Theory of electron nematic order in LaFeAsO

We study a spin S quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large S and large N methods, we show that this model exhibits a sequence of two phase transitions: from a high-temperature symmetric phase to a narrow region of intermediate ``nematic'' phase, and then to a low-temperature spin ordered phase. Identifying phases by their broken symmetries, these phases correspond precisely to the sequence of structural (tetragonal to monoclinic) and magnetic transitions that have been recently revealed in neutron-scattering studies of LaFeAsO. The structural transition can thus be identified with the existence of incipient (``fluctuating'') magnetic order.