Optical Absorption to Probe the Quantum Hall Ferromagnet at Filling Factor $\nu =1$

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 $\nu =1$ and at very low temperatures ($\sim 40\mathrm{mK}$). A small change in filling factor ($\delta \nu \approx \pm 0.01$) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at $\nu =1$ is surprisingly fragile against increasing temperature, or against small changes in filling factor.

Figure 1

(a) and (c) The ${\sigma }^{+}$ and ${\sigma }^{-}$ optical density spectra (minus logarithm of the normalized transmission) as a function of the magnetic field for $n_e=1.67\times {10}^{11}{\mathrm{cm}}^{-2}$ and $T=40\mathrm{mK}$. (b) Simultaneously measured electrical transport showing logarithm of the conductivity versus magnetic field.

Figure 2

Integrated intensity ($I_{{\sigma }^{\pm }}$) of the absorption to the $n=0$ LL measured for both ${\sigma }^{+}$ and ${\sigma }^{-}$ polarizations as a function of filling factor for (a) a constant density of electrons $n_e=1.67\times {10}^{11}{\mathrm{cm}}^{-2}$ and (b) a constant magnetic field $B=11\mathrm{T}$. (c),(d) Optical dichroism (spin polarization) calculated using the data presented in (a) and (b). The calculated depolarization for finite size Skyrmions or anti-Skyrmions is shown by the dashed lines ($A=S=3$) and the dotted lines ($A=S=15$). (e) Shows the spin polarization around filling factor $\nu =1$ measured at $T=40$, 500 mK, and 1.6 K. (f) Shows the detailed temperature dependence of the spin polarization at exactly $\nu =1$ (the solid line is drawn as a guide to the eye). The broken lines are the predicted temperature dependence of the polarization for a spin wave excitation (dash-dotted line) and for two spin levels separated by the single particle Zeeman energy (dashed line) as described in the text.