$^{52}$Cr Spinor Condensate$ -- $ A Biaxial or Uniaxial Spin Nematic

Abstract

We show that the newly discovered $^{52}$Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: A "maximum" polar state, a "co-linear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the Chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.