What Is Magnetic Hysteresis?

Magnetic hysteresis is the phenomenon by which a ferromagnetic material's magnetic flux density (B) depends on both the current applied field strength (H) and the history of previous magnetization. When a virgin ferromagnetic material is subjected to a cycle of increasing and then decreasing applied field, the B-H relationship traces a closed loop rather than a reversible curve; the material's flux density at any given H differs depending on whether H is increasing or decreasing. This path-dependent behavior arises from the irreversible motion of magnetic domain walls within the material: domains aligned with the applied field grow at the expense of unfavorably oriented domains, and this realignment consumes energy that is released as heat when the field is removed or reversed. The phenomenon is named after the Greek word for "deficiency," reflecting the lagging response of magnetization to the applied field.

Hysteresis is central to the design of transformers, inductors, permanent magnets, and magnetic data storage media, each exploiting or minimizing the effect depending on whether retaining or releasing magnetization is the goal.

The B-H Loop and Key Parameters

The hysteresis loop is plotted with H on the horizontal axis (in A/m) and B on the vertical axis (in tesla). Starting from a demagnetized state, as H increases, B rises along the initial magnetization curve until the material reaches saturation, the point at which all domains are aligned and further increases in H produce negligible gains in B. When H is reduced back to zero, B does not return to zero; the remaining flux density is called remanence (Br) or retentivity, representing the material's ability to sustain magnetization without an applied field. To drive B to zero, a reversed field equal in magnitude to the coercive force (Hc) must be applied. A complete cycle returns B to negative saturation and then traces the symmetric lower half of the loop back to positive saturation. The hysteresis loop explanation at the NDT Resource Center describes how the loop's shape reveals permeability, reluctance, and coercive force simultaneously from a single measurement.

Energy Losses and Material Classification

The area enclosed by the B-H loop is proportional to the energy dissipated as heat per unit volume per magnetization cycle, a quantity called the hysteresis loss. At power-line frequencies (50 to 60 Hz), hysteresis loss is a significant contributor to core loss in transformers and induction motors, alongside eddy current loss. Materials are classified by their loop shape and the resulting engineering trade-off. Soft magnetic materials, such as silicon-iron alloys, grain-oriented electrical steel, and ferrite ceramics, have narrow loops with low coercivity, typically below 10 A/m, and low remanence; they magnetize and demagnetize easily, minimizing energy loss per cycle and making them ideal for transformer cores and inductor cores operated at mains frequency. Hard magnetic materials, such as alnico, ferrite, and rare-earth alloys including NdFeB and SmCo, have wide loops with high coercivity, above 400 kA/m in advanced permanent magnet grades, and high remanence; they resist demagnetization and serve as permanent magnets. The NIST units for magnetic properties document defines the SI and CGS quantities used to characterize these materials and facilitates conversion between measurement systems.

Hysteresis in Devices and Circuits

In transformers, hysteresis loss heats the core and reduces efficiency; it is minimized by selecting low-coercivity core materials and by laminating the core to limit eddy currents. In permanent magnet motors and generators, a high coercivity ensures the rotor magnets are not demagnetized by the stator fields or thermal effects. In magnetic recording media, a precisely controlled coercivity sets the field required to write a bit while ensuring that written bits are stable against thermal fluctuations and stray fields. The electronics-tutorials overview of magnetic hysteresis explains how engineers select core materials by inspecting loop parameters to match device operating conditions.

Applications

Magnetic hysteresis has applications in a wide range of disciplines, including:

• Transformer and inductor core material selection to minimize core loss at power-line frequencies
• Permanent magnet design for motors, generators, and actuators, where high coercivity prevents demagnetization
• Magnetic recording media, where coercivity determines write threshold and data retention
• Magnetic brakes and clutches that use hysteresis torque for smooth, contact-free load control
• Nondestructive evaluation, where changes in loop shape indicate stress, fatigue, or microstructural damage