Universal critical behavior in the ferromagnetic superconductor Eu(Fe-0.75 Ru-0.25)(2)As-2

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 Eu-152 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(Fe0.75Ru0.25)(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 systematic study points out a suitable microscopic theoretical model for describing the nature of magnetism in the intriguing Eu-based ferromagnetic superconductors.