# Hysteresis: what is it?

The hysteresis is very common on materials and systems. It’s the capacity to keep a property, after remove the stimulus that induces this property.

## Hysteresis on magnetism

The motion of electric charges produces a magnetic field. Therefore, the movement of electrons around the atom’s nucleus generates a magnetic field. I is the electric current and vector \vec{m} is magnetic dipole moment. Source: Maestrovirtuale.

Due to crystalline structure, a ferromagnetic material is divided in many magnetic domains, these are regions where atoms are oriented in a direction. When a ferromagnetic material is demagnetized, each domain points to a random direction. Source: Bóson treinamentos.

When a ferromagnetic material is submitted to a magnetic field, material’s atoms are aligned with the external magnetic field. Consequently, the material becomes magnetized, with north and south poles.

When all magnetic domains are pointed to direction of external magnetic field, the material reaches the saturation. By that, increasing magnetic flux intensity H, won’t increase flux density B. After the removal of external magnetic field, most of domains keep pointed to same direction and the material keeps magnetized. The magnetization process goes to point a, the latter is saturation point. Removing the external magnetic field, the material still has part of magnetic flux density (point b). Applying an external field in opposite direction, the material is demagnetized (point c) and the domains are pointed to opposite direction until saturation (point f). After removing the external field, material still keeps part of it (point e). Source: Electrical Academia.

Each material has a unique hysteresis loop. The equation below is the relation between magnetic field and flux density.

$B=\mu H$

Where $\mu$ is magnetic permeability, which depends on material.

## Some hysteresis examples in other areas

### Electronics

The comparator electronic circuit called Schmitt-Trigger, has the function to change the output digital signal ($V_{OUT}$) from “LOW” level to “HIGH”, when input voltage ($V_{IN}$) increases to a determined value ($V_{TH}$). If output signal is on “HIGH” level, it will go to “LOW” level, when input voltage reaches a determined value ($V_{TL}$). 