Magnetic domains are the foundation of magnetism. In this post we’ll dive into the world of magnetic domains, and explore how they form, behave and the processes that determine their impact on magnetic materials. Understanding these will give you a deeper appreciation of how magnetism works in everyday applications.
What are Magnetic Domains?
Magnetic domains are tiny regions within ferromagnetic materials where the magnetic moments of the atoms align in the same direction, creating a uniform magnetic field within that domain. Ferromagnetic materials unlike other materials (paramagnetic or diamagnetic) can retain magnetization even after the external magnetic field is removed. This is because of the magnetic domains.
Magnetic Domain Formation
Before magnetization, ferromagnetic materials don’t have a net external magnetic field. This is because at temperatures below the Curie point, large crystals within the material form multiple magnetic domains. Each domain is uniformly magnetized but the direction of magnetization is different between domains and the overall magnetic effect cancels out.
Magnetic domains form because the material wants to minimize its magnetic dipole energy also known as demagnetizing energy. For example a single domain magnet has a large area of stray magnetic field which is energetically unfavorable. To minimize this stray field the magnet internally redistributes its magnetic moments and forms multiple domains with different orientations.
Magnetic Domain Walls
The boundaries between different magnetic domains are called domain walls. These walls can be of different types depending on the angle between the magnetic moments of adjacent domains. For example if the moments are opposite (180° apart) it’s called 180° domain wall. If they are perpendicular (90° apart) it’s called 90° domain wall.
Domain walls are not sharp boundaries but transition zones where the direction of magnetization changes gradually. This transition requires energy which is why domain walls always have higher energy than the interior of the domains.
Technical Magnetization Process
The technical magnetization process includes only the magnetization due to domain wall movement and domain rotation.
According to the changes observed in most ferromagnetic magnetization curves, the technical magnetization process can be generally described as:
- Reversible domain wall movement in weak magnetic field range.
- Irreversible domain wall movement in moderate magnetic field range.
- Reversible domain rotation in strong magnetic field range.
- Irreversible domain rotation in very strong magnetic field.
For a magnetic material, its magnetization process is dominated by one or more magnetization mechanisms and does not have to include all four mechanisms. For general soft magnetic materials, the magnetization process is mostly dominated by domain wall movement. For single domain particle materials, only domain rotation magnetization occurs which can lead to irreversible domain rotation magnetization.
Reversible Domain Wall Movement Magnetization Process
In a magnetic field, the volume of magnetic domains with magnetization direction parallel to the external field H increases while the volume of domains with magnetization direction antiparallel to the external field decreases.
Under a certain external field, the distance a domain wall can move is limited due to the resistance within the magnetic material such as internal stress fluctuations and uneven distribution of components like impurities, pores and non-magnetic phases. As the domain wall moves these inhomogeneities cause fluctuations in internal energy and hence resistance. The internal energy of a magnet mainly includes magnetoelastic energy and domain wall energy.
The total energy per unit volume of a magnet is given by: F = F_H + F_magnetoelastic + F_W
Where F_H is the external magnetic field energy, F_magnetoelastic is the magnetoelastic energy and F_W is the domain wall energy. During domain wall movement the principle of minimum free energy must be satisfied: δΦ = δΦ_magnetoelastic + δΦ_W = 0.
So: -δΦ = δΦ_magnetoelastic + δΦ_W. This physically means the decrease in magnetic potential energy during domain wall movement is equal to the increase in internal energy of the magnet.
To distinguish the spontaneous magnetization within magnetic domains of ferromagnets or ferrimagnets the magnetization in a magnetic field is called technical magnetization.
We know the technical magnetization curve (M~H curve) of ferromagnetic or ferrimagnetic materials is non linear, the vertical axis is the magnetization M and the horizontal axis is the magnetic field strength H. Assume the magnet has two magnetic domains:
When the magnetic field is zero, the number of atomic magnetic moments in the upper and lower magnetic domains are equal and opposite in direction. The vector sum of the atomic magnetic moments is zero, hence the material is zero magnetized as shown in (a).
When an external magnetic field H1 is applied along the positive direction of the horizontal axis, the magnetic moment M of the upper domain makes an angle θ < 90° with the external magnetic field and is more stable due to lower static magnetic energy. The magnetic moment M of the lower domain makes an angle θ > 90° with the external magnetic field and is less stable due to higher static magnetic energy. So under the external magnetic field H1 the upper domain expands and the lower domain shrinks and the 180° domain wall as shown in (b) moves in the direction of the arrow and the magnetization increases along the magnetic field direction. The movement of the 180° domain wall can be very fast and the M~H magnetization curve segment ab becomes very steep.
When the external magnetic field reaches HR as shown in (c) the domain wall movement is complete and the 180° domain wall is expelled from the magnet. The whole magnet becomes a single domain and the atomic magnetic moments are in the original direction of the upper domain’s magnetic moments as shown in (c). The process from (a) to (c) is the technical magnetization process which is the domain wall movement.
As the external magnetic field increases from HR to HS from (c) to (d) the atomic magnetic moments gradually rotate to align with the external magnetic field direction as shown in (d). When the external magnetic field reaches HS the atomic magnetic moments are mostly aligned with the external magnetic field direction and the magnet is in technical magnetization saturation. The magnetization at this point is called saturation magnetization. The technical magnetization process is a combination of domain wall movement and magnetic moment rotation.
If the external magnetic field is zero the atomic magnetic moments will gradually move to the direction of the long axis as shown in (e). This is magnetic moment rotation. It can be seen that after the external magnetic field is removed the magnetization does not go to zero. In the positive direction of the magnetic field a remanent magnetization Mr remains which is called residual magnetization.
Conclusion
Magnetic domains are the key to understanding ferromagnetic materials. From the formation of these domains to the process of magnetization magnetic domains are at the core of magnetism. Their study helps us to know how magnets work and also plays a major role in the development of technologies that rely on magnetic materials.
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