Extended Data Figure 5: T/B scaling of C and (T₁T)⁻¹, and their fitting with the model density of excitations.

B^1/2(C/T) versus T/B (filled symbols, left axis) and B^1/2(T₁T)^−1/2 versus T/B (open symbols, right axis) under various magnetic fields. All of the C(T, B) data points (closed symbols) and T₁(T, B) data points (open symbols) fall onto the respective universal curves at low T/B, indicating a scaling behaviour. Because , the plot for T₁ is another way of representing the same (T/B) scaling as the inset to Fig. 3b. The physical meaning of B^1/2(T₁T)^−1/2 is the Fermi average of D(E) with a renormalization factor B^1/2, which is closely related to B^1/2(C/T). C/T and (T₁T)⁻¹ are given as follows using the standard equations, which express a Fermi averaging of D(E) and D(E)², respectively:

Here, f(T, E) = 1/{exp[(E/(k_BT)] + 1} is Fermi distribution function. The solid and dashed lines indicate B^1/2(C/T) and B^1/2(T₁T)^−1/2, respectively, calculated using the above equations for the model for D(E) shown in Fig. 4c. With α = 2.9 and Γ = 4.3 × 10⁸ J^−1/2 per Ir atom, the two scaling curves observed experimentally for B^1/2(C/T) and B^1/2(T₁T)^−1/2 are well reproduced by the calculations. A_hf = 0.44/μ_B T and γ_n/ 2π = 16.54680 MHz T⁻¹ were used as known parameters for ⁷Li. The calculated B^1/2(C/T) and B^1/2(T₁T)^-1/2 show different behaviour at high T/B (greater than about 1), which reflects the different methods of thermal averaging. This difference reasonably accounts for the difference between the two universal curves at high T/B that was observed experimentally.