Effects of exchange and electron correlation on conductance and nanomagnetism in ballistic semiconductor quantum point contacts

The spontaneous magnetization of a quantum point contact (QPC) formed between two large quantum dots by a lateral confinement of a high-mobility two-dimensional electron gas is studied for a realistic $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ 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 $\sim 0.7\hspace{0.5em}{(2e}^2/h)$ conduction anomaly plus an additional anomaly at $\sim 0.4\hspace{0.5em}{(2e}^2/h)$ below which the magnetization collapses.