Coexisting spin resonance and long-range magnetic order of Eu in EuRbFe4As4

Magnetic excitations and magnetic structure of EuRbFe4As4 were investigated by inelastic neutron scattering (INS), neutron diffraction, and random phase approximation (RPA) calculations. Below the superconducting transition temperature T-c = 36.5 K, the INS spectra exhibit the neutron spin resonances at Q(res) = 1.27(2) and 1.79(3) angstrom(-1). They correspond to the 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-res = 17.7(3) meV corresponding to 5.7(1)k(B)T(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(+/-) superconducting pairing symmetry in EuRbFe4As4. In addition to the neutron spin resonance mode, upon decreasing temperature below the magnetic transition temperature T-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 k = (0, 0, 0.25), representing the three-dimensional antiferromagnetic order. Linear spin wave calculations assuming the obtained magnetic structure with the intra- and interplane nearest neighbor exchange couplings of J(1)/k(B) = -1.31 K and J(c)/k(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 EuRbFe4As4, whereas the coupling between them is rather weak.