Spin polarization of two-dimensional electrons in GaAs quantum wells around Landau level filling $\nu =1\mathrm{}$ from NMR measurements of gallium nuclei

A nuclear magnetic resonance (NMR) study has been carried out on a $\mathrm{GaAs}/{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ multiple-quantum-well sample, containing two-dimensional (2D) electron layers, in the quantum Hall regime. The spin polarization $\mathcal{P}$ of 2D electrons is determined from the hyperfine shift of ${}^{69,71}\mathrm{Ga}$ nuclei, measured by standard pulsed NMR. We have used the tilted-magnetic field technique to investigate the effect of an increasing Zeeman energy on $\mathcal{P}$ around Landau level filling factor $\nu =1.\mathrm{}$ Mostly on the basis of measurements performed at $B=17\mathrm{}\hspace{0.5em}\mathrm{T}$ and $T=1.5\mathrm{}\hspace{0.5em}\mathrm{K},$ we conjecture that in the high-B and low-T limit, $\mathcal{P}\left(\nu \right)$ follows the predictions of the noninteracting-electron model. The low-temperature $\mathcal{P}(\nu =1)$ is found to be far below the expected full polarization, and the observed nuclear spin-lattice relaxation rate is not reduced, in contrast to the observations by optically pumped NMR. The two techniques obtain different results only close to $\nu =1,$ and the reason why remains unclear; simple explanation in terms of the nonuniform electron density does not seem satisfactory.