Figure 2

(a) There is an electric field E in the surface region of a ferromagnet, however for a given wave vector k, the Rashba field B_R, proportional to k × E, has an opposite sign at the two surfaces and the average field is zero. (b) With a finite external field this symmetry is broken and there is a net Rashba field acting upon the electrons. (c) The gate voltage dependence of the anisotropy energy. The internal electric field causes the shift of the parabola in the lateral axis as indicated by V₀ for case i). For cases ii) and iii) the internal field shift is far beyond the external field range and nearly linear E-dependence arises. (d) The symmetry is also broken for a insulator-ferromagnet-metal sandwich. Also despite the electric field being smaller at the right surface, for a suitable metal, the spin-orbit coupling is larger and hence the metal interface can still dominate the net Rashba field. (e) Here the work function is larger for the metal than for the ferromagnet and the field for that surface is reversed. Now the Rashba fields at the two surfaces add. (f), (g) Applying positive gate voltages decreases the Rashba field at the insulating surface which, for this case, causes a net increase/decrease in the average Rashba field.