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Register a new userCoexisting spin resonance and long-range magnetic order of Eu in EuRbFe$_4$As$_4$
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Magnetic excitations and magnetic structure of EuRbFe$_4$As$_4$ were investigated by inelastic neutron scattering (INS), neutron diffraction, and random phase approximation (RPA) calculations. Below the superconducting transition temperature $T_text{c}=36.5$~K, the INS spectra exhibit the neutron spin resonances at $Q_text{res}=1.27(2)$~$text{AA}^{-1}$ and $1.79(3)$~$text{AA}^{-1}$. They correspond to the $mathbf{Q}=(0.5,0.5,1)$ and $(0.5,0.5,3)$ nesting wave vectors, showing three dimensional nature of the band structure. The characteristic energy of the neutron spin resonance is $E_text{res}=17.7(3)$~meV corresponding to $5.7(1)k_text{B}T_text{c}$. Observation of the neutron spin resonance mode and our RPA calculations in conjunction with the recent optical conductivity measurements are indicative of the $s_pm$ superconducting pairing symmetry in EuRbFe$_4$As$_4$. In addition to the neutron spin resonance mode, upon decreasing temperature below the magnetic transition temperature $T_text{N}=15$~K, the spin wave excitation originating in the long-range magnetic order of the Eu sublattice was observed in the low-energy inelastic channel. Single-crystal neutron diffraction measurements demonstrate that the magnetic propagation vector of the Eu sublattice is $mathbf{k}=(0, 0, 0.25)$, representing the three-dimensional antiferromagnetic order. Linear spin wave calculations assuming the obtained magnetic structure with the intra- and inter-plane nearest neighbor exchange couplings of $J_1/k_text{B}=-1.31$~K and $J_c/k_text{B}=0.08$~K can reproduce quantitatively the observed spin wave excitation. Our results show that superconductivity and long-range magnetic order of Eu coexist in EuRbFe$_4$As$_4$ whereas the coupling between them is rather weak.
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We study single crystals of the magnetic superconductor EuRbFe$_4$As$_4$ by magnetization, electron spin resonance (ESR), angle-resolved photoemission spectroscopy (ARPES) and electrical resistance in pulsed magnetic fields up to 630 kOe. The superconducting state below 36.5 K is almost isotropic and only weakly affected by the development of Eu$^{2+}$ magnetic order at 15 K. On the other hand, for the external magnetic field applied along the c-axis the temperature dependence of the ESR linewidth reveals a Berezinskii-Kosterlitz-Thouless topological transition below 15 K. This indicates that Eu$^{2+}$-planes are a good realization of a two-dimensional XY-magnet, which reflects the decoupling of the Eu$^{2+}$ magnetic moments from superconducting FeAs-layers.
The pressure dependencies of the magnetic and superconducting transitions, as well as that of the superconducting upper critical field are reported for single crystalline EuRbFe$_4$As$_4$. Resistance measurements were performed under hydrostatic pressures up to 6.21 GPa and in magnetic fields up to 9 T. Zero-field-cool magnetization measurements were performed under hydrostatic pressures up to 1.24 GPa under 20 mT applied field. Superconducting transition temperature, $T_text c$, up to 6.21 GPa and magnetic transition temperature, $T_text M$, up to 1.24 GPa were obtained and a pressure-temperature phase diagram was constructed. Our results show that $T_text c$ is monotonically suppressed upon increasing pressure. $T_text M$ is linearly increased up to 1.24 GPa. For the studied pressure range, no signs of the crossing of $T_text M$ and $T_text c$ lines are observed. The normalized slope of the superconducting upper critical field is gradually suppressed with increasing pressure, which may be due to the continuous change of Fermi-velocity $v_F$ with pressure.
Transport, magnetic and optical investigations on EuRbFe$_4$As$_4$ single crystals evidence that the ferromagnetic ordering of the Eu$^{2+}$ magnetic moments at $T_N=15$ K, below the superconducting transition ($T_c=36$ K), affects superconductivity in a weak but intriguing way. Upon cooling below $T_N$, the zero resistance state is preserved and the superconductivity is affected by the in-plane ferromagnetism mainly at domain boundaries; a perfect diamagnetism is recovered at low temperatures. The infrared conductivity is strongly suppressed in the far-infrared region below $T_c$, associated with the opening of a complete superconducting gap at $2Delta = 10$ meV. A gap smaller than the weak coupling limit suggests the strong orbital effects or, within a multiband superconductivity scenario, the existence of a larger yet unrevealed gap.
We report an inelastic neutron scattering study on the spin resonance in the bilayer iron-based superconductor CaKFe$_4$As$_4$. In contrast to its quasi-two-dimensional electron structure, three strongly $L$-dependent modes of spin resonance are found below $T_c=35$ K. The mode energies are below and linearly scale with the total superconducting gaps summed on the nesting hole and electron pockets, essentially in agreement with the results in cuprate and heavy fermion superconductors. This observation supports the sign-reversed Cooper pairing mechanism under multiple pairing channels and resolves the long-standing puzzles concerning the broadening and dispersive spin resonance peak in iron pnictides. More importantly, the triple resonant modes can be classified into odd and even symmetries with respect to the distance of Fe-Fe planes within the Fe-As bilayer unit. Thus, our results closely resemble those in the bilayer cuprates with nondegenerate spin excitations, suggesting that these two high-$T_c$ superconducting families share a common nature.
The temperature dependence of the in-plane magnetic penetration depth ($lambda_{ab}$) in an extensively characterized sample of superconducting CaKFe$_4$As$_4$ ($T_{rm c}simeq35$ K) was investigated using muon-spin rotation ($mu$SR). A comparison of $lambda_{ab}^{-2}(T)$ measured by $mu$SR with the one inferred from ARPES data confirms the presence of multiple gaps at the Fermi level. An agreement between $mu$SR and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small supercondcting gaps with an average zero-temperature value of $Delta_{0} =$ 2.4(2) meV. Our data suggest that in CaKFe$_4$As$_4$ the $s^pm$ order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type.
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