# Nematic Bond Theory of Heisenberg Helimagnets

## TL;DR

This paper introduces a new theoretical framework for understanding spin-nematic transitions in frustrated Heisenberg models, highlighting the role of fluctuations and the sensitivity of critical temperatures to magnetic wavevectors.

## Contribution

It develops a self-consistent theory for spin-nematic order in incommensurate Heisenberg models, emphasizing the impact of fluctuations and Lifshitz points on phase transitions.

## Key findings

- Critical temperature depends on helimagnetic wavevector.
- Nematic order vanishes at Lifshitz points.
- Multiple nematic phases can coexist or transition by tuning parameters.

## Abstract

We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-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 wavevector, 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 bicritical points.