Nematic Bond Theory of Frustrated Heisenberg Magnets

We study frustrated Heisenberg models with generically incommensurate ground states. A general theory for the lattice-nematic “order by disorder” transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wave vector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of finite temperature bicritical points.