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(a) Schematic showing our SET channel separated by dielectric from the ferromagnetic (Ga,Mn)As back-gate. The SET comprises Al leads and island, and tunnel barriers. (b) Coulomb oscillations for the SET on ()As for two different polar angles of the magnetization. (c) Magneto-Coulomb oscillations shown by the same SET by varying the angle of magnetization for two different gate voltages. Measurements were performed using a low frequency lock-in technique with excitation voltage 20 and zero dc bias. (d) Magnetization vector with respect to (Ga,Mn)As crystal axes. (e), Schematic explaining the spin gating phenomenon: reorientation of the magnetization from to causes a change in the chemical potential of the (Ga,Mn)As back-gate (BG). This causes charge to flow onto the back-gate from the reservoir (Res.). The net effect is to alter the charge on the back-gate and therefore the SET conductance. We show a decrease in hole chemical potential between and . The externally applied electrochemical potential on the gate is held constant.
(a) SET conductance measurements for azimuthal angle as a function of the out-of-plane polar angles of the ()As magnetization and of the gate voltage. The magnetization is rotated by a 1 T magnetic field. The two lines represent the gate voltage offsets for the data shown inFig. 1(c). (b) ()As hole chemical potential shift () for the out-of-plane magnetization rotation, inferred from measurements in (a). (c) ()As hole chemical potential shift () for the in-plane magnetization rotation.
(a) Experimental values for cubic and uniaxial contributions to the anisotropy, measured for different saturation fields, for the ()As gate material. (b) Theoretical variations of the chemical potential withrespect to the magnetization angle for fixed Mn moment density (corresponding approximately to the measured sample with 3% nominal doping) and compressive growth strain %. The hole density and for curves a, b, andc, respectively. (c) Theoretical chemical potential anisotropies for (corresponding approximately to the measured sample with 6% nominal doping) and charge density . The curve a is for the strain % while curve b is for %.
(a) The chemical potential shift determined for out-of-plane and in plane easy axis sweeps of the magnetic field for the ()As gate material. We refer the chemical potential to its zero field value. (b) The chemical potential shifts for a high field out of plane sweep for ()As and also for a control sample with an Au gate.
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