Coexisting spin resonance and long-range magnetic order of Eu in EuRbFe${}_4$As${}_4$

Abstract

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 $Q_{\text{res}}=1.27(2)$~${\text{A˚}}^{-1}$ and $1.79(3)$~${\text{A˚}}^{-1}$. 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.

8 pages, 4 figures

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