We search for the uniform Hartree-Fock ground state of the two-dimensional electron gas formed in semiconductor heterostructures including the Rashba spin-orbit interaction. We identify two competing quantum phases: a ferromagnetic one with partial spin polarization in the perpendicular direction and a paramagnetic one with in-plane spin. We present a phase diagram in terms of the relative strengths of the Rashba to the Coulomb interaction and the electron density. We compare our theoretical description with existing experimental results obtained in GaAs-AlGaAs heterostructures.

We calculate the critical density of the zero-temperature, first-order ferromagnetic phase transition in n-doped GaAs/AlGaAs quantum wells. We find that the existence of the ferromagnetic transition is dependent upon the choice of well width. We demonstrate rigorously that this dependence is governed by the interplay between different components of the exchange interaction and that there exists an upper limit for the well width beyond which there is no transition. We predict that some narrow quantum wells could exhibit this transition at electron densities lower than the ones that have been considered experimentally thus far. We use a screened Hartree-Fock approximation with a polarization-dependent effective mass, which is adjusted to match the critical density predicted by Monte Carlo calculations for the two-dimensional electron gas.

A different approach in the discussion of the skin effect in a metal cylinder, is described, where the presence of eddy currents is assumed to be a consequence of an equivalent static magnetization. A low-cost, easy to build mutual inductance bridge is used to measure the equivalent magnetic susceptibility—a function of the skin depth. The use of a lock-in amplifier as a null detector clearly shows the concept of complex magnetic susceptibility. The electrical resistivity of a copper rod is measured as an application thereof. The results are shown and compared to theory achieving excellent agreement.

No abstract