# Why do naturally occurring ferromagnetic materials contain a large number of domains?

Why do naturally occurring ferromagnetic materials (e.g. a piece of iron) contain a large number of domains rather than a single domain, and hence, carry no net magnetization? So the question is basically why do domains form.

Besides exchange interaction, you probably know that a magnetic moment, say $\vec m_1$ at the point $\vec r_1$, creates a magnetic field $$\vec B(\vec r_2)={\mu_0\over 4\pi}\left[{(\vec m_1.\vec r_{12})\vec r_{12}\over r_{12}^5}-{\vec m_1\over r_{12}^3}\right]$$ so that a second magnetic moment $\vec m_2$ at $\vec r_2$ feels a torque associated to the potential energy $-\vec m_2.\vec B(\vec r_2)$. This is the so-called dipolar interaction. It tends to align two magnetic moments in the opposite direction. It is weaker than the exchange interaction but falls as the third power of the distance. This dipolar interaction stabilizes magnetic configurations with magnetic domains in different orientations.