Conserved nonlocal dynamics and critical behavior of uranium ferromagnetic superconductors

A recent theoretical study [Phys. Rev. Lett. 112, 037202 (2014)10.1103/PhysRevLett.112.037202] has revealed that systems such as uranium ferromagnetic superconductors obey conserved dynamics. To capture the critical behavior near the paramagnetic to ferromagnetic phase transition of these compounds, we study the conserved critical dynamics of a nonlocal Ginzburg-Landau model. A dynamic renormalization-group calculation at one-loop order yields the critical indices in the leading order of ε=d_{c}-d, where d_{c}=4-2ρ is the upper critical dimension, with ρ an exponent in the nonlocal interaction. The predicted static critical exponents are found to be comparable with the available experimentally observed critical exponents for strongly uniaxial uranium ferromagnetic superconductors. The corresponding dynamic exponent z and linewidth exponent w are found to be z=4-ρε/4+O(ε^{2}) and w=1+ρ+3ε/4+O(ε^{2}).