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Ferromagnetic (FM) and incommensurate spin-density wave (ISDW) states are an unusual set of competing magnetic orders that are seldom observed in the same material without application of a polarizing magnetic field. We report, for the first time, the discovery of an ISDW state that is derived from a FM ground state through a Fermi surface (FS) instability in Fe$_3$Ga$_4$. This was achieved by combining neutron scattering experiments with first principles simulations. Neutron diffraction demonstrates that Fe$_3$Ga$_4$ is in an ISDW state at intermediate temperatures and that there is a conspicuous re-emergence of ferromagnetism above 360 K. First principles calculations show that the ISDW ordering wavevector is in excellent agreement with a prominent nesting condition in the spin-majority FS demonstrating the discovery of a novel instability for FM metals; ISDW formation due to Fermi surface nesting in a spin-polarized Fermi surface.
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We use the renormalization group method to study the normal state of quasi-one-dimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas, the integration of the renormalization group equations for the two-loop single particle Matsubara self-energy leads to a nonFermi-liquid temperature downturn of the momentum-resolved quasi-particle weight over most part of the Fermi surface. The amplitude of the downturn correlates with the entire instability line for superconductivity, defining an extended quantum critical region of the phase diagram as a function of nesting deviations of the Fermi surface. One also extracts the downward renormalization of interchain hopping amplitudes at arbitrary low temperature in the normal phase. By means of analytical continuation of the Matsubara self-energy, one-particle spectral functions are obtained with respect to both energy and temperature and their anomalous features analyzed in connection with the sequence of instability lines of the phase diagram. The quasi-particle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic $T$ dependences. The nonFermi-liquid linear-$T$ component correlates with the temperature scale $T_c$ of the superconducting instability over an extended range of nesting deviations, whereas its anisotropy along the Fermi surface is predicted to parallel the momentum profile of a d-wave pairing gap on the Fermi surface. We examine the implications of our results for low dimensional unconventional superconductors, in particular the Bechgaard salts series of quasi-1D organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.
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