# Hysteresis loop magnetization of Gadolinium

• gony rosenman
In summary, the author has an experiment in which they take a piece of gadolinium and cool it using liquid nitrogen. They put the gadolinium in an apparatus which induces an oscillating magnetic field, forcing some inner magnetization to arise within the metal. The author learned that in hysteresis loops, the inner magnetization is measured as the magnitude of B at the retentivity point. However, the author is confused because that value is in units of Tesla/Gauss and they want to find the Magnetization in amper/meter units. The author found that their CFtool data fit reasonably well using a similar equation to Bloch's law. The author has questions about whether it is a coincidence that their proportional
gony rosenman
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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/Tcurie)3/2)
M(T) - inner magnetization
M(0) - inner magnetization at absolute zero
T - Temperature
Tcurie - 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 !

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.

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

gony rosenman said:
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.

Last edited:
alright , thank you for the quick reply! (:

gony rosenman said:
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.

## 1. What is a hysteresis loop?

A hysteresis loop is a graphical representation of the relationship between the magnetic field strength and the magnetization of a material. It shows the behavior of a material when it is subjected to changing magnetic fields.

## 2. What is the significance of studying the hysteresis loop magnetization of Gadolinium?

Gadolinium is a commonly used material in magnetic devices and its hysteresis loop behavior can provide valuable information about its magnetic properties. Understanding this behavior can help in designing and optimizing magnetic devices for various applications.

## 3. How is the hysteresis loop of Gadolinium affected by temperature?

The hysteresis loop of Gadolinium is greatly influenced by temperature. As the temperature increases, the hysteresis loop becomes smaller and shifts towards lower magnetic field strengths, indicating a decrease in the material's magnetic properties.

## 4. What factors can affect the hysteresis loop magnetization of Gadolinium?

The hysteresis loop magnetization of Gadolinium can be affected by factors such as temperature, impurities in the material, and the presence of external magnetic fields. The composition and microstructure of the material can also have an impact on its hysteresis loop behavior.

## 5. How does the hysteresis loop of Gadolinium differ from other magnetic materials?

The hysteresis loop of Gadolinium has a unique shape compared to other magnetic materials. It has a narrow loop with a steep slope, indicating a high susceptibility to changes in magnetic field strength. This makes Gadolinium a suitable material for use in sensors, actuators, and other magnetic devices.

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