IntRoduction to solid state physics

Second Semester Lecture Course

Sheng Yun Wu

Week 6: Magnetism in Solids (Continued)

Lecture Topics:

Ferromagnetism (Continued)
- Magnetic domains and domain wall motion:
  - Recap of magnetic domains: Small regions within ferromagnetic materials where magnetic moments are aligned.
  - Domain wall: The boundary between adjacent magnetic domains where the direction of magnetization changes.
  - Domain wall motion: When an external magnetic field is applied, domain walls shift, causing certain domains to grow at the expense of others, leading to changes in overall magnetization.
- Magnetic anisotropy:
  - Definition: The dependence of a material’s magnetic properties on the direction of magnetization.
  - Types of anisotropy:
    - Crystalline anisotropy: Anisotropy that arises due to the crystal structure, favoring specific magnetization directions.
    - Shape anisotropy: Anisotropy resulting from the shape of a material, especially in small particles or thin films.
  - Importance of anisotropy: Controls the ease of magnetization and affects coercivity and remanence in hysteresis loops.
Antiferromagnetism
- Definition: A type of magnetism where adjacent magnetic moments align in opposite directions, resulting in no net magnetization.
- Neel temperature:
  - The temperature below which antiferromagnetic order exists.
  - Above the Neel temperature, the material behaves as a paramagnet.
- Exchange interactions in antiferromagnetism:
  - Strong interactions between neighboring magnetic moments result in an alternating spin pattern.
- Examples of antiferromagnetic materials: Manganese oxide (MnO), iron oxide (FeO).
- Magnetic susceptibility: Below the Neel temperature, antiferromagnetic materials exhibit a characteristic susceptibility behavior distinct from paramagnets.
Ferrimagnetism
- Definition: Similar to antiferromagnetism, but with unequal magnetic moments in opposing directions, resulting in a net magnetization.
- Structure: Ferrimagnetic materials often have a complex crystal structure with multiple sublattices of magnetic ions.
- Curie temperature:
  - The temperature above which ferrimagnetic order is lost, and the material becomes paramagnetic.
- Applications of ferrimagnets:
  - Ferrites (a class of ferrimagnetic materials) are widely used in magnetic cores for inductors, transformers, and antennas due to their low electrical conductivity and high magnetic permeability.
Magnetic Hysteresis and Applications
- Magnetic hysteresis (revisited):
  - Recap of hysteresis: Ferromagnetic and ferrimagnetic materials exhibit a loop when subjected to a cyclic magnetic field.
  - Coercivity and remanence: Key properties that determine the material’s magnetic performance in practical applications.
- Soft and hard magnetic materials:
  - Soft magnetic materials: Have low coercivity and are easy to magnetize and demagnetize. They are used in transformers, inductors, and electromagnets.
  - Hard magnetic materials: Have high coercivity and retain their magnetization, making them suitable for permanent magnets and data storage.
- Applications of hysteresis:
  - Magnetic storage: Data is stored in hard disk drives by magnetizing tiny regions of a material. The hysteresis loop allows data to be written and retained.
  - Transformers and inductors: Soft magnetic materials are used to enhance magnetic flux and reduce energy losses.
Magnetic Domains and Microstructure
- Domain theory:
  - Explanation of why ferromagnetic materials spontaneously form domains to minimize internal energy.
  - Domain wall types:
    - Bloch wall: A domain wall where the magnetization rotates gradually through the thickness of the wall.
    - Neel wall: A domain wall where the magnetization rotates within the plane of the material.
- Magnetostriction:
  - The change in dimensions of a material in response to a change in magnetization.
  - Applications in magnetostrictive sensors and actuators.
- Magnetic microstructure:
  - How grain size, crystallographic orientation, and impurities influence the formation of domains and domain walls.
  - Influence of microstructure on the magnetic performance of materials.
Magnetic Materials in Technology
- Soft magnetic materials:
  - Materials with low coercivity and high permeability, used in applications requiring rapid magnetization changes.
  - Examples: Silicon steel (used in transformers), ferrites (used in high-frequency inductors and antennas).
- Hard magnetic materials:
  - Materials with high coercivity and strong remanence, used in permanent magnets and data storage.
  - Examples: Alnico, NdFeB (neodymium magnets), and SmCo (samarium-cobalt magnets).
- Magnetic data storage:
  - Hard disk drives: Use magnetic materials to store binary data as magnetized regions on a disk.
  - Magnetic random-access memory (MRAM): A type of non-volatile memory that uses magnetic tunneling junctions to store data.

Examples:

Calculation of the magnetic moment and susceptibility of an antiferromagnetic material below and above its Neel temperature.
Design of a transformer core using soft magnetic materials, with consideration of its hysteresis properties.
Plotting a hysteresis loop for a hard magnetic material and calculating the coercivity and remanence values.
Explanation of the role of anisotropy in controlling the magnetic behavior of ferromagnetic materials and its impact on technological applications.

Homework/Exercises:

Describe the differences between antiferromagnetic and ferrimagnetic materials in terms of their atomic arrangements and magnetic behavior.
Calculate the Neel temperature for an antiferromagnetic material and explain how its susceptibility changes with temperature.
Compare soft and hard magnetic materials in terms of their coercivity and applications, and explain why one is used in transformers and the other in permanent magnets.
Explain the concept of magnetic anisotropy and how it affects the behavior of a ferromagnetic material in an external field.