Aharonov-Casher Effect in One-Dimensional Wigner Crystals

We theoretically study the effects of spin-orbit coupling on spin exchange in a low-density Wigner crystal. In addition to the familiar antiferromagnetic Heisenberg exchange, we find general anisotropic interactions in spin space if the exchange paths allowed by the crystal structure form loops in real space. In particular, it is shown that the two-electron exchange interaction can acquire ferromagnetic character. Tserkovnyak and Kindermann, Phys. Rev. Lett. 102 (2009) 126801.