We investigate the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field-suppression effect on the longitudinal thermal conductivity ${\kappa }_{xx}$ sets in below approximately 25 K. This field-suppression effect at 15 T becomes as large as 80% at low temperatures, suggesting a large spin contribution ${\kappa }_{xx}^{\mathrm{sp}}$ in ${\kappa }_{xx}$. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity ${\kappa }_{xy}$ shows a significant dependence on the sample’s scattering time, as seen in the rise of the peak ${\kappa }_{xy}$ value in almost linear fashion with the magnitude of ${\kappa }_{xx}$. On the other hand, the temperature dependence of ${\kappa }_{xy}$ is similar in all Cd-K samples; ${\kappa }_{xy}$ shows a peak at almost the same temperature of the peak of the phonon thermal conductivity ${\kappa }_{xx}^{\mathrm{ph}}$ which is estimated by ${\kappa }_{xx}$ at 15 T. These results indicate the presence of a dominant phonon thermal Hall ${\kappa }_{xy}^{\mathrm{ph}}$ at 15 T. In addition to ${\kappa }_{xy}^{\mathrm{ph}}$, we find that the field dependence of ${\kappa }_{xy}$ at low fields turns out to be nonlinear at low temperatures, concomitantly with the appearance of the field suppression of ${\kappa }_{xx}$, indicating the presence of a spin thermal Hall ${\kappa }_{xy}^{\mathrm{sp}}$ at low fields. Remarkably, by assembling the ${\kappa }_{xx}$ dependence of ${\kappa }_{xy}^{\mathrm{sp}}$ data of other kagome antiferromagnets, we find that, whereas ${\kappa }_{xy}^{\mathrm{sp}}$ stays a constant in the low-${\kappa }_{xx}$ region, ${\kappa }_{xy}^{\mathrm{sp}}$ starts to increase as ${\kappa }_{xx}$ does in the high-${\kappa }_{xx}$ region. This ${\kappa }_{xx}$ dependence of ${\kappa }_{xy}^{\mathrm{sp}}$ indicates the presence of both intrinsic and extrinsic mechanisms in the spin thermal Hall effect in kagome antiferromagnets. Furthermore, both ${\kappa }_{xy}^{\mathrm{ph}}$ and ${\kappa }_{xy}^{\mathrm{sp}}$ disappear in the antiferromagnetic ordered phase at low fields, showing that phonons alone do not exhibit the thermal Hall effect. A high field above approximately 7 T induces ${\kappa }_{xy}^{\mathrm{ph}}$, concomitantly with a field-induced increase of ${\kappa }_{xx}$ and the specific heat, suggesting a coupling of the phonons to the field-induced spin excitations as the origin of ${\kappa }_{xy}^{\mathrm{ph}}$.

中文翻译：

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Kagome反铁磁体Cd-Kapellasite中自旋和声子的热霍尔效应

我们研究了kagome反铁磁体Cd-kapellasite（Cd-K）的热传递性质。我们发现场抑制对纵向热导率的影响${\kappa }_{XX}$ 在低于25 K的温度下凝固。在15 T时的这种场抑制作用在低温下高达80％，表明自旋贡献很大 ${\kappa }_{XX}^{\mathrm{SP}}$ 在 ${\kappa }_{XX}$。我们还在所有Cd-K样品的自旋液相中发现了清晰的热霍尔信号。霍尔热导率的大小${\kappa }_{Xÿ}$ 从峰的上升可以看出，它对样品的散射时间有很大的依赖性 ${\kappa }_{Xÿ}$ 值几乎呈线性，幅度为 ${\kappa }_{XX}$。另一方面，温度依赖性${\kappa }_{Xÿ}$ 在所有Cd-K样品中均相似； ${\kappa }_{Xÿ}$ 在几乎与声子热导率峰相同的温度下显示峰 ${\kappa }_{XX}^{\mathrm{酸碱度}}$ 据估计 ${\kappa }_{XX}$ 在15 T时。这些结果表明存在显性声子热霍尔 ${\kappa }_{Xÿ}^{\mathrm{酸碱度}}$ 15 T时 ${\kappa }_{Xÿ}^{\mathrm{酸碱度}}$，我们发现 ${\kappa }_{Xÿ}$ 在低温下的结果证明是非线性的，伴随着磁场抑制的出现。 ${\kappa }_{XX}$，表明存在自旋热霍尔 ${\kappa }_{Xÿ}^{\mathrm{SP}}$在低地。值得注意的是，通过组装${\kappa }_{XX}$ 的依赖 ${\kappa }_{Xÿ}^{\mathrm{SP}}$ 我们发现其他kagome反铁磁体的数据 ${\kappa }_{Xÿ}^{\mathrm{SP}}$ 在低位保持恒定${\kappa }_{XX}$ 地区， ${\kappa }_{Xÿ}^{\mathrm{SP}}$ 开始增加 ${\kappa }_{XX}$ 在高${\kappa }_{XX}$地区。这个${\kappa }_{XX}$ 的依赖 ${\kappa }_{Xÿ}^{\mathrm{SP}}$表明在kagome反铁磁体的自旋热霍尔效应中同时存在内在和外在机理。此外，两者${\kappa }_{Xÿ}^{\mathrm{酸碱度}}$ 和 ${\kappa }_{Xÿ}^{\mathrm{SP}}$磁场在低磁场下在反铁磁有序相中消失，表明仅声子不会表现出热霍尔效应。高于约7 T的高场感应${\kappa }_{Xÿ}^{\mathrm{酸碱度}}$，伴随着磁场的增加 ${\kappa }_{XX}$ 和比热，表明声子与场致自旋激发的耦合是 ${\kappa }_{Xÿ}^{\mathrm{酸碱度}}$。