Fig. 2: Longitudinal thermal conductivity and magnetic excitation gap of NdAlSi.

a κ_xx measured at various temperatures plotted as a function of H (applied along c). Curves are vertically shifted by 1 W m⁻¹K⁻¹ for clarity. Short-dashed line denotes the electronic contribution estimated based on the WF law at T = 4 K. Characteristic fields H_min (T ≥ 12 K) and \({H}_{min}^{1}\), \({H}_{min}^{2}\) (T < 12 K) are marked by hollow and solid triangles, respectively. H_m and H_p (see Fig. 1b) are indicated by black and gray bars, respectively. b T dependence of the characteristic fields defined in (a). Magenta thick line indicates a quasi-linear H_min  − T relationship extrapolating to T = 0, H = 0 (dashed line). c Magnetothermal conductivity normalized to the zero-field value, \(\Delta {\kappa }_{xx}(H)/{\kappa }_{xx}(0)=[{\kappa }_{xx}(H)-{\kappa }_{xx}(0)]/{\kappa }_{xx}(0)\left.\right]\), plotted against H/T. Error bars in (b) are defined as the half widths of the field range wherein in the H derivative of Δκ_xx(H)/κ_xx(0) changes its value by 1. d Specific heat of NdAlSi measured under μ₀H = 0 T (blue), 6 T (brown) and 14 T (yellow). The two vertical lines denote the magnetic transitions at T_m = 7.3 K and T_com = 3.3 K; the latter marks an incommensurate-to-commensurate transition inside the ferrimagnetic state¹⁸. Inset: Best fits of magnetic heat capacity C_m at 14 T to a thermal activation model (see Methods). Fits were applied to a temperature range 2 K < T < 10 K. e The magnon excitation gap Δ (left axis) and corresponding temperature scale ℏΔ/k_B (right axis) determined from fits of C_m(T) with the exponent n = 0 (green squares), n = −1 (purple circles), and analysis of the spin-lattice relaxation time T₁ (red star). The evolution of Δ under magnetic field is approximately linear with an gap opening field 3.5–4 T. Inset: \({T}_{1}^{-1}\) plotted against T for μ₀H = 12 T. The solid line is a fit to an exponential function yielding the magnon gap (“Methods”).