Why can an unmagnetized piece of iron still contain magnetic domains?

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An unmagnetized piece of iron still contains magnetic domains because its internal structure is composed of many small regions, known as ferromagnetic domains, where the atomic magnetic moments are already aligned to saturation.12

The reason the iron appears unmagnetized as a whole is that the directions of these individual domain magnetizations are distributed at random. Because these domains are oriented in various, opposing directions, their individual magnetic fields cancel each other out, resulting in a net magnetization of zero for the entire object.132

When an external magnetic field is applied, these domains can rotate or grow to align with the field, which is how the material becomes magnetized. In the absence of such a field, however, the random orientation of the domains persists, maintaining the material's unmagnetized state.123