What is ferromagnetism?

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Magnetic behavior in materials

A typical magnet consists of a north and south pole. Unlike charges, the poles always occur in pairs. The major contribution to the magnetic behavior is due to the electrons. The electron has a spin magnetic moment on its own in two possible states with opposite magnetic moments. These states are called 'spin-up and spin-down states. So, every orbital can accommodate two electrons with spin up and spin down each. If the orbital is filled, the net magnetic moment due to the pair would be zero. So, the magnetic behavior of the atom or molecule depends on the number of unpaired electrons. Hence, the magnetic behavior of a material is based on the properties of the individual particles (atoms/molecules) and their arrangements.

The reaction or behavior of the material towards an applied external field is given by its magnetization (M), which says how much the material is influenced either positively or negatively by the external field.  The magnetization is related to the applied external field as, $M=XH$

Here, Χ (Greek alphabet Chi) is magnetic susceptibility. Based on their intrinsic properties and their behavior in the presence of a magnetic field, the materials are classified into different categories.

Ferromagnetism

Ferromagnetism is shown by materials that have two or more unpaired electrons. This results in a high magnetic moment of the individual atom/molecule. Hence, the individual dipoles are very strong, and they influence the neighboring dipoles to get aligned in a particular direction. However, this alignment does not stretch to the whole bulk of the material. It forms a region of dipoles with similar alignment, which is referred to as a 'domain'. Many such domains are formed inside the material upon magnetization. Usually, these domains are oriented in random directions as shown in the figure below and the magnetic moments of the domains cancel out. Hence, the material doesn't have a bulk magnetic behavior.

Ferromagnetic materials are strongly attracted by a magnetic field, and they retain their magnetic behavior even after the field is removed. When an external magnetic field is applied, the domains align themselves. This makes the net magnetic moments of all the domains add up, resulting in a strong attraction in terms of an external field. When the field is removed, some of these domains retain the same orientation. As a result, the material retains the magnetic behavior even after the external field is applied.

Diamagnetism

It is induced by a change in the orbital motion of electrons because of an applied magnetic field. It is a very weak form of magnetism. The materials are not attracted by the applied magnetic field. For example-water wood, etc.

Paramagnetism

Some materials show a weak attraction towards an applied magnetic field. It is due to the alignment of unpaired spins of electrons in atoms of the material. For example-oxygen, titanium, aluminum, etc.

Long-range order

The long-range order in ferromagnets, which is responsible for the formation of magnetic domains in ferromagnetic materials, is due to atomic quantum mechanical interaction. These interactions freeze the magnetic moments of nearby atoms in a fixed parallel order extending over many atoms. These magnetic moments are retained despite the thermal excitation which can lead to randomization of any order at the atomic level. The size of domains can lie in the range from 0.01 cm to a few cm. Upon application of an external magnetic field, the parallel aligned magnetic domains along the direction of this external magnetic field grow by aligning the magnetic moments with that neighbor, hence merging with them. If in an Iron sample all the spins are aligned parallel, the total magnetic field has a magnitude of approximately 2.1 Tesla. Whereas in the case of annealed iron sample a magnetic field strength of about 1 T can be produced by an external magnetic field of about 0.2 mT, this is scaling up of the external magnetic field by a factor of 5000. 

Ferromagnets can stay magnetized to some extent after they are removed from an external magnetic field. This property to retain some part of its magnetic history is called hysteresis. The fraction of the maximum magnetization that is retained when the external magnetic field is removed is known as the remanence of the ferromagnetic material.

The strong magnetic behavior is used in making electromagnets. The retentivity of the magnetization is amplified to form permanent magnets. Examples of such materials are Iron, Cobalt, Nickel, etc. Ferromagnetic materials have applications in various fields ranging from communication to computing. They are also used in the power generation industry like a dynamo, transformers, etc.

