Magnetism Basics: Definition, Types, & Temperature Dependence

Introduction to magnetism:

When we see fridge magnets in our house that stick to the fridge door or any iron plate, we are puzzled by how they stick and what attracts them to iron. Does it specifically apply to iron, or is it in some other materials as well? In this article, you will learn what magnetism is and how many types of magnetism exist, alongside an introduction to each of them separately.

Historical Background of Magnetism:

The word magnetism comes from the Greek word “magnētis”, based on the place Magnesia, where the first magnetic materials were found in the Western world. In the early centuries, only magnetic materials, such as iron, were considered, and it was always about the attraction of iron ore and its use in navigation. 

In 1845, Michael Faraday conducted an experiment in which he observed that external electric and magnetic fields repel certain materials. These materials are diamagnets. Simultaneously, he discovered that some remaining materials were weakly attracted to the external fields; these are paramagnets. Materials that have a strong magnetic attraction and retain magnetism in the absence of an external field are called ferromagnets. Ferromagnetism was historically discovered in Greece and China. While studying the fundamentals, Louis Néel predicted the existence of materials with opposite magnetic moments in 1932, and he was awarded the Nobel Prize in 1970 for the discovery of antiferromagnets. Louis Néel also explained that if the moments are unequal, the material is termed a ferrimagnet. Recently, a new class of magnets, termed Altermagnets, has been emerging. Altermagnets were presented by Libor Šmejkal and his colleagues in 2019 in a previous study of the same materials, which showed simultaneous ferromagnetic and antiferromagnetic behavior.

Types of magnetic materials:

There are various types of magnetic materials found in nature and those synthesized in laboratories by scientists. In a broad sense, magnetic materials are classified based on the alignment of their spin and orbital angular momenta, as well as the flow of electronic charge, within a relativistic framework. The different types of magnetic materials found in nature are listed below.

1. Diamagnetic Materials
2. Paramagnetic Materials
3. Ferromagnetic Materials
4. Antiferromagnetic Materials
5. Ferrimagnetic Materials
6. Altermagnetic Materials

Magnetic Materials and Their Temperature Dependence

Each type of magnetic material has a distinct property based on its internal electric structure. Before examining the electronic structure, the basic behavior of all types of magnetic materials can be understood by the following details and the effects of temperature on their properties. Here, statements about those behaviors have been presented: magnetic materials exhibit temperature dependence and different behaviors with temperature changes. 

1. Diamagnetic Materials:

The class of materials that have fully occupied electronic valence orbitals and therefore repel external magnetic fields. Magnetic induction (B) is independent of temperature. These are basically the non-magnetic materials around us.

2. Paramagnetic materials:

The class of materials that have partially filled electronic valence orbitals and therefore their spin try to align in the direction of the magnetic field, but lose their response in the absence of external magnetic fields. Magnetic induction (B) is inversely proportional to temperature as explained by the Curie-Weiss law, which is given below:

\[\mathrm{B(T)}=\mathrm{\mu_0}H\left(1+\frac{C}{T-\theta}\right)\tag{1}\]

\( \theta\) is positive for the ferromagnetic transition from paramagnetic states and negative for the antiferromagnetic transition to paramagnets.

3. Ferromagnetic Materials:

The class of materials that have spontaneous magnetization in them due to the Heisenberg exchange interaction, and in the presence of an external magnetic field, they try strongly to align in the direction of the external magnetic field, and after the removal of the magnetic field, they sustain the magnetic moments. The temperature dependence of the Magnetic induction (B) can be given by the following equation:

\[B(T)=
\begin{cases}
\mu_0 H + \mu_0 M_0 \left(1 – \dfrac{T}{T_c}\right)^{\beta} & \hspace{1cm}; T < T_c \\[6pt] \mu_0 H \left(1 + \dfrac{C}{T – \theta}\right) & \hspace{1cm}; T \ge T_c \; (\theta > 0)
\end{cases}
\tag{2}\]

is the Weiss temperature. And θ is a positive value, M0 magnetization at absolute zero, T is the temperature, and TC is the Curie temperature at which ferromagnets turn into paramagnets, and β is the critical exponent whose value is 0.33 for 3D ferromagnets. The figure below represents its graphical interpretation.

4. Antiferromagnetic Materials:

The class of materials that follow the Heisenberg exchange interaction, but their magnetic moments are aligned antiparallel to each other, and cancel out each other, resulting in net zero magnetic moments. Therefore, these materials lose their net magnetization in the absence of external magnetic fields. The temperature dependence of the Magnetic induction (B) can be given by the following equation in the given format:

\[
B(T)=
\begin{cases}
\mu_0 H \hspace{1cm}; & T \le T_N \\[6pt]
\mu_0 H \left(1 + \dfrac{C}{T – \theta}\right)\hspace{1cm}; & T > T_N \; (\theta < 0)
\end{cases}
\tag{3}\]

5. Ferrimagnetic Materials:

This class of materials has spins aligned antiparallel to their neighbors, but the magnitude of one spin is larger than that of its neighbors, resulting in a net magnetic moment after the external magnetic field is removed. The temperature dependence of the Magnetic induction (B) can be given by the following equation in the given format:

\[
B(T)=
\begin{cases}
\mu_0 H+\mu_0M_{0a}\left(1 – \dfrac{T}{T_c}\right)^{\beta a} – \mu_0M_{0b}\left(1 – \dfrac{T}{T_c}\right)^{\beta b} \hspace{1cm}; & T \le T_N \\[6pt]
\mu_0 H \left(1 + \dfrac{C}{T – \theta}\right) \hspace{6.5cm}; & T \ge T_c \
\end{cases}
\tag{4}\]

6. Altermagnetic Materials:

The class of magnetic materials that exhibit ferromagnetic properties in an intrinsic way but have spin alignment similar to that of antiferromagnets. This class of magnetism is relatively new and requires specific crystal symmetries in the materials.

Real-world examples:

References

1. Coey, John, MD. Magnetism and magnetic materials. Cambridge University Press, 2010.
2. Néel, Louis. “Antiferromagnetism and ferrimagnetism.” Proceedings of the Physical Society. Section A 65.11 (1952): 869-885
3. Mazin, Igor. “Altermagnetism then and now.” Physics 17, 4 (2024)