Spin Transition in the Half-Filled Landau Level

The transition from partial to complete spin polarization of two-dimensional electrons at half filling of the lowest Landau level has been studied using resistively detected nuclear magnetic resonance (RDNMR). The nuclear spin-lattice relaxation time is observed to be density independent in the partially polarized phase but to increase sharply at the transition to full polarization. At low temperatures the RDNMR signal exhibits a strong maximum near the critical density.

Figure 1

(a) Resistivity at $\nu =1/2$ vs magnetic field at $T=45\mathrm{mK}$. (b) Typical response of resistivity at $\nu =1/2$ when rf frequency is brought on and off resonance with the ${}^{75}\mathrm{As}$ NMR line. (c) Typical RDNMR line shape. (d) Temperature dependence of RDNMR signal at peak of line at $\nu =1/2$ and $B=4.01\mathrm{T}$.

Figure 2

(a) Derivative $S\equiv (d{\rho }_{xx}/d{E}_Z)/{\rho }_{xx}$ vs magnetic field at $\nu =1/2$ at $T=45\mathrm{mK}$ (solid dots) and 100 mK (open dots). (b) Nuclear spin-lattice relaxation time $T_1$ vs field at $\nu =1/2$ at the same temperatures.

Figure 3

Temperature dependence of $T_1^{-1}$ at $\nu =1/2$. The solid lines are straight line and parabolic fits to the data, with the dashed portions being extrapolations to $T=0$.