Past exam of the condensed matter physics course of the University of Oxford / 2014 / 4 / b

A point magnetic dipole $\mathbf{\mu }$ producesFor $|\mu |\sim {\mu }_B$ and neighbour separation $r\sim 0.2\mathrm{nm}$, its characteristic magnitude isThe axial field is twice this scale; the exact orientation and crystal geometry are unspecified. The corresponding pair magnetic dipole interaction has energy scale $U_{\mathrm{dip}}\sim {\mu }_B{B}_{\mathrm{dip}}\simeq 1.08\times 10^{-24}\mathrm{J}$, givingAn axial orientation changes this to about $0.16\mathrm{K}$. A real ordering temperature depends on a lattice sum, symmetry and fluctuations, so this is a nearest-neighbour energy estimate, not a complete ordering calculation. It establishes that ordinary dipolar coupling is far too weak to explain a thousand-kelvin ferromagnetic transition.