Figure 1

Schematic depiction of the states with different polarizations in the filling factor range $1<{\nu }^{*}<2$ (top), $2<{\nu }^{*}<3$ (middle), and $3<{\nu }^{*}<4$ (bottom). Composite fermions are pictured as electrons carrying two arrows (representing bound vortices). The horizontal lines represent the CF $\Lambda \mathrm{Ls}$, with the spin-up $\Lambda \mathrm{Ls}$ on the left and spin-down $\Lambda \mathrm{Ls}$ on the right. The states are labeled (${\nu }_{\uparrow }^{*}$, ${\nu }_{\downarrow }^{*}$); the filling factor of the partially filled $\Lambda$ level is $\overline{\nu }$.Reuse & Permissions

Figure 2

The energy per particle for various states (${\nu }_{\uparrow }^{*}$, ${\nu }_{\downarrow }^{*}$) in the filling factor range $1<{\nu }^{*}<4$. The energy $E$ is quoted in units of $e^2/ϵ\ell$, where $\ell =\sqrt{\hslash c/eB}$ is the magnetic length and $ϵ$ is the dielectric constant of the host material, and includes interaction with a uniform neutralizing background. The dark (open) symbols correspond to states in which the partially filled $\Lambda \mathrm{L}$ contains a crystal of CF particles (holes).Reuse & Permissions

Figure 3

Difference between the energies (per particle) of the states with different polarizations, shown near each line, in the filling factor range $1<{\nu }^{*}<4$.Reuse & Permissions

Figure 4

The calculated polarization phase diagram of various states (${\nu }_{\uparrow }^{*}$, ${\nu }_{\downarrow }^{*}$) in the CF filling factor range $1<{\nu }^{*}<4$ ($1/3<\nu <4/9$) as a function of $\kappa =E_{\mathrm{Z}}/(e^2/ϵ\ell )$. The thick blue lines are for a system of zero thickness; the dashed red lines correspond to a quantum well width of 40 nm for density ${10}^{11}{\mathrm{cm}}^{-2}$; and thin green lines indicate the phase boundaries predicated by a model of noninteracting composite fermions. The blue triangles indicate the spin phase transitions at ${\nu }^{*}=n$ identified previously [24]. The yellow shade depicts the region where Skyrmions are present, and the vertical blue shaded regions depict fillings where transitions take place from one fraction to the next. The inset shows the polarization $P=({\nu }_{\uparrow }^{*}-{\nu }_{\downarrow }^{*})/{\nu }^{*}$ as a function of ${\nu }^{*}$ for fixed values of $\kappa =0.0225$ (black solid line), 0.0125 (purple crosses), and 0.005 (red circles), as evaluated for a zero thickness sample.Reuse & Permissions