Stoner Wohlfarth Model_lecture 9 #undergraduate and graduate students

Summary

This lecture covers the Standard Version model of ferromagnetism, focusing on its application in understanding hysteresis in nanoscale materials. Introduced by Stoner and Wohlfarth in 1948, the model describes the magnetic properties of single-domain ferromagnetic nanoparticles, with an emphasis on anisotropy. It explores how the angle between the magnetic field and the easy axis affects hysteresis behavior. Although the model assumes non-interacting particles and lacks interaction considerations, it remains highly useful for simulations in fields like magnetic storage and rock magnetism, with some suggested modifications to account for nanoparticle interactions.

Takeaways

• 😀 The Stoner-Wohlfarth model is used to describe the magnetic properties of small nanoparticles, particularly single-domain ferromagnets.
• 😀 This model was first introduced by Stoner and Wohlfarth in 1948 and remains useful for understanding hysteresis in nanoscale materials.
• 😀 The model focuses on how anisotropy in the material affects magnetic behavior, especially in terms of the angle between the magnetic field and the easy axis of a nanoparticle.
• 😀 The energy function of the system includes terms related to anisotropy constant and interaction with the applied magnetic field.
• 😀 The angle between the applied magnetic field and the easy axis is crucial in determining the stability of the magnetization in the material.
• 😀 The Stoner-Wohlfarth model predicts the occurrence of hysteresis loops, with the characteristics depending on the angle between the field and the easy axis.
• 😀 The model simplifies the behavior of fine, non-interacting particles, assuming they are sufficiently separated from each other.
• 😀 Key parameters like saturation magnetization, the magnetic moment, and the volume of the particle are involved in the model’s energy calculations.
• 😀 The anisotropy field, calculated as K/Ms, plays a significant role in determining the system's response to external fields.
• 😀 The model's practical applications include simulating magnetic behavior in systems such as data storage and rock magnetism, where small magnetic particles are used.
• 😀 A limitation of the Stoner-Wohlfarth model is that it does not account for interactions between the nanoparticles, which can be important in practical systems.

Q & A

What is the Stoner-Wohlfarth Model?

The Stoner-Wohlfarth model is a simple and widely used model to describe the magnetic properties of single-domain ferromagnetic nanoparticles, particularly for understanding hysteresis behavior in such materials.

Who first described the Stoner-Wohlfarth model?

The Stoner-Wohlfarth model was first described by External Word for in 1948.

What are the main assumptions of the Stoner-Wohlfarth model?

The main assumptions of the model are that the material consists of small, non-interacting particles that are sufficiently separated from each other.

What is the importance of the Stoner-Wohlfarth model in nanomagnetism?

The model is important in nanomagnetism as it provides a simple yet effective method for analyzing the magnetic hysteresis of single-domain ferromagnetic nanoparticles and is used in practical applications like magnetic storage and rock magnetism.

What does the total energy of the system in the Stoner-Wohlfarth model depend on?

The total energy of the system depends on the anisotropy of the material and the interaction between the magnetic moment and the applied magnetic field.

How does the model calculate the stable direction of magnetization?

The stable direction of magnetization is found by minimizing the energy function, which involves taking the first derivative of the energy equation, setting it to zero, and checking the second derivative to determine stability.

What is the anisotropic field in the Stoner-Wohlfarth model?

The anisotropic field is the field at which the magnetization becomes unstable, calculated as H_k = K1 / M_s, where K1 is the anisotropy constant and M_s is the saturation magnetization.

How does the angle between the magnetic field and the easy axis affect the hysteresis curve?

The hysteresis curve is strongly influenced by the angle between the magnetic field and the easy axis. When the field is parallel to the easy axis (θ = 0°), the magnetization stays aligned until it becomes unstable. When the field is perpendicular (θ = 90°), the magnetization quickly reverses direction.

What are the main limitations of the Stoner-Wohlfarth model?

The main limitation of the Stoner-Wohlfarth model is that it does not account for interactions between nanoparticles, which can be important in real-world systems. However, some modifications have been suggested to address this issue.

How is the Stoner-Wohlfarth model applied in real-world systems?

The model is used for simulating systems with randomly oriented nanoparticles and for calculating important properties like the effective anisotropy constant, coercivity, and magnetization response. It is applied in areas like magnetic storage, rock magnetism, and nanoparticle-based sensors.