Spin-dependent Hall effect in a parabolic well with a quasi-three-dimensional electron gas

Abstract

We study the Hall effect in wide ${\mathrm{Al}}_{c}{\mathrm{Ga}}_{c\ensuremath{-}1}\mathrm{As}$ parabolic wells in the presence of the tilted magnetic field. The Hall resistance is described by equations ${R}_{xy}∕\mathrm{cos}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Theta}=\ensuremath{-}B∕e{n}_{s}$ at $B<4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, and ${R}_{xy}∕\mathrm{cos}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Theta}=\ensuremath{-}A\ifmmode\times\else\texttimes\fi{}(B\ensuremath{-}{B}_{0})∕e{n}_{s}$ at $B>4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, where ${n}_{s}$ is the electron density, ${B}_{0}=2--2.6\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, $A$ is the temperature dependent coefficient, and $\ensuremath{\Theta}$ is the angle between the magnetic field and the normal to the well plane. The effective $g$ factor in such materials depends on the Al composition and changes the sign along the well width. In the presence of the strong tilted magnetic field electron moving along the $z$ direction acquires a spin flip process, which is strongly suppressed at low temperatures, and leads to the change of the Hall effect slope.