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The Stoner–Wohlfarth model is a physical model explaining hysteresis in terms of anisotropic response ("easy" / "hard" axes of each crystalline grain). Micromagnetics simulations attempt to capture and explain in detail the space and time aspects of interacting magnetic domains, often based on the Landau-Lifshitz-Gilbert equation .
This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material. [2] Jiles–Atherton model enables calculation of minor and major hysteresis loops. [1] The original Jiles–Atherton model is suitable only for isotropic materials. [1]
Usually only the hysteresis loop is plotted; the energy maxima are only of interest if the effect of thermal fluctuations is calculated. [1] The Stoner–Wohlfarth model is a classic example of magnetic hysteresis. The loop is symmetric (by a 180 ° rotation) about the origin and jumps occur at h = ± h s, where h s is known as the switching field.
Calculated magnetization curve for a superconducting slab, based on Bean's model. The superconducting slab is initially at H = 0. Increasing H to critical field H* causes the blue curve; dropping H back to 0 and reversing direction to increase it to -H* causes the green curve; dropping H back to 0 again and increase H to H* causes the orange curve.
Hysteresis can be a dynamic lag between an input and an output that disappears if the input is varied more slowly; this is known as rate-dependent hysteresis. However, phenomena such as the magnetic hysteresis loops are mainly rate-independent, which makes a durable memory possible.
In electromagnetism, the Preisach model of hysteresis is a model of magnetic hysteresis. Originally, it generalized hysteresis as the relationship between the magnetic field and magnetization of a magnetic material as the parallel connection of independent relay hysterons .
Typically the coercivity of a magnetic material is determined by measurement of the magnetic hysteresis loop, also called the magnetization curve, as illustrated in the figure above. The apparatus used to acquire the data is typically a vibrating-sample or alternating-gradient magnetometer. The applied field where the data line crosses zero is ...
Figure 1: The ideal magnetic hysteresis loop of an exchange spring magnet (dashed), as well as the hysteresis loops of its isolated hard (Blue) and soft (Red) components. H is the applied external magnetic field, M is the total magnetic flux density of the material.