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Register a new userUniversal critical behavior in the ferromagnetic superconductor Eu(Fe$_{0.75}$Ru$_{0.25}$)$_{2}$As$_{2}$
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The study of universal critical behavior is a crucial issue in a continuous phase transition, which groups various critical phenomena into universality classes for revealing microscopic electronic behaviors. The understanding of the nature of magnetism in Eu-based ferromagnetic superconductors is largely impeded by the infeasibility of performing inelastic neutron scattering measurements to deduce the microscopic magnetic behaviors and the effects on the superconductivity, due to the significant neutron absorption effect of natural $^{152}$Eu and unavailability of large single crystals. However, by systematically combining the neutron diffraction experiment, the first-principles calculations, and the quantum Monte Carlo simulations, we have obtained a perfectly consistent universal critical exponent value of $beta=0.385(13)$ experimentally and theoretically for Eu(Fe$_{0.75}$Ru$_{0.25}$)$_{2}$As$_{2}$, from which the magnetism in the Eu-based ferromagnetic superconductors is identified as the universal class of a three-dimensional anisotropic quantum Heisenberg model with long-range magnetic exchange coupling. This study not only clarifies the nature of microscopic magnetic behaviors in the Eu-based ferromagnetic superconductors, but also opens a new avenue of systemic methodology for studying the universal critical behaviors associated with magnetic phase transitions in the area of magnetism and the spin fluctuations effects on the unconventional superconductivity.
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We used high-energy resolution angle-resolved photoemission spectroscopy to extract the momentum dependence of the superconducting gap of Ru-substituted Ba(Fe$_{0.75}$Ru$_{0.25}$)$_2$As$_2$ ($T_c = 15$ K). Despite a strong out-of-plane warping of the Fermi surface, the magnitude of the superconducting gap observed experimentally is nearly isotropic and independent of the out-of-plane momentum. More precisely, we respectively observed 5.7 meV and 4.5 meV superconducting gaps on the inner and outer $Gamma$-centered hole Fermi surface pockets, whereas a 4.8 meV gap is recorded on the M-centered electron Fermi surface pockets. Our results are consistent with the $J_1-J_2$ model with a dominant antiferromagnetic exchange interaction between the next-nearest Fe neighbors.
Using complementary polarized and unpolarized single-crystal neutron diffraction, we have investigated the temperature-dependent magnetic structures of Eu$_{0.5}$Ca$_{0.5}$Fe$_{2}$As$_{2}$. Upon 50 % dilution of the Eu sites with isovalent Ca$^{2+}$, the Eu sublattice is found to be still long-range ordered below $mathit{T_{Eu}}$ = 10 K, in the A-typed antiferromagnetic (AFM) structure. The moment size of Eu$^{2+}$ spins is estimated to be as large as 6.74(4) $mu_{B}$ at 2.5 K. The Fe sublattice undergoes a spin-density-wave transition at $mathit{T_{SDW}}$ = 192(2) K and displays an in-plane AFM structure above $mathit{T_{Eu}}$. However, at 2.5 K, the Fe$^{2+}$ moments are found to be ordered in a canted AFM structure with a canting angle of 14(4){deg} out of the $mathit{ab}$ plane. The spin reorientation of Fe below the AFM ordering temperature of Eu provides a direct evidence of a strong interplay between the two magnetic sublattices in Eu$_{0.5}$Ca$_{0.5}$Fe$_{2}$As$_{2}$.
