We find a novel topological defect in a spin-nematic superfluid theoretically. A quantized vortex spontaneously breaks its axisymmetry, leading to an elliptic vortex in nematic-spin Bose-Einstein condensates with small positive quadratic Zeeman effect. The new vortex is considered the Joukowski transform of a conventional vortex. Its oblateness grows when the Zeeman length exceeds the spin healing length. This structure is sustained by balancing the hydrodynamic potential and the elasticity of a soliton connecting two spin spots, which are observable by in situ magnetization imaging. The theoretical analysis clearly defines the difference between half quantum vortices of the polar and antiferromagnetic phases in spin-1 condensates.
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