Materials Science: Magnetic Properties: Magnetic Hysteresis
Magnetic hysteresis is a phenomenon crucial to understanding the behavior of magnetic materials under varying external magnetic fields. This topic is often studied within the broader field of materials science, focusing on the magnetic properties of various substances.
Overview of Magnetic Hysteresis
In simple terms, magnetic hysteresis describes how a magnetic material responds to changes in an external magnetic field (H) and involves the lag between the applied field and the resultant magnetization (M) of the material. This effect is particularly prominent in ferromagnetic materials, which include common substances like iron, nickel, and cobalt.
Hysteresis Loop Characteristics
The relationship between the magnetic field strength (H) and the magnetization (M) is typically represented by a hysteresis loop. To generate this loop, one measures the magnetization of a material while cyclically varying the applied magnetic field. The key features of a hysteresis loop include:
Saturation Magnetization (M_s): This represents the maximum magnetization a material can achieve in an external magnetic field. At this point, further increases in field strength do not increase magnetization.
Remanent Magnetization (M_r): This is the residual magnetization that remains after the external magnetic field is reduced to zero. It shows the material’s ability to retain a magnetic moment.
Coercive Field (H_c): This is the magnitude of the reverse magnetic field required to reduce the residual magnetization to zero. It is a measure of the material’s resistance to becoming demagnetized.
Mathematical Description
The phenomenon can be mathematically described using differential equations that encapsulate the non-linear behavior of the material’s response to the external magnetic field. One common approach is to employ the Preisach model, which approximates the hysteresis loop as:
\[ M(H) = \int \mathcal{P}(\alpha, \beta) \ \gamma(\alpha, \beta) \ d\alpha \ d\beta \]
where:
- \( \mathcal{P}(\alpha, \beta) \) is the Preisach density function representing the distribution of hysteretic units within the material.
- \( \gamma(\alpha, \beta) \) signifies a simple hysteresis operator.
- \( \alpha \) and \( \beta \) are switching (or threshold) values of the microscopic hysteretic units.
Practical Implications
Understanding magnetic hysteresis is not just of theoretical interest; it has profound practical implications. The concepts are essential for the design and optimization of magnetic storage devices, electrical transformers, and other electromagnetic applications. For example, materials with high coercivity are preferred in permanent magnets, while those with low coercivity are desirable in cores for transformers and inductors to minimize energy losses.
In summary, magnetic hysteresis is a fundamental property of magnetic materials that demonstrates the non-linear and history-dependent nature of magnetization. Its study is essential for both theoretical exploration and practical applications in modern technology.