The Magnetism of Small Particles

Summary

This video explores the magnetism of small particles, focusing on three key aspects: the single domain behavior of small particles, the effects of this on hysteresis, and the phenomenon of superparamagnetism. It explains how particles below a certain size have only one domain, resulting in distinct magnetic properties and hysteresis. The video also delves into how thermal effects lead to the loss of coercivity in particles that are small enough to enter the superparamagnetic state, where the magnetization fluctuates due to thermal energy, resembling the behavior of paramagnets.

Takeaways

• 😀 A small magnetic particle can be a single domain when its size is below a critical threshold, meaning it has no domain walls.
• 😀 The size of the particle directly affects its magnetic properties, with smaller particles favoring a single-domain configuration due to energy considerations.
• 😀 Domain walls have an energy associated with their formation, balancing exchange energy (which favors wide walls) and magneto-crystalline anisotropy energy (which favors narrow walls).
• 😀 For ferromagnetic materials like iron, the domain wall width is typically around 100 nanometers, leading to a critical size above which domain walls cannot form.
• 😀 The magnetostatic energy in a particle increases with the cube of the radius, while the domain wall energy increases with the square of the radius.
• 😀 There is a critical particle size where the energy configuration shifts from multi-domain to single-domain. Below this size, single-domain particles are more stable.
• 😀 Hysteresis in small single-domain particles, especially elongated ones, is influenced by shape anisotropy, with magnetization naturally lying along the long axis (easy axis).
• 😀 The reversal of magnetization in small particles involves rotation through the hard axis, which requires overcoming significant anisotropy energy.
• 😀 A small particle’s hysteresis loop is characterized by a large coercive field, and magnetization switches abruptly once this field is reached.
• 😀 In very small particles, superparamagnetism occurs when thermal energy is sufficient to spontaneously flip the magnetization, causing the coercivity to drop to zero.

Q & A

What happens to a magnetic particle when it is smaller than a certain size?

When a magnetic particle is below a certain size, it contains only one domain, meaning there are no domain walls present.

How does the absence of domain walls in small magnetic particles affect their magnetic response?

The absence of domain walls leads to a unique hysteresis behavior. Since there are no domain walls to move, the magnetization can only be reversed by rotating the magnetization direction through the hard axis.

What is the significance of the competition between exchange energy and magneto-crystalline anisotropy in determining the domain wall width?

The exchange energy prefers a wide domain wall, as it favors neighboring magnetic moments to be parallel, while the magneto-crystalline anisotropy energy prefers a narrow domain wall by aligning spins along a crystallographic direction. The balance between these two forces determines the typical width of the domain wall.

Why does a small particle not form a domain wall if it is smaller than a certain size?

If the particle is smaller than a certain size (around 100 nm), the domain wall cannot fit within the particle, so it remains a single domain.

What factors influence the crossover point where a particle becomes single domain?

The crossover point occurs when the energy contributions of magnetostatic energy and domain wall energy balance. Magnetostatic energy depends on the particle's volume (r³), while domain wall energy depends on the particle's surface area (r²). The crossover happens at a critical particle radius.

How does the shape anisotropy of an elongated particle affect its magnetization?

In elongated particles, the magnetization tends to align along the long axis (the easy axis) because this configuration minimizes the magnetostatic energy. Magnetization along the short axis (the hard axis) leads to higher magnetostatic energy.

What is the mechanism of magnetization reversal in a single domain particle?

In a single domain particle, magnetization reversal occurs through the rotation of the magnetization vector, which must pass through the hard axis before reorienting to the opposite direction. This process is energetically costly due to the anisotropy energy.

What does the hysteresis loop of a small single domain particle look like?

The hysteresis loop of a small single domain particle is typically square-shaped, with a large coercive field and a large magnetization. The particle resists rotating its magnetization along the hard axis, leading to a sharp switch in magnetization at a high coercive field.

How does the coercive field change with particle size?

For small particles, the coercive field is large because the particles are single domain. As the particle size increases and the particles become multi-domain, the coercive field decreases. In extremely small particles, the coercive field drops to zero, leading to superparamagnetism.

What is superparamagnetism and why does it occur in very small particles?

Superparamagnetism occurs in very small particles where the thermal energy is sufficient to randomly flip the magnetization direction, even without an external magnetic field. This happens when the anisotropy energy becomes comparable to thermal energy, leading to spontaneous magnetization reversal.