http://prb.aps.org/abstract/PRB/v71/i10/e104405

Both the superparamagnetism and spin glass systems exhibits what is called slow dynamics or memory effects. Peak in ZFC magnetization data, nonexponential relaxation behaviour and high-field irreversibility in magnetization curves are characteristics of both the states.

Superparamagnetism is a property arising out of single-domain behaviour when a bulk Ferro-magnetic or an ant ferromagnetic specimen is reduced to a size below about 50 nm. In such a small particle nearly 105 magnetic moments are coherently locked together resulting into a giant or super magnetic moment. Obviously this can happen only when surrounding temperature is less than bulk ordering temperature. It is known that because of thermal fluctuations the direction of the supermoment also fluctuates with relaxation time which depends on energy barrier KV. It can be easily shown that slight variation in size of the particles say from 10 nm to 15 nm can change the relaxation time from 0.1 sec. to 109 sec. Hence, when this Neel’s relaxation time is less than measurement time the net moment becomes zero while if it is more than the measurement time the moment is frozen which results into ‘magnetic viscosity’.

Spin glass behaviour results from frustration and disorder. Here to also exponential order is stretched as in the case of superparamagnetism-which is mainly due to size of the Ferro- or anti-ferromagnetic particles. Magnitude of the field cooled samples magnetization memory effect in the spin glass system will be significantly larger than that of superparamagnetism. This serves as a signature for spin glass system. Details are discussed in Ref.: M. Bandyopadhyay and S. Dattagupta, Arxiv.cond-matt/06606233v1 9 June 2006.

It may be remarked here that ESR technique is a complimentary method to discriminate between superparamagnetic and spin glass system. This is described in our paper - JMMM 252 (2002)35-38.

One can distinguish between antiferromagnetic(AFM) and ferromagnetic (FM) ordering by ploting the reciprocal dc-susceptibility (FC magnetization curve measured in a low-field can be used for that purpose) vs. temperature. For FM the extension of a linear part cuts the T-axis on its positive side, while for AFM on its negative site. Concerning spin-glass (SG), one of features in favour of SG is a bifurcation between ZF- and ZFC-curves. The temperature at which it occurs defines the spin-freezing temperature, while the maximum in the ZFC-curve marks a cross-over into a strong irreversibility state of SG. As superparamagnetism shows a similar behaviour, one should measure the ac susceptibility. If there is a cusp in the real part of this suceptibility than it speaks in favour of SG. The position of the cusp defines again the spin freezing temperature, but it value is a function of frequency (usually increases with the frequency as log(f)).

[I]Effect of field strengths onFM,SPM, SG , ZFC and FC:

Before answering, I humbly make three points.Firstly I wll try to explain the effect on these five phenomena individually; secondly taking an example of substance which exhibits all these five phenomena and thirdly the fact that all these phenomena are both temperature and field dependents.

The FM substances having permanent magnetic moment align themselves into small uniform regions called magnetic domains(Weiss domains).When put in magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure.

When put in VERY strong field, the prevailing domain overruns all others to result in only one single domain,i.e . the material is magnetically saturated.

When the field is CONTINUOUSLY DECREASED AND ULTIMATELY REMOVED, the domains may not return to an unmagnetized state. This results in the FM being magnetized and form a permanent magnet.

In SPM,on applying the magnetic field, magnetic moments of the ferro/ferrimagnetic SPM NPs tend to align along the applied field, leading to a net magnetization. The magnetization curve being a function of the applied field, is a COMPLICATED REVERSIBLE S-SHAPED INCREASING FUNCTION.

In SG, the characteristic phenomena observed is the occurrence of SHARP CUSP in the frequency and field dependent AC susceptibility in LOW FIELDS at VERY LOW temperatures called freezing point (Tf) indicating metastable MAGNETISM in SG.

Both zfc and fc being temperature dependent, the behavoiur of the magnetic moments of ZFC andFC processes as follows.

When a substance is COOLED TO NONZERO TEMPERATURE (FC), the angles between spin moments and applied field lie within pi/2. So THE SAMPLE SHOWS A NON ZERO MAGNETIZATION EVEN IF THE MAGNETIC FIELD REDUCES TO ZERO,When the sample is COOLED TO ZERO DEGREE, the spin domains are totally disordered and the SAMPLE SHOWS ZERO MAGNETIZATION WHEN THE FIELD IS ZERO.