Effect of temperature on ferromagnetism

All ferromagnetic materials have a certain temperature at their behavior ferromagnetism vanishes due to of thermal excitation of atoms and hence randomization of magnetic moments. This temperature is called the Curie temperature. At the high-temperature, the material behaves as a paramagnet.

For ferromagnetism materials, the magnetic susceptibility is given in terms of Curie temperature by the expression,

$X=\frac{C}{T-T_C}$

Here, the temperature Tc is called as the Curie temperature. Graphically, it is shown as,

As can be seen from the image above, the ferromagnetic behavior (in brown) vanishes and the material shows paramagnetic behavior (in black). 

The magnetic susceptibility of a ferromagnetic in a paramagnetic region is above the Curie temperature point is described in Curie-Weiss law. It is due to moments of ferromagnetic materials are magnetized spontaneously. It implies that there is a presence of an internal field to produce this magnetization. According to Weiss, this field is proportional to the magnetization, i.e. T.

Hall effect in ferromagnetic materials

When an electric conductor is placed in a magnetic field, there is a production of potential difference across the material in a direction perpendicular to the flow of the current. This is known as the Hall effect. In ferromagnetic materials, the Hall effect is much larger than the ordinary Hall effect. This additional contribution is known as the anomalous Hall effect

Ferromagnetism vs other types of magnetism

Context and Applications

This topic is studied under the following courses:

• Bachelors in Technology (Mechanical Engineering)
• Masters in Technology (Mechanical Engineering)
• Bachelors in Science (Physics)
• Masters in Science (Physics)

Practice Problems

Q1. If a magnetic dipole is broken, how many poles in total would it result in?

1. Two
2. Three
3. Can’t be determined
4. Four

Answer- (d) 

Explanation- A magnet has two poles. When it is broken, the broken ends result in a pair of opposite poles. So, the initial two poles plus additional two, collectively result in four poles.

Q2. Which of the following magnetic material has three unpaired electrons in elemental form?

1. Ferromagnetic material
2. Diamagnetic material
3. Paramagnetic material
4. Both (b) and (c)

Answer- (b) 

Explanation- A material with more than two unpaired electrons shows ferromagnetic behavior as the magnetic dipoles are strong. 

Q 3. What is the magnetization of diamagnetic materials?

1. Very low and positive
2. Very low and negative
3. Very high and positive
4. Very high and negative

Answer- (b)

Explanation- Higher the susceptibility, the higher the magnetization. Diamagnetic materials have a very low negative magnetic susceptibility. As a result, their magnetization is very low and negative.

Q4. What is the ferromagnetic region of aligned dipoles called?

1. Regions
2. Grains
3. Domains
4. None of these

Answer- (c) 

Explanation- The regions of aligned magnetic dipoles are called ‘domains’

Q5. What is the temperature Tc, in ferromagnetic susceptibility called?

1. Curie temperature
2. Weiss temperature
3. Critical temperature
4. Both (a) and (b)

Answer: (a)  Curie temperature

Explanation- Curie temperature is the temperature Tc, in ferromagnetic susceptibility.

Common Mistakes

It is often argued that oxygen cannot be paramagnetic, as it does not have an unpaired electron in its elemental state of $O_2$. But molecular orbital theory explains that the overall molecular orbitals of $O_2$ molecule when all the shells are filled with the electrons, end up with an unpaired electron which is responsible for its paramagnetic nature.

Formulae used

• The magnetization is related to the applied external field is given by the equation ,

$M= XH$

• The variation of paramagnetic susceptibility with temperature is given by Curie-Wiess law as,

$\chi =\frac{C}{T}$

• For materials showing ferromagnetism, the magnetic susceptibility varies with temperature as given by, 

$\chi =\frac{C}{(T-T_C)}$

Related Concepts

• Electricity and Magnetism
• Magnets
• Magnetic field
• Curie-Wiess law
• Diamagnetism
• Paramagnetism
• Antiferromagnetism
• Ferrimagnetism
• magnetic susceptibility
• magnetization
• Hysteresis loop