Evolution from helical to collinear ferromagnetic order of theEu2+spins inRbEu(Fe1−x

The ground-state magnetic structures of the ${\mathrm{Eu}}^{2+}$ spins in recently discovered $\mathrm{RbEu}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ superconductors have been investigated by neutron powder diffraction measurements. It is found that as the superconductivity gets suppressed with the increase in Ni doping, the magnetic propagation vector of the Eu sublattice diminishes, corresponding to the decrease in the rotation angle between the moments in neighboring Eu layers. The ferromagnetic Eu layers are helically modulated along the $\mathit{c}$ axis with an incommensurate magnetic propagation vector in both the ferromagnetic superconductor $\mathrm{RbEu}{({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05})}_{4}{\mathrm{As}}_{4}$ and the superconducting ferromagnet $\mathrm{RbEu}{({\mathrm{Fe}}_{0.93}{\mathrm{Ni}}_{0.07})}_{4}{\mathrm{As}}_{4}$. Such a helical structure transforms into a purely collinear ferromagnetic structure for nonsuperconducting $\mathrm{RbEu}{({\mathrm{Fe}}_{0.91}{\mathrm{Ni}}_{0.09})}_{4}{\mathrm{As}}_{4}$, with all the ${\mathrm{Eu}}^{2+}$ spins lying along the tetragonal (1 1 0) direction. The evolution from helical to collinear ferromagnetic order of the ${\mathrm{Eu}}^{2+}$ spins with increasing Ni doping is supported by first-principles calculations. The variation of the rotation angle between adjacent ${\mathrm{Eu}}^{2+}$ layers can be well explained by considering the change of magnetic exchange couplings mediated by the indirect Ruderman-Kittel-Kasuya-Yosida interaction.