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Match the type of magnetism given in Group I with the material given in Group II:

$$
beginarrayll
hline
& textbfGroup I & & textbfGroup II \
hline
textP & textFerromagnetic & 1 & textNickel oxide \
textQ & textFerrimagnetic & 2 & textSodium \
textR & textAntiferromagnetic & 3 & textMagnetite \
textS & textParamagnetic & 4 & textCobalt \
hline
endarray
$$

A) P-4, Q-3, R-1, S-2
B) P-4, Q-1, R-3, S-2
C) P-1, Q-2, R-4, S-3
D) P-3, Q-2, R-1, S-4

It was taken from a mock test sheet for GATE in India.
With regard to whether a material is ferromagnetic or paramagnetic etc. All that I know is to check the magnetic domains and decide. However, with regard to such compounds I have been facing extreme difficulties. Is this something that is totally experimental and that I need to know by information? Or is there a certain intrinsic property of the elements which can help me to decide? If yes, please explain how to solve such questions.

I believe GATE is a university entrance exam in India, so they will not expect you to solve an extremely complicated equation to predict ferromagnetism or to memorize an infinite list of substances. Sadly, there is some element of rote memorization still lingering like a pest in the educational testing system.

Good news for you is that relatively few compounds and metals show ferromagnetism or ferrimagnetism. Find out the list of ferromagnetic metals from the web, you might end up with very few elements and oxides, such as iron compounds, iron oxide containing materials. Later you can attempt the multiple choice questions by the process of elimination. For example, in the given choices, choose the answers which show that magnetite is ferrimagnetic.

Lo and behold, there is only ONE choice which matches with Q-3!

Historically, the term ferromagnetism was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field (Wikipedia). However, in 1948, Louis Néel showed that there are two levels of magnetic alignment that result in this behavior (Ref.1):

1. One is ferromagnetism in the strict sense, where all the magnetic moments are aligned A few examples of this type are $ceFe$, $ceCo$, and $ceNi$.


2. The other is ferrimagnetism, where some magnetic moments point in the opposite direction but have a smaller contribution, so there is still a spontaneous magnetization. The oldest known magnetic substance, magnetite ($ceFe3O4$), which contains both iron(II) and ion(III) oxides is a well-known ferrimagnet ($ceFe3O4$ was originally classified as a ferromagnet before Néel's discovery). The other cubic ferrites composed of iron oxides with other elements such as $ceMg$ (e.g., $ceMgOFe2O3$), $ceCu$ (e.g., $ceCuOFe2O3$), and $ceNi$ (e.g., $ceNiOFe2O3$) are also examples of ferrimagnets.


3. Néel had discovered a third level of magnetism called antiferromagnetism. In a special case where the opposing magnetic moments balance completely, the alignment is known as antiferromagnetism; but antiferromagnets do not have a spontaneous magnetization. A well-known antiferromagnets are common Iron oxide, hematite ($ceFe2O3$), the trasition metal oxides such as nickel oxide ($ceNiO$), and alloys such as iron manganese ($ceFeMn$).

All of these three levels of magnetisms have a kryptonite temperature, above which all of them become paramagnetic. For ferromagnetism and ferrimagnetism, it is called Curie temperature while for antiferromagnetism, it is Néel temperature.

Thus, M. Farooq gave an excellent way to answer your question for novices. Mostly, known ferromagnets are metals and metal oxides are usually ferrimagnets, except for $ceNiO$, which is a known antiferromagnet. You have two metals and two oxides in RHS column. Now, it is easy to figured out.

References:

1. M. Louis Néel, "Propriétés magnétiques des ferrites ; ferrimagnétisme et antiferromagnétisme (Magnetic properties of ferrites: ferrimagnetism and antiferromagnetism)," Annales de Physique (Paris) 1948, 12(3), 137-198 (https://doi.org/10.1051/anphys/194812030137).