2 η =  E / V (a) (b) (c) n = 3.6 x 10 cm ν  = 1, B = 15.1 T v C n = 2.4 x 10 cm ν  = 1/3, B = 30.2 T n = 4.8 x 10 cm ν  = 5/3, B = 12.0 T  / V C ε  (10 ) -4 (K) (10 ) -3 11 -2 11 -2 11 -2 -0.04 -0.02 0.00 0.02 0 50 100 150 200 -1.4 -0.7 0.0 0.7 0 15 30 45 -0.02 0.00 0.02 0 4 8 12 16 -1.4 -0.7 0.0 0.7 0 2 4 6 -0.04 -0.02 0.00 0.02 0 2 4 6 -1.2 -0.6 0.0 0.6 0.0 0.5 1.0 1.5 Δ Δ FIG. 2. Energy gaps vs. ϵ for sample A for (a) ν = 1, (b) ν = 1 / 3, and (c) ν = 5 / 3. Both the x and y axes are also indicated normalized to the Coulomb energy, V C . The single-particle prediction, Δ = ϵE$_{2}$ (with E$_{2}$ = 5.8 eV) is shown as dashed lines. widths of 15 nm each. Measurements were done in either a 20 mK base temperature dilution refrigerator or a 300 mK $^{3}$He system using standard lock-in methods. The 2D electrons in our samples occupy two conduc- tion band valleys with elliptical Fermi contours [10]. In our system, the Zeeman energy ( E Z ) of electrons is typ- ically larger than their cyclotron energy [10]. Since the FQH states around ν = 1 / 2 and 3/2 are formed in the first and second LLs respectively, ours is a single-spin, two-valley system. The valley degeneracy can be con- trollably lifted by uniaxial strain applied in the plane of the sample. Experimentally, this is achieved by gluing the sample to a piezoelectric (piezo) stack which expands in one direction and contracts in the perpendicular direc- tion when an external voltage is applied. A schematic is shown in Fig. 1(a). The single-particle energy splitting between the two in-plane valleys is given by E v = ϵE$_{2}$ ; ϵ = ϵ$_{[100]}$ − ϵ$_{[010]}$ where ϵ$_{[100]}$ and ϵ$_{[010]}$ are the strains along the [100] and [010] crystal directions [10] and E$_{2}$ is the deformation potential, which has a band value of 5.8 eV in AlAs. This dependence of the energy levels on strain is shown schematically in Fig. 1(b). present the highlights of our study. For comparison, we also include in Fig. 2(a) a plot of the measured gaps for the ν = 1 QH state for the same sample. In all three plots, the x and y axes are also shown normalized to the Coulomb energy, V C = e $^{2}$/ 4 πκϵ$_{0}$ l$_{B}$ where κ = 10 is the dielectric constant of AlAs, l$_{B}$ = √ ¯ h/eB is the magnetic length and B is the magnetic field. This normalization allows easier comparison of our results with theoretical calculations. As seen in Figs. 2(b) and 2(c), there are finite gaps at ϵ = 0 at both ν = 1 / 3 and 5/3. This is con- sistent with the well-developed FQH minima observed in Fig. 1 and is the signature of a QH ferromagnet. Before discussing Fig. 2 in detail, we present data used to deduce the gaps reported in Figs. 2(b) and 2(c). In Fig. 3 we show the T -dependence of magnetoresistance traces taken around ν = 1 / 2. Figure 3(a) corresponds to the condition of ϵ = 0 while Fig. 3(b) is for ϵ = − 1 . 35 × 10 − 4 which belongs to the saturated region in Fig. 2(b). The corresponding Arrhenius plots used to deduce the gaps at ν = 1 / 3 are shown as insets. Figure 4 shows data for the case of ν = 5 / 3. Figure 4(a) contains examples of Arrhe- nius plots at ν = 5 / 3 for sample C for three different ϵ . A summary of all our gap measurements at ν = 5 / 3 from three samples is shown in Fig. 4(b). In our data, the Ar- rhenius plots deviate from a strictly activated behavior at low and high temperatures. This is not uncommon [14– 16] and previous studies have concluded that the value of the energy gap can be deduced reasonably accurately from the maximum slope in such cases. In Figs. 1(c) and 1(d) we show magnetoresistance traces taken for sample A at different ϵ . Figure 1(c) focuses on the evolution of various FQH states around ν = 3 / 2. In Fig. 1(d) we present data from a different cooldown showing states around ν = 1 / 2. The varying strengths of the different FQH resistance minima around ν = 3 / 2 as a function of ϵ have been explained by the concept of composite fermions with a valley degree of freedom [12, 13]. Here, we focus on the states at ν = 1 / 3 and 5/3. The QH minima at both these fractions are well-developed even when ϵ = 0 indicating the presence of a finite energy gap. This strongly suggests ferromag- netic ground states at ϵ = 0 at these fractional fillings. We now discuss various aspects of our gap data, start- ing with ν = 1 in Fig. 2(a). A simple fan diagram of energy vs. ϵ for (spinless) non-interacting electrons is shown in Fig. 1(b). At a fixed B , the cyclotron energy ( E c ) is constant while the energy levels for the [010] and [100] valleys split in response to ϵ , with the splitting given by E v = ϵE$_{2}$ . It is clear that at ϵ = 0 the state at ν = 1 is expected to be gapless. As the system is tuned away from ϵ = 0, a QH state should appear and its gap should In Figs. 2(b) and 2(c) we show a summary of our mea- sured energy gaps (Δ) for ν = 1 / 3 and 5/3 as a function of strain-induced valley splitting E v = ϵE$_{2}$ . These plots