Tunable interlayer exchange coupling energy by modification of Schottky barrier potentials

We theoretically demonstrate that the interlayer exchange coupling (IEC) energy can be manipulated by means of an external bias voltage in a F1/NM/F2/S (F1: ferromagnetic, NM: nonmagnetic metallic, F2: ferromagnetic, S: semiconductor layers) four-layer system. It is well known that the IEC energy between two ferromagnetic layers separated by nanometer thick nonmagnetic layer depends on the spin-dependent electron reflectivities at the interface in F1/NM/F2 trilayer system. We apply such dependence to the F1/NM/F2/S four-layer system, where the reflectivity of NM/F2 interface also depends on F2/S interface due to the multiple reflection of an electron like optics. Finally, the IEC energy depends on the spin-dependent electron reflectivity not only at the interfaces of F1/NM/F2, but also at the interface of F2/S. Naturally the Schottky barrier is formed at the interface between metallic ferromagnetic layer and semiconductor, the Schottky barrier height and thickness can be tailored by an external bias voltage, which causes the change of the spin-dependent reflectivity at F2/S interface. We show that the IEC energy between two ferromagnetic layers can be controlled by an external bias voltage due to the electron-optics nature using a simple free-electron-like one-dimensional model.