have little effect on the electronic state. The relationship between electron number density and the Pontryagan index density of the local spin orientation, valid for slow spin-orientation variation and nearly constant charge density,[@general] is [*not*]{} valid in this regime. Still, the collective nature of the 2DES manifests itself in the nonzero spin polarization density perpendicular to the Zeeman field. As interactions strengthen further, the local charge density smoothes out favoring the minimization of Coulomb energy at a cost in disorder energy. (See Fig. 2 (b) and 3 (b) for $\gamma\approx 1.5$.)

Experimentally, the effects of disorder can be seen most directly in the NMR spectral line shape obtained at the lowest possible temperatures where the spin profile is frozen on the experimental time scale. [@Jairo; @Yalegrouppapers] The NMR intensity spectrum in this regime is given by $$I(f,\gamma)\propto \int d{\bf r} \rho_N(z)e^{
-\frac{1}{2\sigma^2}(2\pi f -2\pi K_s \rho_e(z) \langle \vec{S}({{\bf r}};\gamma)\rangle)}
\,,
\label{NMRspectra}$$ with $\sigma=9.34 {\rm ms}^{-1}$ and $K_s\sim 25{\rm KHz}$. Here $\rho_N(z)$ is the nuclear polarization density and $\rho_e(z)$ is the electron density envelope function in the quantum well. The evaluation of such spectra has been outlined elsewhere;[@Jairo; @Yalegrouppapers] here we simply show results for several interaction strengths in Fig. \[NMR2\]. 