Phase Diagram of Vortices in Superfluid ³He-A

We have made numerical calculations of the vortex structures in rotating superfluid ³He-A. We find six different types of periodic vortex structures, out of which five are shown here. The relative stability of the different vortices depends on the rotation velocity and the magnetic field, as shown in the phase diagram at middle left in the figure. The five vortex structures are illustrated by drawing the orbital (l, red) and spin (d, blue) anisotropy vectors in the x-y plane, perpendicular to the rotation axis z. The yellow shading denotes regions where the vorticity is concentrated, whereas the blue shading denotes regions without vorticity. Similar to vortices in superfluid ⁴He, the continuous unlocked vortex and the singular vortex have a line structure. The vortex sheet and the locked vortex 3 are 2-dimensional objects. In the locked vortex 1 the vorticity is nonzero everywhere. NMR experiments have identified four of the structures: the difference between the locked vortices has still escaped experimental observation. The measured phase diagram is in semiquantitative agreement with theoretical calculations.

The vortices are created in a rotating container when the critical velocity is exceeded.

There are also several types of vortices in the B phase.

Publications

• Ü. Parts, J.M. Karimäki, J.H. Koivuniemi, M. Krusius, V.M.H. Ruutu, E.V. Thuneberg, and G.E. Volovik: Phase diagram of vortices in superfluid ³He-A, Phys. Rev. Lett. 75, 3320 (1995).
• E.V. Thuneberg and J.M. Karimäki: Structure of continuous vortices in superfluid ³He-A, Physica B 194-196, 777 (1994).
• J.M. Karimäki and E.V. Thuneberg: Periodic vortex structures in superfluid ³He-A, Phys. Rev. B 60, 15290 (1999), cond-mat 9902207.
• O.V. Lounasmaa and E. Thuneberg: Vortices in rotating superfluid ³He, Proc. Natl. Acad. Sci. USA 96, 7760 (1999).

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