A pathway to design non-magnetic artificial molecules which display controllable magnetic properties is addressed theoretically by studying the effects of in-plane electrical field, spinorbit interaction (SOI) and geometrical parameters on the magnetic phase transitions in few-electron lateral double quantum dots (DQDs). We demonstrate the tunability of the magnetic phase diagram of two-electron DQDs as the system is changed from a molecule to an atom, in both weak and strong SOI regimes. We find an unusual jump in the magnetization and an asymmetric peak of the magnetic susceptibility. In addition, both the asymmetric susceptibility peak position and the magnetic phase diagram are strongly dependent on the interdot tunnel coupling, which can be tuned effectively by changing repulsive barrier voltage and/or interdot distance, the number of electrons and the SOI strength. With increasing interdot tunnel-coupling strength, for instance, the rate of paramagnetic-to-diamagnetic phase area increases. The SOI makes the paramagnetic phase more stable under magnetic field. Moreover, the effects of geometry deviation on the electronic structure and magnetic property of the DQD are also discussed.
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