${}^{52}\mathrm{Cr}$ Spinor Condensate: A Biaxial or Uniaxial Spin Nematic

We show that the newly discovered ${}^{52}\mathrm{Cr}$ Bose condensate in zero magnetic field can be a spin nematic of the following kind: a “maximum” polar state, a “colinear” 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.

Figure 1

Phase diagram in zero magnetic field for $\gamma >0$. The dashed line (referred to as the Cr line) is where the physical system lies. The solid lines are first order boundaries. The nature of the phases displayed is discussed in Fig. 3.

Figure 2

Phase diagram in zero magnetic field for $\gamma <0$. The solid and gray lines are first and second order boundaries, respectively. The nature of the phases is discussed in Fig. 3.

Figure 3

Phases present at $p=0$. $a,b,c,d$, and $\delta$ are real numbers.

Figure 4

The eigenvalues ${\lambda }_a$ of $\mathcal{N}$ and the magnetization $⟨\mathbf{S}⟩$ along the Cr line in Fig. 1.

Figure 5

Left panel: phase diagram for nonzero magnetic field along the Cr line in Fig. 1. The solid and gray lines are first and second order boundaries, respectively. Right panel: explanation of the phases in the diagram. The numbers $a,b,c,d$ are real. All entries of the wave functions for the $Z_j$ phases are generally nonzero. It is not clear they can be represented in a simple form as the other phases.