Gate-tunable indirect exchange interaction in spin-orbit–coupled mesoscopic rings

We study the carrier-mediated exchange interaction, the so-called Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, between two magnetic impurity moments embedded in a semiconductor mesoscopic ring. We treat the ring in the presence of an Aharonov-Bohm–type magnetic flux and the Rashba and Dresselhaus spin-orbit interactions (RSOI and DSOI). Energy eigenvalues of the system are obtained within a tight-binding framework and the strength of the indirect exchange interaction vs. RSOI strengths are plotted for different values of DSOI strength. The results show that the type of the impurity magnetic order, ferromagnetic (F) or antiferromagnetic (AF), depends on the RSOI and DSOI strengths. This leads to a full electrical control on the magnetic alignment of the system through, e.g., an external gate voltage