We study effects of spin-orbit coupling and electron-electron correlation, which can be electrically tuned, on the singlet-triplet entanglement in double lateral quantum dots charged with two electrons. We have found that the magnetic character of a double-dot system can be changed from diamagnetic to paramagnetic, only by adjusting the strength of spin-orbit coupling. Coulomb interaction leads to an unusual singlet-triplet energy splitting, accompanied by a shift of this transition energy to the lower magnetic field side in the energy spectrum.

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