The effects of hydrostatic pressure on the static magnetism in Eu(Fe$_{0.925}$Co$_{0.075}$)$_{2}$As$_{2}$ are investigated by complementary electrical resistivity, ac magnetic susceptibility and single-crystal neutron diffraction measurements. A specific pressure-temperature phase diagram of Eu(Fe$_{0.925}$Co$_{0.075}$)$_{2}$As$_{2}$ is established. The structural phase transition, as well as the spin-density-wave order of Fe sublattice, is suppressed gradually with increasing pressure and disappears completely above 2.0 GPa. In contrast, the magnetic order of Eu sublattice persists over the whole investigated pressure range up to 14 GPa, yet displaying a non-monotonic variation with pressure. With the increase of the hydrostatic pressure, the magnetic state of Eu evolves from the canted antiferromagnetic structure in the ground state, via a pure ferromagnetic structure under the intermediate pressure, finally to a possible novel antiferromagnetic structure under the high pressure. The strong ferromagnetism of Eu coexists with the pressure-induced superconductivity around 2 GPa. The change of the magnetic state of Eu in Eu(Fe$_{0.925}$Co$_{0.075}$)$_{2}$As$_{2}$ upon the application of hydrostatic pressure probably arises from the modification of the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu$^{2+}$ moments tuned by external pressure.
Using polarized neutron diffraction and x-ray resonant magnetic scattering (XRMS) techniques, multiple phase transitions were revealed in an underdoped, non-superconducting Eu(Fe$_{1-x}$Ir$_{x}$)$_{2}$As$_{2}$ ($mathit{x}$ = 0.06) single crystal. Compared with the parent compound EuFe$_{2}$As$_{2}$, the tetragonal-to-orthorhombic structural phase transition and the antiferromagnetic order of the Fe$^{2+}$ moments are significantly suppressed to $mathit{T_{S}}$ = 111 (2) K and $mathit{T_{N,Fe}}$= 85 (2) K by 6% Ir doping, respectively. In addition, the Eu$^{2+}$ spins order within the $mathit{ab}$ plane in the A-type antiferromagnetic structure similar to the parent compound. However, the order temperature is evidently suppressed to $mathit{T_{N,Eu}}$= 16.0 (5) K by Ir doping. Most strikingly, the XRMS measurements at the Ir $mathit{L_{3}}$ edge demonstrates that the Ir 5$mathit{d}$ states are also magnetically polarized, with the same propagation vector as the magnetic order of Fe. With $mathit{T_{N,Ir}}$ = 12.0 (5) K, they feature a much lower onset temperature compared with $mathit{T_{N,Fe}}$. Our observation suggests that the magnetism of the Eu sublattice has a considerable effect on the magnetic nature of the 5$mathit{d}$ Ir dopant atoms and there exists a possible interplay between the localized Eu$^{2+}$ moments and the conduction $mathit{d}$-electrons on the FeAs layers.
The magnetic ground state of the Eu$^{2+}$ moments in a series of Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals grown from the Sn flux has been investigated in detail by neutron diffraction measurements. Combined with the results from the macroscopic properties (resistivity, magnetic susceptibility and specific heat) measurements, a phase diagram describing how the Eu magnetic order evolves with Co doping in Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ is established. The ground-state magnetic structure of the Eu$^{2+}$ spins is found to develop from the A-type antiferromagnetic (AFM) order in the parent compound, via the A-type canted AFM structure with some net ferromagnetic (FM) moment component along the crystallographic $mathit{c}$ direction at intermediate Co doping levels, finally to the pure FM order at relatively high Co doping levels. The ordering temperature of Eu declines linearly at first, reaches the minimum value of 16.5(2) K around $mathit{x}$ = 0.100(4), and then reverses upwards with further Co doping. The doping-induced modification of the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu$^{2+}$ moments, which is mediated by the conduction $mathit{d}$ electrons on the (Fe,Co)As layers, as well as the change of the strength of the direct interaction between the Eu$^{2+}$ and Fe$^{2+}$ moments, might be responsible for the change of the magnetic ground state and the ordering temperature of the Eu sublattice. In addition, for Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals with 0.10 $leqslant$ $mathit{x}$ $leqslant$ 0.18, strong ferromagnetism from the Eu sublattice is well developed in the superconducting state, where a spontaneous vortex state is expected to account for the compromise between the two competing phenomena.
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