Frustrated diamond lattice antiferromagnet

We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on a diamond lattice with first- and second-neighbor interactions. Using series expansions at $T=0$, we find an apparent second-order transition from collinear N\'eel order to an incommensurate spiral with wave vector $(k,k,0)$ at ${J}₂/{J}₁\ensuremath{\sim}0.18$, considerably higher than the classical value $\frac{1}{8}$. We extend the calculation to the case of tetragonal distortion, as occurs in the material ${\mathrm{CuRh}}₂{\mathrm{O}}₄$. Here we find a clear second-order transition from N\'eel order to a $(0,0,k)$ spiral.