Hysteresis loop magnetization of Gadolinium

[gony rosenman]

hello i have a few questions regarding hysteresis loop in ferromagnets as showen here .

i had an experiment in which i took a piece of gadolinium and cooled it down using liquid nitrogen , than i put it in an apparatus as showen here , so i induct an oscillating magnetic field on it , forcing some inner magnetization to arise within the metal , according to blochs law .

M(T) = M(0)*(1-(T/T_curie)^3/2)
M(T) - inner magnetization
M(0) - inner magnetization at absolute zero
T - Temperature
T_curie - curie temperature , in which the magnetic domains cannot form a unified direction and the metal become paramagnetic

now things get tricky for me

i learned that in hysteresis loops , the inner magnetization is measured as the magnitude of B at the retentivity point (which makes sense cause that's the field that remain in the metal when there is no magnetic field induced) , but that is confusing because that value is in units of Tesla/Gauss , and i wanted to find the Magnetization in amper/meter units .
am i getting something wrong , or should i just convert to amper/meter , and if so - which formula should i use ?

further more , in the experiment i measure the voltage drop on the capacitor C2 (shown in figure) and get a signal proportional to B , with an unknown factor which i am unable to attain from the lab ( apparently no one knows the precise inductance of the coil , i measured it by myself but decided i rather keep the whole data with volatages and show proportionality) , so in the end the value extracted from the hysteresis loop was only proportional to B at the retentivity point .

nevertheless , i decided to fit the data using CFtool (matlab) and a costume equation similar to bloch's law (meaning i took the value of V proportional to B at the retentivity point of each hysteresis loop corresponding to a different Temperature , and plot it against the matching temperature , and tried to make a fit with bloch's law equation)

the striking part , the results were surprisingly close to the expected values . for example , i looked up the inner magnetization and saw the following for gadolinium :
The saturation magnetization at absolute zero, determined by extrapolation is 253.6±0.9 cgs units .
This saturation moment corresponds to 7.12 Bohr magnetons.

the value i got in the CFtool for M(0) was around 700 , which is in the same order of magnitude . so my final question , is it a coincidence or does it make sense somehow that my proportional measurment somehow corresponds well to the actual value , and that my measurement was in units of B when maybe it should have been somehow converted to units of magnetization .that is a very long question , i hope someone out there might be able to assist with some clarification , there's not much i can do in return but send honest gratitude !

 

[Charles Link]

A google shows the Curie temperature for gadolinium is $T_c \approx 293 \, K$. One comment on your laboratory experiment is that it looks like you only have a couple of different temperatures for data points. Bloch's equation will probably work moderately well, but there is an equation that will likely give a better experimental data fit: See https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/ where a couple of students did a similar type of experiment, using a couple of permanent magnets that have much higher Curie temperatures. (They also had the problem that they didn't collect data points at enough different temperatures).$\\$ Presumably, the gadolinium sample that you had did not make a permanent magnet, but instead, gave a response approximately proportional to the applied magnetic field, with the temperature dependence of the response obeying an equation similar to Bloch's formula, or this other formula, with the $\gamma$ exponent. $\\$ Your experiment doesn't appear to have measured $M(0)$ or $M(T)$. To get a good curve fit, (basically graphing $\frac{M(T)}{M(0)}$ vs. $T$ ), you really need measurements at quite a few different temperatures below the Curie temperature. $\\$ In any case, a lab experiment such as this does give the student a reasonably good introduction to the idea of the Curie temperature.

 

[gony rosenman]

i'm not sure where you got the idea that i didn't have enough data points . i used liquid nitrogen and sampled the hysteresis loop many times while the Gd heated back up so i have about a hundred samples of Hysteresis loops with temperature varying between -120 celsius and 30 celsius .
my questions remain , simply put - how can i convert the value of the retentivity point (which is in units of tesla for that matter) to magnetization ? (amper/meter)
thank you

 

[Charles Link]

i'm not sure where you got the idea that i didn't have enough data points . i used liquid nitrogen and sampled the hysteresis loop many times while the Gd heated back up so i have about a hundred samples of Hysteresis loops with temperature varying between -120 celsius and 30 celsius .
my questions remain , simply put - how can i convert the value of the retentivity point (which is in units of tesla for that matter) to magnetization ? (amper/meter) thank you ]

Depending on the units/definition you use for magnetization $M$, $B=\mu_o H+M$ or $B=\mu_o(H+M)$. The magnetic field $B$ is measured in Tesla. The $H$ will have MKS units of Amperes/meter. If you use the second definition of $M$, then $M=\frac{B}{\mu_o}$, and the result will be in Amperes/meter.

 

[gony rosenman]

alright , thank you for the quick reply! (:

 

[Charles Link]

alright , thank you for the quick reply! (:

I had to edit it a couple of times. Either my computer or the processor copied it incorrectly.