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The specific heat and thermal conductivity of the insulating ferrimagnet Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG) single crystal were measured down to 50 mK. The ferromagnetic magnon specific heat $C$$_m$ shows a characteristic $T^{1.5}$ depend ence down to 0.77 K. Below 0.77 K, a downward deviation is observed, which is attributed to the magnetic dipole-dipole interaction with typical magnitude of 10$^{-4}$ eV. The ferromagnetic magnon thermal conductivity $kappa_m$ does not show the characteristic $T^2$ dependence below 0.8 K. To fit the $kappa_m$ data, both magnetic defect scattering effect and dipole-dipole interaction are taken into account. These results complete our understanding of the thermodynamic and thermal transport properties of the low-lying ferromagnetic magnons.
The in-plane resistivity $rho$ and thermal conductivity $kappa$ of extremely overdoped KFe$_2$As$_2$ ($T_c$ = 3.0 K) single crystal were studied. It is found that $rho sim T^{1.5}$ at low temperature, a typical non-Fermi liquid behavior of electrons scattered by antiferromagnetic spin fluctuations. In zero field, we observed a large residual linear term $kappa_0/T$, about one third of the normal-state value. In low magnetic fields, $kappa_0/T(H)$ increases very fast. Such a behavior of $kappa_0/T$ mimics the d-wave cuprate superconductors, therefore provides clear evidence for nodes in the superconducting gap of KFe$_2$As$_2$. Based on the Fermi surface topology of KFe$_2$As$_2$, it is believed that the dominant intraband pairing via antiferromagnetic spin fluctuations results in the unconventional superconducting gap with nodes.
The in-plane thermal conductivity $kappa$ of overdoped FeAs-based superconductor BaFe$_{1.73}$Co$_{0.27}$As$_2$ ($T_c$ = 8.1 K) single crystal was measured down to 80 mK. In zero field, the residual linear term $kappa_0/T$ is negligible, suggesting a nodeless superconducting gap in the $ab$-plane. In magnetic field, $kappa_0/T$ increases rapidly, very different from that of conventional s-wave superconductors. This anomalous $kappa_0/T(H)$ may reveal an exotic superconducting gap structure in overdoped BaFe$_{1.73}$Co$_{0.27}$As$_2$: the vanishing hole ($beta$) pocket has a much larger gap than the electron ($gamma$ and $delta$) pockets which contain most of the carriers. Such an exotic gap structure is an evidence for superconducting state induced by interband interactions, in which the band with the {it smaller} density of states has a {it larger} gap.
The in-plane thermal conductivity $kappa$ of the iron selenide superconductor FeSe$_x$ ($T_c$ = 8.8 K) were measured down to 120 mK and up to 14.5 T ($simeq 3/4 H_{c2}$). In zero field, the residual linear term $kappa_0/T$ at $ T to 0$ is only about 16 $mu$W K$^{-2}$ cm$^{-1}$, less than 4% of its normal state value. Such a small $kappa_0/T$ does not support the existence of nodes in the superconducting gap. More importantly, the field dependence of $kappa_0/T$ in FeSe$_x$ is very similar to that in NbSe$_2$, a typical multi-gap s-wave superconductor. We consider our data as strong evidence for multi-gap nodeless superconductivity in FeSe$_x$. This kind of superconducting gap structure may be generic for all Fe-based superconductors.
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