Is zero coercivity always appears as a characteristics of a superparamagnetic material or it can be non-zero also?
Paramagnetism refers to a positive, finite magnetic susceptibility. It includes the notion of zero magnetic polarization in the absence of an external field. Therefore yes, according to the definition of superparamagnetism, there is, strictly speaking, neither coercivity nor remnant magnetization. The notion of "super" in paramagnetism is that the individual moment reacting to the external field is larger than that of an individual atom. A superparamagnetic object thus possesses coupled moments (through ferro- or ferrimagnetic coupling) but insufficient coupling of that total moment to the atomic lattice (i.e. anisotropy) to prevent thermal averaging (fluctuations) of the moment(s) to zero on the timescale of the measurements.
Paramagnetism refers to a positive, finite magnetic susceptibility. It includes the notion of zero magnetic polarization in the absence of an external field. Therefore yes, according to the definition of superparamagnetism, there is, strictly speaking, neither coercivity nor remnant magnetization. The notion of "super" in paramagnetism is that the individual moment reacting to the external field is larger than that of an individual atom. A superparamagnetic object thus possesses coupled moments (through ferro- or ferrimagnetic coupling) but insufficient coupling of that total moment to the atomic lattice (i.e. anisotropy) to prevent thermal averaging (fluctuations) of the moment(s) to zero on the timescale of the measurements.
Having zero coercivity, it is not necessary be a superparamagnetic material but a superparamgnetic material should have zero coercitivity.
@Herojit Loushambam: My question was; is superparamgnetic material always show zero coercivity? and I got the answer as given by @?Kai Fauth...thanx for your reply
Dear Oleg, if you take it this way then we shall have to walk through arguments that are a little less trivial. If you look to my first answer then it mentions "averaging to zero on the time scale of the measurement". So it assumes that the magnetization measurement is (nearly) representing equilibrium. If the relaxation rate is sufficiently slow then you will get dynamic hysteresis. In fact - seen this way, the observation of hysteresis is always a manifestation of non-equilibrium! (I don't think you can get hysteresis from the Gibbs free energy of ensembles of finite objects).
This is - by the way - not unique to superparamagnets but would apply to paramagnets, too.
You should also observed a "blocking temperature" when measuring "field cooled" "zero field cooled" magnetization.
Daniel
Dear Oleg,
I'm not sure I ever " call the blocked case "ferromagnetic" !
Please re-read quietly. I just mentioned the existence of specific temperature. The blocking temperature which is determined thanks to FC/ZFC (field cooled,/ Zero field Cooled measurements. Below this temperature the fluctuations of magnetization in time are strongly reduced (i.e. blocked sate)
Sincerely ours,
Daniel
With respect to Daniel O.'s comment: the blocking temperature is not universal, therfore, but a function of the characteristic measurement time. When you can manage to do measurements at vastly different tiime scales (on identical specimens) then this gives a new quality to your results. You get a better handle on the barrier height and ultimately could get access to the numerical value of the prefactor ("attempt frequency").
The another signature is that superparamagnetic material doesn,t show wait time dependence of relaxation of the thermo-remanent magnetization ...
@Daniel Ortega n Kai Fauth: what we actually mean by blocking temperature in ZFC/FC measurement (M vs.T).Because in ZFC (M vs.T) measurements, we get a peak temperature but it changes with applied magnetic field. So what actually called the blocking temperature?
@Daniel Ortega: thanx for the reply. But I still could not convey myself to understand that how the temperature which is a function of field can be identified as a characteristic temperature. Because most of the time people say that the blocking temperature of this system is e.g 50K. So precisely how we can say about the blocking temperature like we say about ferromagnetic temp, anti-ferromagnetic temperature ?
I agree with practically all posts above... But, in my opinion, a very remarkable feature present in the magnetization data of a superparamagnetic material lies in the fact that it can be closely fitted by a Langevin function (or a Brillouin function considering a very large value of J) when the system is unblocked. This is easily noted when the size distribution of the system's particles (in the case of superparamagnetic nanoparticles, for instance) is narrow making easier unblock all of them. Another important feature was pointed above by Daniel Ortega: "...(i) plotting the reduced magnetisation (M/Ms) curves versus H/T for a set of temperatures below the blocking temperature, they tend to superimpose into a single one and, (ii) there is neither coercivity nor remanence above the blocking temperature"
@Walter Folly: Thanx for reply. As you told there is neither coercivity nor remanence above the blocking temperature. But how one identify that blocking temperature value?
@Kai Fauth : thanks for the reply. did you mean that we should measure ZFC data in minimum possible measuring field in warming cycle?
Hm, not necessarily. In experimental work, it is important to mention the field used. If you use different ones and observe different "peak magnetization temperatures", then working out on the theory might even provide additional information about your specimens.
Most important to me, howewver, is to understand that the blocking temperature as such is not a term which is (or could be) defined in a unique hard way. The very nature of what is being probed here makes it a quantity which does necessarily depend on the measurement technique, especially the inherent characteristic time scale of the measurement.
