Nematic spin fluid in the tetragonal phase of BaFe$_{2}$As$_{2}$

We use inelastic neutron scattering to demonstrate the presence of a large spin anisotropy above $T_{N}$ in the unstressed tetragonal phase of BaFe$_{2}$As$_{2}$. In the low-temperature orthorhombic phase, we find highly anisotropic spin waves with a large damping along the AF $a$-axis direction. On warming the system to the paramagnetic tetragonal phase, the low-energy spin waves evolve into quasi-elastic excitations, while the anisotropic spin excitations near the zone boundary persist. These results strongly suggest that the spin nematicity we find in the tetragonal phase of BaFe$_{2}$As$_{2}$ is the source of the electronic and orbital anisotropy observed above $T_{N}$ by other probes, and has profound consequences for the physics of these materials.