paper that attach you. I recommend you to have a look to my contributions in research gate because I have others which could be more specific and applied.
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