If the field (Ha) is applied at low temperatures, the spin moments rotate towards the direction of the applied field and the substance shows a net magnetization. The larger the value of Ha, the larger will be Mfc and zfc.So zfc at any temperature(Ta) is proportional to fc (Ta) and Ha. The relation becomes

zfc α fc (Ta).Ha.

In order change any proportionality into equality, we need a constant which in this case, is 1/Hc.

In fact, it is 1/2Hc.

because experimentally it is observed that in most of the SPM materials, zfc was observed to the half of fc. So the relation becomes:

zfc=fc.Ta.1/2Hc.

[II]Lastly all the FIVE phenomena together in ONE magnetosuperconductor:

A single phase RuSr2Eu1.4Ce0.6Cu2O10-δ (EuRu-1222) magnetosuperconductor system shows all these FIVE magnetic phenomena. A PM to FM transition at about 110 K ; SG transition temperature (Tf) around 82 K and formation of non-homogeneous FM clusters at further lower temperature. The DC and AC susceptibility studies reveal that a SG state exists with non-homogeneous FM clusters. The FM order and SG state co-exist below freezing temperature (Tf).Superconductivity is not affected by various co-existing magnetic phenomena.

The ZFC curve shows a peak at around Tf = 85 K, just below the temperature where ZFC and FC curve separates. At Tmag, the ZFC and FC curves branch out and the system enters into SG state. (Tmag indicates the onset of the freezing process) . The ZFC curve has a peak at Tf = 85 K and the FC magnetization increases as temperature is decreased. In ZFC curve the system undergoes a superconducting transition at Tc = 30 K.

I want to add the following comment concerning a possibility of distinguishing between SG and superparamagentism: Both these magnetic phenomena exhibit a frequency dependence of the cusp in the ac susceptibility, however computing a quantity K permits to make the distinction, as for the sping glasses K should of the order of 0.01 while for superparamagnets K > 0.1. K is equal to a relative change of the spin-freezing temperature per a decade of a corresponding change in the frequency. For details see:

JE Greedan et al, Phys. Rev. B, 54 (1996) 7189

Drs. Dubiel and Manohar are discussing frequency dependent data. The original question is to distinguish SG and SPM using DC magnetization data. II discussed the question from that point of view.

Separation temperature between ZFC and FC curve is a common feature of spin glass (SG) or superparamagnetism (SP). However, we can distinguish SG and SP from ac susceptibility measurement using different type of equations such as frequency per decade P = Tf(p)/(Tf(p)logf), critical spin dynamics and Vogel–Fulcher law.

Thanks Dr. Mehta, I get a magnetic material that it's ZFC/FC is quenched by a strong fields, May be I should elaborate the Xac separately.

First of all, very sorry for reverting very late and thank you all for your interesting advice and fruitful discussions.

Of them, I found the observed behavior well suited to Griffiths like ferromagnetic interactions, which appear as short range ferromagnetic order in the long range anti-ferromagnetic or para-magnetic phase. As discussed above nicely, the bifurcation in ZFC/FC may appear due to several effects but the strong bifurcation at low field and disappearance of the same at high field may be guessed as short range ferromagnetic interactions. Although, the direct evidence of this observation is very rare but there are several steps even with DC magnetization data are followed in the literature which can be taken as the same prototype.

The origin of such interactions in a material completely depends on its synthesis condition.  

Some of the relevant reports are:

http://dx.doi.org/10.1063/1.4940972

https://doi.org/10.1016/j.materresbull.2016.04.002

http://onlinelibrary.wiley.com/doi/10.1111/jace.14357/epdfDOI: 10.1111/jace.14357

Cheers

1.Superparamagnet:-A ferromagnet with a particle size that is too small to sustain the multidomain structure. Thus the particle behaves as one large paramagnetic ion

2.Spin Glass:- A random orientation of frozen spin orientations (While in a paramagnet the spin orientations are fluctuating.) Can occur when the concentrations of magnetic ions are dilute or the magnetic exchange interactions are frustrated.

3.Ferromagnetism:- magnetic moments of atoms align to produce a strong magnetic effect• For ferromagnetism, the Curie Law becomes c = C/(T-Tc), where Tc is the Curie Temperature.Below Tc it exhibits spontaneous magnetization even in the absence of external magnetic field (while random magnetic moments are in paramagnet if external magnetic field is removed)