Spin-Polarization of $\nu =$ 3/2 Composite Fermions

We report the observation of ballistic transport commensurability minima in the magnetoresistance of $\nu =$ 3/2 composite fermions (CFs) in high-quality two-dimensional electron systems confined to wide GaAs quantum wells and subjected to a unidirectional periodic potential modulation. The positions of the minima are consisted with the magnetic commensurability condition implying the commensurability features originate from a periodic magnetic field. Their distance away from $\nu =$ 3/2 yields the size and shape of the CF Fermi contour. At a fixed electron density of n $\approx $ 1.8 x 10$^{11}$ cm$^{-2}$, as the quantum well width increases from 30 to 60 nm, the CFs become fully spin-polarized. The application of an additional parallel magnetic field (B$_{\mathrm{\vert \vert }})$ leads to a significant distortion of the CF Fermi contour. The distortion is much more severe compared to the $\nu =$ 1/2 CF case at comparable B$_{\mathrm{\vert \vert }}$. Furthermore, the applied B$_{\mathrm{\vert \vert }}$ spin-polarizes the $\nu =$ 3/2 CFs as evinced from the size of the CF Fermi contour.