Dynamical thermal near-field routing with the non-reciprocal Weyl semi-metal Co$_3$Sn$_2$S$_2$

Abstract

We demonstrate theoretically the non-reciprocal heating dynamics of two nanoparticles in the vicinity of a substrate all made of the ferromagnetic Weyl semi-metal Co$_3$Sn$_2$S$_2$. We show that the thermal routing effect is due to a spin-spin coupling mechanism between the nanoparticle resonances and the non-reciprocal surface modes of the substrate. Our numerical results indicate that the non-reciprocal heating effect is on the order of 22.5% of the applied temperature differences. This strong rounting effect paves the way for first experimental realizations employing Weyl semi-metals and applications in nanoscale thermal management.

Figures (5)

• Figure 1: Sketch of the WSM router in symmetric configuration (SC) and asymmetric configuration (AC) of two WSM nanoparticles (NPs) above a substrate. The direction of the Weyl node seperation vector $2 \hat{b}$ is indicated in the NPs and in the substrate showing in $\pm y$ direction. The radii of the NPs are $R = 20\,{\rm nm}$ and $d = h = 5 R = 100\,{\rm nm}$. The initial temperatures are $T_b = 100\,{\rm K}$ and $T_1 = T_2 = 80\,{\rm K}$ and the heat flow from the substrate to the NPs is monitored.
• Figure 2: Spectral power $P_1(\omega)$ and $P_2(\omega)$ received by NP $1$ and $2$ for $T_1 = T_2 = 80\,{\rm K}$ and $T_b = 100\,{\rm K}$ for the SC and AC. The horizontal dashed lines mark the dipolar resonance frequencies $\omega_{m = 0, \pm 1}$ of the two NPs.
• Figure 3: Plot of $1 -|r_{\rm pp}|^2$ for propagating waves ($|k_x| < \omega/c$) and ${\rm Im}(r_{pp})$ for evanescent waves ($|k_x| > \omega/c$) with $k_y = 0$ for the Co$_3$Sn$_2$S$_2$ substrate at temperature $T_b = 100\,{\rm K}$. The black dashed lines are the dispersion relations of the non-reciprocal surface modes obtained with the same method as in Ref. Naeimi2025. The horizontal lines indicate the three dipolar resonances of the NPs at $T_1 = T_2 = 80\,{\rm K}$. The circles/boxes indicate the intersections of the localized NP resonances and the short range (circles) and the long-range (boxes) surface mode resonances which are spin-spin coupled to the corresponding NP resonances.
• Figure 4: Spectral mean Poynting vector (Ws/m$^2$) from Eq. (\ref{['poyntingsurf']}) for $T_1 = T_2 = 80\,{\rm K}$ and $T_b = 100\,{\rm K}$ evaluated at the NP resonances $\omega_{m = \pm 1}$ for the SC (left) and the AC (right).
• Figure 5: Dynamical evolution of the temperatures $T_1$ and $T_2$ of NPs $1$ and $2$ and the relative non-reciprocal heating efficiency $\eta = (T_1 - T_2)/\Delta T$ for the AC. The initial temperatures are $T_1 = T_2 = 80\,{\rm K}$ and the substrate temperature is fixed to $T_b = 100\,{\rm K}$. Inset: Experimental results (circles) for molar heat capacity $C_m$ (J/K mol) of Co$_3$Sn$_2$S$_2$ in the temperature range of $80\,{\rm K}$ to $100\,{\rm K}$ from Ref. heatcapacity together with the fit (solid blue line) used in our simulations.