On the origin of spin nematic order in Sr$_2$IrO$_4$

Quantum spin nematics, a quantum analog of liquid crystals, can be thought of as an intermediate state between magnetically ordered, and spin-liquid phases. To date spin nematics have mostly been discussed in the context of spin-1 magnets with strong biquadratic interactions, or spin-1/2 frustrated ferromagnets in high magnetic field. Recent experiments suggest that a spin-nematic may also be found at high temperatures in the strongly spin-orbit-coupled antiferromagnet Sr$_2$IrO$_4$. However the mechanism for stabilizing this spin-nematic state remains mysterious.

In this talk we explore the conditions needed for spin-nematic order to arise in Sr$_2$IrO$_4$, using a combination of symmetry analysis and large-scale numerical simulation.