Why does dipole-dipole interaction not lead to ferromagnetic ordering? Why does the magnetic dipole-dipole interaction between the magnetic moments of the atoms in a ferromagnetic material such as iron not lead to ferromagnetism?
 A: The magnetic dipole dipole interaction is just by far too weak. In Stephen Blundell: "Magnetism in Condensed Matter" this is estimated to be on an energy scale of about $10^{-23}$J which may play a role at temperatures of about 1K or so. But when we are talking about magnetism we typically talk about much higher temperatures.
In detail the energy due to this interaction is
$E=\frac{\mu_0}{4\pi r^3} \left[ \boldsymbol{\mu}_1 \cdot\boldsymbol{\mu}_2 - \frac{3}{r^2}(\boldsymbol{\mu}_1\cdot \textbf{r})(\boldsymbol{\mu}_2\cdot \textbf{r}) \right]$
where $\boldsymbol{\mu}_i$ are the magnetic moments and $\textbf{r}$ is the separation vector. Assuming the magnetic moments to be on the order of $1 \mu_\text{B}$ and the separation to be on the order of 1 Angstrom one obtains the mentioned energy scale.
A: Ferromagnetism requires parallel alignment of magnetic moments. However, the dipole -dipole interaction $$E(r)=\frac{\mu_0}{4\pi r^3}[\boldsymbol{\mu}_1\cdot\boldsymbol{\mu}_2-\frac{3(\boldsymbol{\mu}_1\cdot \textbf{r})(\boldsymbol{\mu}_2\cdot \textbf{r})}{r^2}]$$ favours anti-parallel alignment of the dipoles because that would have lower energy compared to a parallel configuration. This rules out dipole-dipole interaction as far as the origin of ferromagnetism is concerned. However, one might think that it might lead to anti-ferromagnetism. But it's too weak to produce even anti-ferromagnetic order at room temperature.
