hysteresecurve

A hysteresecurve, commonly called a hysteresis curve or hysteresis loop, is a graphical representation of the relationship between an output and an input in a system that exhibits hysteresis. In such systems the current state depends on the history of the input, so cycling the input traces a loop rather than a single-valued line.

In magnetism, the curve often plots magnetization (M) against the applied magnetic field (H). As H increases, M grows toward saturation; when H is reduced and reversed, M follows a different path, forming a closed loop. Key features include saturation magnetization, remanent magnetization (the residual M at zero applied field), and coercivity (the field required to bring M to zero). The area inside the loop represents energy lost as heat per cycle, arising from processes such as domain-wall pinning and domain rotation.

Hysteresis curves also appear in other domains, such as mechanics, where stress versus strain forms a loop during loading and unloading in viscoelastic or plastic materials; and in ferroelectric or piezoelectric materials, where polarization versus electric field yields a loop. The shape and size of the loop reveal material properties, rate of cycling, and energy dissipation.

Applications include characterizing magnetic materials for transformers and recording media, evaluating mechanical damping, and informing the design of memory elements. Mathematical models, such as the Preisach model and the Jiles–Atherton model, are used to describe and predict hysteresis behavior in complex systems.