We investigate Abrikosov lattice structures in the unconventional superconductor $\mathrm{UPt}{}_3$ under magnetic field parallel to the hexagonal crystal axis. Only the two-dimensional $E_2$ superconducting state among the many other states of different symmetry is compatible with the recent observation [A. Huxley et al., Nature (London) 406, 160 (2000)] of the flux lattice in the $A$ phase misaligned with crystallographic directions. It is shown that the inequality of the London penetration depths in the basal plane directions resulting from the superposition of hexagonal crystal and superconducting state anisotropies leads for $E_2$ to a slightly distorted triangular flux lattice.

• Received 9 February 2001

DOI:https://doi.org/10.1103/PhysRevLett.86.4903