Spin-orbit coupling effects in the quantum Hall regime probed by electron spin resonance

Abstract

The spin resonance of two-dimensional (2D) electrons confined in a high-quality 4.5-nm AlAs quantum well was studied in the regime of the integer quantum Hall effect. The electron $g$-factor extracted from the magnetic field position of the spin resonance at a fixed microwave frequency demonstrated a strong nonlinear dependence on the magnetic field with discontinuities around even filling factors. The value of the $g$-factor tended to increase with a decrease of the magnetic field around each odd filling. Furthermore, the $g$-factor at the exactly odd filling factor $\ensuremath{\nu}$ turned out to be dependent on $\ensuremath{\nu}$, suggesting the entanglement between the spin degree of freedom and the orbital motion of the electrons in the regime of the integer quantum Hall effect. This suggestion is further supported, as all the experimental data are well described, when a Dresselhaus-type spin-orbit interaction is introduced into the Hamiltonian of a single electron in the quantizing magnetic field. Surprisingly, such excellent agreement was observed even in the case of tilted magnetic fields. The fitting procedure allowed us to determine the strength of the Dresselhaus spin-orbit term in a 2D electron system and to extract the fundamentally important Dresselhaus constant for bulk AlAs. Unexpectedly, not only was single spin resonance observed around even fillings, it tended to split into two well-resolved lines. Yet this finding remains a mystery and highlights the need for further experimental and theoretical efforts.