Scaling in spin-degenerate Landau levels in the integer quantum Hall effect

In a low-mobility Inₓ{Ga}_{1{{-}}x}$As/InP heterostructure, we find that the quantized Hall resistance plateau, ${{{ρ}}}xy$=h/${ie}²$ with i=3, starts developing only when T is below 50 mK. For higher T, the plateau and the associated minimum in the diagonal resistivity ${{{ρ}}}ₓₓ$ can be made to appear by tilting the sample with respect to the B field. We have studied the T dependence of the ${{{ρ}}}ₓₓ$ minimum and deduced the thermal-activation energy ({Δ}). We find that {Δ} is 67 times smaller than the Landau-level broadening deduced from the electron mobility. This result implies that there is no gap in the density of states and that, for T>50 mK, the Landau level is spin degenerate. In this higher T range, we observe a T^-0.21 power law for the maximum value of dρxy/dB between the i=2 and 4 plateaus, and T^-0.42 for the minimum value of d²{{{ρ}}}ₓₓ$/${dB}²$. These exponents are a factor 2 smaller than those for spin-polarized levels.