Helical spin texture in a thin film of superfluid ${}^3\mathrm{He}$

We consider a thin film of superfluid ${}^3\mathrm{He}$ under conditions that stabilize the $A$ phase. We show that in the presence of a uniform superflow and an external magnetic field perpendicular to the film, the spin degrees of freedom develop a nonuniform, helical texture. Our prediction is robust and relies solely on Galilei invariance and other symmetries of ${}^3\mathrm{He}$, which induce a coupling of the orbital and spin degrees of freedom. The length scale of the helical order can be tuned by varying the velocity of the superflow and the magnetic field and may be in reach of near-future experiments.

Figure 1

Helical spin texture in a film of ${}^3\mathrm{He}$ $A$. The orbital vector $\widehat{\mathit{l}}$ is forced by surface interactions to be perpendicular to the film. The magnetic field $\mathit{H}$ is chosen to point in the same direction. The local, in-plane spin vector $\widehat{\mathit{d}}$ varies along the superflow velocity $\mathit{u}$ but remains uniform in the transverse direction.