Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field

The insulator terminating the fractional quantum Hall series at low Landau level filling \nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. Systematically studying the resonance in a high quality sample for carrier densities, n, between 1.8 and 5.7 x 10^{10} cm^-2, we find maxima in resonance peak frequency, f_pk, vs magnetic field, B. L, the domain size, or correlation length of Wigner crystalline order, is calculated from f_pk. For each n, L vs \nu tends at low \nu toward a straight line with intercept; the linear fit is accurate over as much as a factor of 5 range of \nu. We interpret the striking linear behavior as due to B compressing the electron wavefunctions, to alter the effective electron-impurity interaction.