  The two-electron exchange coupling in a nanowire double quantum dot (DQD) is
shown to possess Moriya's anisotropic superexchange interaction under the
influence of both the Rashba and Dresselhaus spin-orbit couplings (SOCs) and a
Zeeman field. We reveal the controllability of the anisotropic exchange
interaction via tuning the SOC and the direction of the external magnetic
field. The exchange interaction can be transformed into an isotropic Heisenberg
interaction, but the uniform magnetic field becomes an effective inhomogeneous
field whose measurable inhomogeneity reflects the SOC strength. Moreover, the
presence of the effective inhomogeneous field gives rise to an energy-level
anticrossing in the low-energy spectrum of the DQD. By fitting the analytical
expression for the energy gap to the experimental spectroscopic detections [S.
Nadj-Perge et al., Phys. Rev. Lett. 108, 166801 (2012)], we obtain the complete
features of the SOC in an InSb nanowire DQD.