Rephrasing what whas said before, if you base your expectations on the behavior of M(H,T) on the Gibbs free energy (=canonical ensemble in equilibrium), then it is a single valued function. The very fact that experimentally it is multivalued (field cooling and field warming after ZFC yield different curves) tells you, that some premise to this Ansatz must be wrong in your experiment: it is out of equilibrium, relaxation is slower than your experiment.
Dear sir thanks for the nice reply. as you mentioned that multivalue of the observed temperature tells that the onset of this temperature must be wrong in your experiment. Did you mean that the rate of temperature change during the the measurements is not suitable or anything else. Because it is still somewhat not clear to me that the very common statements regarding SPM systems that there is neither coercivity nor remanence above the blocking temperature. So what is that temperature actually?
@ Daniel Ortega: thanx again for the reply. In my earlier comment "wait time dependence of relaxation of the thermo-remanent magnetization" I actually mean by wait time before measuring the TRM. ( e.g.first sample was cooled in field down to the temperature at which TRM is to be measured and then wait for the time tw ,switch off the field and then record the TRM as a function of time. For different wait time a SPM system will show the same relaxation ).
Dear Pankaj, when the system is composed by magnetic entities with a distribution of magnetic momenta, e.g., a system of magnetic nanoparticles presenting a size distribution, there is no an unique well defined blocking temperature. That is, if you consider the size of particles grouped in several classes (an histogram of sizes), each class will present an average blocking temperature. So, supposing the system in low temperature totally blocked, if you start to increase its temperature you will unblock first the smaller particles... So, in response to your last question, there are several ways to determine the average blocking temperature of the system. I will describe one of them:
1- Measure the FC and ZFC magnetization of the system in an as wide as possible temperature range
2- Separate the FC data from ZFC and perform the subtraction FC - ZFC for each measurement temperature (I usually do such calculations using the Microcal Origin software)
3- Calculate the derivative of resulting data with respect the temperature in order to obtain the blocking temperature distribution f(Tb)
4- The average blocking temperature of the system now may be calculated integrating Tb * f(Tb) * dTb from zero to a sufficiently large value then dividing the result by the integral f(Tb) * dTb (if the blocking temperature distribution was not previously normalized)
A similar procedure can be performed by deriving the remanent magnetization with respect the temperature to obtain f(Tb). I suppose that you may be interested in the following references (the reference [2] was co-authored for me and can be downloaded here from RG):
[1] N. Peleg, S. Shtrikman, G. Gorodetsky, and I. Felner, J. Magn. Magn. Mater. 191, 349 (1999).
[2] W. C. Nunes, W. S. D. Folly, J. P. Sinnecker, and M. A. Novak, Phys. Rev. B 70, 014419 (2004).
This is good practical advice. Do also consider the recent work of A. Tamion and collaborators for more extensive and exhaustive types of evaluations (they call it "triple fit").
Nevertheless I stress that even in an ensemble of identical particles the quantity called blocking temperature does depend on the time scale of the measurement.
Consider this ensemble as fully polarized at some time t_0 and leave the ensemble alone. It's magnetic polarization shall vary with time as exp(-(t-t_0)/ \tau), where \tau is the time constant, essentially given by E_A / (k_B T) with E_A the anisotropy energy (Kv*V, if you like), k_B the Boltzmann constant and T the temperature. The rate of depolarization varies with temperature but is finite at any finite temperature (though arbitrarily large at arbitrarily low temperature). The equilibrium polarization is zero at any T>0 (and even at T=0 if there is a finite magnetic tunneling amplitude...). Strictly speaking, this kind of result is still an approximation, consisting of rate equations set up in the framework of some transition state formulation.
What would you consider stable or a really small rate of change. You could impose that if a single particle has a chance of 50% of still being in the original state after 10 years (without having flipped in the mean time), then you'll call that "blocked". This gives you some ratio of anisotropy energy to thermal energy above which you pull the name "blocked". A common definition used to be E_A / (k_B T_B) =25, but lately I have also seen E_A / (k_B T_B) =40, used to define the blocking temperature.
Again: this is an (arbitrary) definition, based on some relation deemed practical, a convention. It applies to an ensemble of identical, uniaxial single domain particles, which both are more or less (many a times "more" rather than "less") severe idealizations for real specimens, and this for a whole bunch of reasons (not really uniaxial magnetic energy landscape, moment distributions, anisotropy barrier distributions, interactions between particles).
As you apply a magnetic field, the two magnetic energy minima are not on the same level any more - this does influence the transition rates (slowing down in one direction, speeding up in the other). The dynamic behavior of a specimen changes as a consequence. This may lead to a different evaluation of T_B if it is only taken from a peak value of a warming-up measurement after ZFC. It would be more appropriate to model the whole curve. But you have seldom inough information to make such a modelling physically meaningful.
For a comparison of sufficiently similar specimens, such determinations may still make a lot of sense, though.
The unsaturated sate of the MH loops and maxima in ZFC process is also a signature of the superparamagetism in the samples.
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