The spontaneous magnetization of a quantum point contact ͑QPC͒ formed between two large quantum dots by a lateral confinement of a high-mobility two-dimensional electron gas is studied for a realistic GaAs/Al x Ga 1Ϫx As heterostructure. The model of the device incorporates the contributions from a patterned gate, doping, surface states, and mirror charges. To explore the magnetic properties, the Kohn-Sham local spin-density formalism is used with exchange and correlation potentials that allows for local spin polarization. Exchange is the dominant mechanism behind local magnetization within the QPC, while the correlation part is less prominent. However, the correlation potential gives rise to an important correction in the QPC potential. Below the first conduction plateau we thus find a magnetized regime corresponding approximately to a single electron spin. Using an approximate separable saddle potential we compute the conductance and recover the so-called ϳ0.7 (2e 2 /h) conduction anomaly plus an additional anomaly at ϳ0.4 (2e 2 /h) below which the magnetization collapses.

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We consider a two-dimensional ͑2D͒electron gas residing on the surface of a cylinder of a given radius R in the presence of a parabolic confinement along the axis of the cylinder. In this way the system of electrons forms a closed cylindrical stripe ͑wire͒. Using the local spin-density technique we first consider localization of electrons within of a potential barrier embedded in the wire. Barriers with sharp retangularlike features are populated in steps because of Coulomb blockade. The nature of a single bound state in a short soft barrier ͑quantum point contacts͒ at pinch-off is discussed in terms Coulomb blockade. For a shallow barrier-free wire we retrace the structural transitions at low electron densities from a single chain of localized states to double and triple chains ͑Wigner spin lattices͒. The present system is related to the model of a inhomogeneous quantum wire introduced recently by Güçlü et al. ͓Phys. Rev. B 80, 201302͑R͒ ͑2009͔͒. An important aspect is, however, the present extension into higher electron densities as well as to the low-density regime and the formation of 2D Wigner microlattices.

Electron states and local magnetization in quantum point contacts (QPCs) with different geometries and applied gate voltages are examined for a model GaAs/AlGaAs device. Using the local spin density approximation (LSDA) we recover ferromagnetic spatially split solutions in the pinch-off regime as well as antisymmetric solutions that occur with decreasing gate voltage. These kinds of spin states, which may appear in a repeated fashion in the few-electron regime, are precursors to an extended ferromagnetic state that may be associated with the 0.7 conductance anomaly. We briefly comment on some recent experiments indicating the presence of bound states (Yoon et al 2007 Phys. Rev. Lett. 99 136805). We have not found any indication of such states but suggest that the accumulations of spin and charge at the two ends of a QPC and associated singlet and triplet states are relevant in this context.