We discover a robust coexistence of superconductivity and ferromagnetism in an iron arsenide RbEuFe4As4. The new material crystallizes in an intergrowth structure of RbFe2As2 and EuFe2As2, such that the Eu sublattice turns out to be primitive instead of being body-centered in EuFe2As2. The FeAs layers, featured by asymmetric As coordinations, are hole doped due to charge homogenization. Our combined measurements of electrical transport, magnetization and heat capacity unambiguously and consistently indicate bulk superconductivity at 36.5 K in the FeAs layers and ferromagnetism at 15 K in the Eu sublattice. Interestingly, the Eu-spin ferromagnetic ordering belongs to a rare third-order transition, according to the Ehrenfest classification of phase transition. We also identify an additional anomaly at ∼ 5 K, which is possibly associated with the interplay between superconductivity and ferromagnetism.further revised the electronic phase diagram because of the discovery of a reentrant spin glass state. Recent x-ray resonant magnetic scattering[3] and neutron scattering[4] experiments however indicated long-range ferromagnetic orderings for Eu spins in superconducting EuFe 2 (As 1−x P x ) 2 with x = 0.19 and 0.15, respectively. It was demonstrated that the Eu spins align exactly along the c axis, in contradiction to the spin-canting scenario. So far, this discrepancy remains unresolved. Note that the spin-tilting angle (∼20 • from the c axis, as detected by Mössbauer measurements[2]) coincides with the direction that connects the interlayer next-nearest (NN) Eu atoms because of the body-centered Eu sublattice. To clarify whether the Eu-sublattice type is relevant to Eu spin orientations, it is desirable to study a related material system in which Eu atoms form a primitive tetragonal lattice.Local-moment FM and spin-singlet SC are known to be mutually incompatible [20][21][22], which makes their coexistence (hereafter abbreviated as FM+SC) very rare [23]. The FM+SC phenomenon observed in FeSCs has been ascribed to the multi-orbital character as well as the robustness of superconductivity against magnetic fields [10,24]. On the one hand, the zero-temperature upper critical magnetic field, H c2 (0), of FeSCs is typically higher than 50 T [25,26], which is large enough to fight the internal exchange field that is comparable to the hyperfine field on the Eu nucleus (∼ 25 T) [2]. On the other hand, the Eu-spin FM can be satisfied even in the presence of SC, because the Fe-3d multi-orbitals enable both superconducting pairing (dominated by the d yz and d zx electrons [27]) and the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between Eu local moments. The RKKY interaction can be mediated arXiv:1605.04396v3 [cond-mat.supr-con]