Vortex Formation and Annihilation in Three Textures of Rotating Superfluid ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$-$A$

Textures, textural transformation, and formation and annihilation of a single vortex were investigated in narrow cylinders with $100\mu \mathrm{m}$ radius in $A$-phase under rotation up to $6.28\mathrm{r}\mathrm{a}\mathrm{d}/\sec $. Three textures were found, depending on the cooling conditions of the sample through the superfluid transition temperature $T_{\mathrm{c}}$. We found the gyromagnetic effect of textures; that is, two textures ($A$ or $B$) could be selected either by applying a magnetic field in parallel or anti-parallel to the rotation axis. The critical angular speed of a single vortex formation ${\Omega }_{\mathrm{f}}$ and that of annihilation ${\Omega }_{\mathrm{a}}$ for each texture were measured. The textural transformation in type $A$ texture was induced by rotation. Both type $A$ and $B$ textures held macroscopic angular momentum along the rotation axis. We identified the texture for type $A$, $B$, and $C$ as Mermin-Ho, radial disgyration, and a soliton type of defect along the axis, respectively.

Figure 1

NMR absorption spectra for $\Omega =0$ at $T/T_{\mathrm{c}}=0.75$ as a function of frequency shift from the Larmor frequency. Spectra for three textures, labeled by a dotted line for $A$, a dashed line for $B$, and a solid line for $C$ are shown. Textures were controlled by the condition of cooling through $T_{\mathrm{c}}$.

Figure 2

NMR absorption spectra for type $A$ at $T/T_{\mathrm{c}}=0.75$ as a function of frequency shift from Larmor frequency with increasing rotation speeds, $\Omega =0,4.0,4.8$, and $6.28\mathrm{r}\mathrm{a}\mathrm{d}/\sec $. The spin wave peak for a vortex was observed at $R_{\mathrm{t}}^2=0.31$.

Figure 3

NMR absorption of the main peak at $R_{\mathrm{t}}^2=1.0$ as a function of rotation speed $\Omega$ during acceleration and deceleration cycle. The conditions of cooling the sample though $T_{\mathrm{c}}$ are: (a) ($+2\mathrm{r}\mathrm{a}\mathrm{d}/\sec $, $-22\mathrm{m}\mathrm{T}$), (b) ($+2\mathrm{r}\mathrm{a}\mathrm{d}/\sec $, $+22\mathrm{m}\mathrm{T}$), (c) ($-2\mathrm{r}\mathrm{a}\mathrm{d}/\sec $, $+22\mathrm{m}\mathrm{T}$), (d) ($-2\mathrm{r}\mathrm{a}\mathrm{d}/\sec $, $-22\mathrm{m}\mathrm{T}$). The spectra (a) and (c) correspond to type $A$ texture and (b) and (d) to type $B$. Thin arrows indicate the direction of taking data and vertical lines are ${\Omega }_{\mathrm{f}}$ and ${\Omega }_{\mathrm{a}}$ for type $A$.

Figure 4

The critical speed for vortex formation ${\Omega }_{\mathrm{f}}$ shown by solid circles and annihilation ${\Omega }_{\mathrm{a}}$ shown by open circles as a function of temperature for type $A$ texture.