While plotting dM/dH vs H for a oxide powder sample, I am getting a gaussian type peak at a particular field before it return to zero value at zero field. What is the significance of this field value where I am getting the peak.
Dear Alorika
Please see if you plot M vs H or B vs H , you you will get a sigmoid like curve. Means if you take the derivative you will get a Gaussian curve.
I can't understand actually what else you want to be clarified.
Love and Regards
N Das
Thanks Nityananda Das. I wanted to know what is the significance of this field value where we are getting the gaussian peak.
The curve dM/dH is bell-shaped but almost surely not gaussian. Besides, it is highly unlikely that dM/dH (at H=0) is equal to 0 -- this would mean nothing else but null magnetic susceptibility.
The location of dM/dH peak is usually quite well correlated with coercivity field - a characteristic point of ordinary hysteresis loop. It also estimates the location of the peak on Preisach map (FORC diagram), i.e. the maximum density of Preisach hysterons. All I said is best applicable when the curve dM/dH is obtained by differentiation of M(H) dependence, not by direct dM/dH measurements. However, the differences are not drastic.
dM/dH is the susceptibility, which at zero field has a peak in the vicinity of the Curie point. Not all bell-shaped curves are Gaussians.
At non-zero field, there is a particular order that's the result of the competition between the effect of the field and the stiffness, so that's what the peak means.
Dear Marek,
I do not quite agree with your statement that " when the curve dM/dH is obtained by differentiation of M(H) dependence, not by direct dM/dH measurements. However, the differences are not drastic. " in particular that the two susceptibilities are not much different. (greetings Karel)
Dear Alorika,
you may forget about the shape of the curve dM/dH vs H (actually it cannot be Gaussian, as it is from pysical reasons asymmetric) - the important fact is that it has a maximum and and you are asking what this maximum means. The formal answer is simple: at this field the processes realizing the change of magnetization, be it wall motion or rotation of magnetic moment of the domains, are most numerous and thus the susceptibility is maximum.
As Marek remarks, the magnitude of this field is normally close to the coercive field, if I am measuring the full hysteresis loop from positive to negative saturation and back. The subtle point lies in the way, how you measure dM/dH: is it the slope of the static M(H) curve measured from zero field after demagnetization od the sample or the value of the slope of minor hysteresis loop, where you start from the point M(Hi) and use small negative amplitude delta H (and possibly back to Hi)? The susceptibility along this minor loop is usually much smaller than the one derived from the virgin curve and its maximum need not be at the same field.
Let's look at the original question again. It seems that the measurement of dM/dH starts at zero field, and readings are recorded during field increase, then during the field decrease to zero. Magnetization itself is probably not investigated, and dM/dH is obtained via small H-field vibrations around its current value. The measured quantity, dM/dH(H), is called dynamic susceptibility, while ordinary magnetic susceptibility is defined as a ratio M/H near H=0 (mathematicians prefer to write it as lim dM/dH as H-->0).
The observed curves obtained during field increase and decrease are different, namely the first one exhibits a peak at some field. This can only happen when the original curves M(H: 0-->Hmax) and M(H: Hmax-->0) are different. It means that the sample under investigation (and at given temperature!) is neither paramagnetic nor diamagnetic but exhibits hysteretic behavior. It is most likely a ferromagnet -- but other situations are also possible (ferrimagnetism, antiferromagnetism, weak ferromagnetism, and so on). The location of dM/dH peak is close to coercivity field, but only when observed during examination of major hysteresis loop. Note that for a paramagnetic sample, the peaks on both dM/dH branches should be present, symmetric and centered at the same position, namely at H=0.
I have to agree with Karel, my previous answer wasn't precise enough. Indeed, the amplitudes of dM/dH curves obtained on two ways may differ a lot, but peak locations should be very close to each other, if not identical (dynamic susceptibility is frequency dependent!).
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