hysteresisloop

A hysteresis loop is a graphical representation of a system that exhibits hysteresis, meaning the output depends on the history of the input and does not respond instantly to changes. It is commonly plotted as a response variable versus the controlling stimulus, such as magnetization versus applied magnetic field, polarization versus electric field, or stress versus strain, typically forming a closed loop when the input is cycled.

In magnetic materials, the loop shows how magnetization M changes with an applied field H as H is increased and then decreased. The loop arises from the behavior of magnetic domains and domain walls, which respond to H with irreversible and reversible processes. Key features are the coercive field Hc, where M crosses zero, the remanent magnetization Mr, the residual magnetization when H is removed, and the saturation magnetization Ms, where further increases in H produce little change in M. The area of the loop represents energy loss per cycle, known as hysteresis loss. Soft magnetic materials have narrow loops (low Hc and small Mr) suitable for transformers, while hard magnetic materials have wide loops (high Hc and large Mr) useful for permanent magnets.

Hysteresis loops also occur in other systems, including piezoelectric or ferroelectric materials (P versus E loops) and mechanical systems (stress–strain loops). They provide insight into memory effects, nonlinearities, and dissipation, and are used to characterize material properties, design magnetic circuits, and assess energy losses. Factors such as sweep rate, temperature, and frequency can influence loop shape and size.