Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor ν = 1 and at very low temperatures (∼ 40 mK). A small change in filling factor (δν ≈ ±0.01) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at ν = 1 is surprisingly fragile against increasing temperature, or against small changes in filling factor.
PACS numbers:Electron-electron interactions in two dimensions dominate in many cases over the single particle physics leading to new collective ground states of the system. This is particularly true in GaAs due to the small value of the single particle Zeeman energy. The physics in the vicinity of filling factor ν = 1 is particularly rich. The system behaves as a half empty Landau band in which all the electrons have the same orbital quantum number and only the spin degree of freedom remains. At exactly ν = 1, the predicted ground state is an itinerant quantum Hall ferromagnet [1,2], while on either side of ν = 1 the system depolarizes more rapidly than predicted by the single particle picture, due to the formation of spin textures (Skyrmions or anti-Skyrmions) in the ground state [3,4,5,6,7,8]. The strong coupling between the nuclear and electronic spin systems, observed close to ν = 1 in specific heat capacity [9], and resistively detected nuclear magnetic resonance (NMR) measurements [10], strongly suggest the existence of gapless spin excitations of the electronic system. Such Goldstone modes are consistent with a breaking of the spin rotational symmetry due to the formation of a Skyrme crystal in the ground state [11].Electrical transport measurements, which have been extensively used to investigate the quantum Hall effect, are not an incisive probe of the physics of the ground state at exactly integer filling factor, since the Fermi energy lies deeply inside localized states. Optical techniques such as photoluminescence, absorption and inelastic light scattering have been widely applied [8,12,13,14,15,16]. Surprisingly, techniques which give a direct measure of the spin polarization, suggest that the system is not fully spin polarized at ν = 1 [8,13,16], despite the large exchange enhanced spin gap which remains open even in the absence of the single particle Zeeman energy [7].In this paper we report on optical absorption (transmission) measurements to directly probe the subtle physics of the n=0 Landau level (LL) via the spin polarization of the system. We find that full spin polarization does indeed occur, but only at exactly filling factor ν = 1 and at very low (40 mK) temperatures. This suggest that the quantum Hall ferromagnet at ν = 1 is surprisingly fragile, collapsing, with either a small change of filling factor or temperature, into a lower energy ground state with a large number of reversed spins.To measure the absorption spectrum of a single GaAs quantum well (QW) at low temperatures we have used a structure which for...