Quantum spin nematic phase in a square-lattice iridate.

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid 1,2 . Particularly intriguing is a valence-bond spin nematic 3-5 , in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr 2 IrO 4 , which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit 6-9 . Upon cooling, the transition into the spin nematic phase at T C  ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below T N  ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state 10,11 . Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity 12,13 .