The FC procedure differed from the ZFC measurements only in that the sample was cooled in a nonzero magnetic field. FC and ZFC curves of magnetically inhomogeneous magnetic materials typically coincide at high temperatures but differ below their blocking temperature.

Their ZFC curves have a maximum at blocking temperature, whereas their FC curves usually rise monotonically down to very low temperatures

(8) (PDF) Magnetic properties of nickel ferrite nanoparticles prepared using flotation extraction. Available from: https://www.researchgate.net/publication/257835141_Magnetic_properties_of_nickel_ferrite_nanoparticles_prepared_using_flotation_extraction [accessed Jan 26 2019].

How can we find a field that really exists on two curves?

I think you must specify the Tr (irreversibility temperature point) then you must find the corresponding magnetization, then from magnetization one can convert it to field. That is what I expect, I hope it is useful.

In my opinion, the concept of irreversibility field is related to an experiment in which the field is being varied, not the temperature.

Imagine taking a major M(H) loop (i.e. one where the M(H) partial curves taken at increasing and decreasing field, respectively, coincide on a finite range of fields[i.e. in the high field regions]). Then the irreversibility field is said to be the field value at which the two curves start to diverge.

The ZFC plot is considerably different from that of FC reflecting, irreversible behavior observed in the FC/ZFC curves due to a process of blocking and unblocking magnetic nanoparticles resulting from variation in thermal energy, which is a characteristic feature of superparamagnetism. In the ZFC process, the direction of each particle is frozen in a random direction as the samples are cooled in the absence of filed down low temperature, and the applied nominal magnetic field is not sufficiently strong enough to reorient the particles in field direction, showing a zero magnetization as a result.

Please see the paper: Article Structural, Optical, Room-temperature and Low-temperature Ma...

When the samples are cooled in the presence of a magnetic field, an irreversibility will be observed in the ZFC/FC curves, which bifurcated from each other at a temperature (around 300K) , where it said to reached the thermomagnetic irreversibility (TMI) temperature, Tirr. There was a significant difference between Tirr and TB for sample .... see the above article

Syed Ismail Ahmad, there is no question that the bifurcation of ZFC and FC curves is related to irreversability and/or equilibrium vs. non equilibrium states. The "bifurcation point" yields a temperature as a result. The OP asked for the irreversibility field, however.

Thus, I argue that from ZFC/FC experiments you will obtain some characteristic temperature, which in turn may depend on the field magnitude chosen for field cooling, on the cooling rate and on the (usually small, whatever might be adequate to qualify as "small") field chosen for measuring the actual curves.

To obtain a characteristic field, you need to do a field dependent measurement, e.g. major M(H) cycles. The characteristic field (irreversability field) may then depend on measurement temperature and, in practice, on the field sweep rate.

At this point I would suggest that the OP (Mudassar Nazir) clarifies what he is actually looking for.

(just my $0.02)

Dear Kai,

Your interpretation of field irreversibility is quite, logic but I'm afraid that the question was made in a different context: similarities between superparamagnetism and spin glass behaviors. Perhaps I'm wrong and we can wait for Mudassar answer.

As you know very well the magnetic nanoparticles show some characteristic features which are common to both spin glasses and superparamagnets. These include what is called irreversibility in the field cooled (FC) and zero field cooled (ZFC) magnetizations, i.e., a peak in ZFC magnetization, which slows magnetic relaxation and hysteresis at low temperature. However, some important features

distinguish these two are well known:

(a) FC magnetization goes on increasing as the temperature is decreased in superparamagnets while it tends to saturate below the freezing temperature in particles showing spin glass behavior.

(b) In systems showing spin glass like behavior, wait time dependence of relaxation (aging) and memory effects are present in both FC and ZFC magnetizations.

(c)The field dependence of temperature at which the ZFC magnetization peaks (TP ) is known to behave differently in the two cases.