I guess you misunderstood my question. I know that VSM and SQUID can measure MH-loop. But I am asking how to explain the physical meaning if the resultant loop was reversed such that the coercivity of the descending part have a positive value and the coercivity of the ascending part have a negative value. Anyway, thanks for your answer.

You may find an answer if you go through the concept of 'Giant Magnetoresistance'

Dear Faris,

the phenomenon you are talking about is called "proteresis" (or inverted clockwise hysteresis). Its thermodynamic origin is still rather obscure. Below is some speculations on proteresis in core-shell structures from my previous discussion on this subject. Take a look.

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Just a sheer speculation. As I understand, this proteresis is observed in core-shell structures with FM core (like Co) and AFM shell (like CoO). Since Co itself exhibits a normal hysteresis and AFM CoO is not supposed to show any hysteresis at all (at least in theory), we can reasonably assume that something fishy is going on at their interface. To start with, let us compare the first parts of the loops for both types of hysteresis, normal and inverted.

(1) Here is a sequence of events for conventional hysteresis loop. After reaching a saturation point, we start to decrease the magnetic field to zero and watch the behavior of the field-induced magnetization. We see it decreasing and the first stop in our journey is the POSTIVE remanent magnetization Mr at zero field, that is M(0)=Mr>0, meaning that some finite magnetic moment has been "trapped" (pardon my French) in a sample after field treatment. The origin of Mr is not important right now. To restore a status quo and bring back the situation to zero magnetization at zero magnetic field, we change the field direction and try to squeeze the "trapped" moments by forcing on them the coercive (compensating) NEGATIVE field Hc. So, by definition, M(-Hc)=0. Or, in other words, Mr-Hc=0. Full compensation. Then we reach a saturation point at negative field and repeat the first half of the cycle to close the loop.

(2) Here is a sequence of events for inverted hysteresis loop. After reaching a saturation point, we start to decrease the magnetic field to zero and watch the behavior of the field-induced magnetization. We see it decreasing and the first stop in our journey is the POSITIVE coercive field Hc at which magnetization disappears restoring a status quo (which strictly speaking has not even been violtated yet!). Anyway, we have M(Hc)=0. Let us try to think this exp. fact over. What does it mean? We remember that for normal hysteresis we needed a NEGATIVE coercive force Hc to compensate for POSITIVE remanence Mr. Makes sense. Now, the only possible solution for inverted hysteresis wich brings a rather unusual condition M(Hc)=0 would be an assumption that after the field treatment our sample acquired (somehow?) quite a substantial amount of "DIAMAGNETIC" like phase, because the above condition looks to me very much like a field expulsion. Indeed, let us specuate and imagine that due to some field-mediated processes near the FM-AFM interface (some spin interference, tunneling, fluctuations, etc), the resulting magnetization, in addition to the initial POSITIVE FM and AFM phases Mi, includes also a NEGATIVE DM contribution Md=-H (for simplicity). That is, M(H)=Mi(H)-H. Only in this case we can see the condition M(Hc)=0 fulfilled giving us some POSITIVE value of the coercive field Hc=Mi(Hc). Ok, let us continue our journey along the inverted hysteresis loop. By further decreasing field, below Hc our magnetization turns NEGATIVE. According to the above assumption, it means that the DM contribution finally exceeded the initial magnetization because only in this case we will have the situation with M(H)

@Sergei Sir....it was a nice explanation by you given above about inverted hysteresis. Could you please explain a little about "some field-mediated processes near the FM-AFM interface (some spin interference, tunneling, fluctuations, etc)"?

This is actually from another discussion on possible depression mechanisms for exchange bias (EB) energy Eex near FM-AFM interface. I suggested a new expression for EB based on analogy with tunneling and proximity phenomena. It means that, in the first approximation, Eex should look more like this: Eex=exp(-t/L)J, where t is the interface layer thickness, L is a characteristic length defined by the interface structure, and J is the energy of FM layer. For tunneling like processes in the vicinity of the interface between FM and AFM, we have L=1/sqrt{U}, where U is the height of the potential barrier, while for proximity like events, we have L=sqrt{D/T} where D is spin diffusion coefficient and T is the temperature. Now, the suggested approximate expression for Eex contains the necessary info about the interface and explicitly shows how Eex is changing depending on the variation of the two independent parameters, t and L. Notice that it predicts a depression of the EB effects for many diferent reasons: (1) if the interface barrier is too thick (irrespective of the thicknesses of FM and AFM layers!), (2) if the potential barrier is too high, (3) if the spin diffusion thru the barrier is too slow, or (4) if the barrier temperature.is too high. More importantly, you can experimentally tune the above parameters (during the synthesis of your Co-CoO bilayer) in order to achieve the best performance by enhancing the EB coupling at the interface.

Now, in applied magnetic field H, both the barrier potential U and spin diffusion D will become field dependent. As a result, Josephson-like interference effects between two spins (at different sides of the interface) will take place. In particular, a quasi-periodic Fraunhoffer like pattern for spin current thru the interface will appear. It has the form of Sin(H)/H and could potentially produce a negative (diamagnetic) contribution (when normalized applied field H is in-between Pi and 2Pi) which is needed to outweigh the positive FM magnetization and to explain the "proteresis". A similar contribution can appear from the proximity effect in applied magnetic field. But keep in mind that these are just theoretical speculations. I'm actually unaware of any experimental results on such events taking place at the FM-AFM interface.

@Sergei Sir......Thanks for your valuable comments.

Your comment is really very helpful. I need to do some studies about the exchange bias.

If you are measuring hysteresis loop using quantum design SQUID then its most likely due to rest or trapped field of superconducting magnet. Please refer to this link http://www.qdusa.com/sitedocs/appNotes/ppms/1070-207.pdf to get an idea. The above argument is true if your coercivity values are small. For instance, around 20 Oe when using system whose max field is 7 T.

The sample's location was not correct. The machine located the sample at the wrong maximum.

I would supplement Stefan Glatzel comment with the fact that the tracking procedure implemented in Quantum Design software in order to correct centering with temperature variation is not that reliable. If you perform a centering at low temperature, then you get an error of about 1mm around room temperature, and vice-versa. This is true for QD supplied sample holders, even more so when sample holders are home-made. There are only two solutions since QD has not (and will not as they stopped developping the MPMS software) provided an option to retreat data after the measurement

1) retreat the data yourself (it can give very nice results, we've had quite some experience with it on measurements on very small quantities of paramagnetic substances)

2) perform centering regularly

In conclusion, the SQUID remains a magnetic field-to-voltage transducer, and the magnetic moment it reports is only the result of a fit assuming a lot of hypotheses (good centering, point dipole). If those hypotheses are not complied with, the reported magnetic moment is at the least dubious and error-prone.

Dear Patrick Rosa ,

thanks for your precious advices. Since I'm experiencing the same behaviour in some of my samples, can I ask you how you are retreating the data obtained from the measurements? And, regarding the centering, do you think that a centering measurement done at 35 K would be trustable to measure data at 3K-20K.

Thanks for your help and sorry for posting again on this old question.

Dear @Sergio Fiorito

We systematically record .raw and .diag files. They contain the raw data. From those you can fit again with either a dipolar (there's an application note on that) or multipolar model which allows to correct centering problems, and obtain a reliable value of the fit error, which is NOT calculated by the QD soft, unbelievingly so. We routinely perform photomagnetic measurements with samples giving moments in the 1e-6 range and typically the QD soft gives results far from reliable.... The background substraction procedure is not reliable most particularly when sweeping T (as said by QD themselves...). If you want more details feel free to contact me directly.