Impurity-induced magnetic droplet in unconventional superconductors near a magnetic instability: Application to Nd-doped CeCoIn5

Abstract

Beside the spin density wave (SDW) order inside the superconducting phase in CeCoIn 5 at high magnetic fields, recent neutron scattering measurements have found Bragg peaks in 5% Nd doped CeCoIn 5 at low fields. The intensity of Bragg peaks in low fields is suppressed by increasing field. Based on the phenomenological and microscopic modeling, we show that for the Pauli limited d-wave superconductors in the vicinity of SDW instability relevant for CeCoIn 5 , magnetic impurities locally induce droplets of SDW order. Because of the strong anisotropy in the momentum space in the spin fluctuations guaranteed by the d-wave pairing symmetry, sharp peaks in spin structure factor at Qs are produced by the impurities, even when the droplets of SDW do not order. At zero field, the Nd impurity spins are along the c axis due to the coupling to the conduction electrons with an easy c axis, besides their own crystal field effect. The in-plane magnetic field cants the impurity moments toward the ab plane, which suppress the droplets of SDW order. At high fields, the long-range SDW inside the superconducting phase is stabilized as a consequence of magnon condensation. Our results are consistent with the recent neutron scattering and thermal conductivity measurements.

Evolution of Magnetic Order from the Localized to the Itinerant Limit

“…A similar controversy has also arisen lately for magnetic order in Nd 1−x Ce x CoIn 5 at small x [41][42][43][44].…”

“…De Haas-van Alphen effect measurements on Nd 1−x Ce x CoIn 5 , predictions on the behavior of the static spin susceptibility upon (non-)magnetic substitution of Ce in CeCoIn 5 and the observation of magnetic order in 5% Gd-doped CeCoIn 5 suggest that magnetic order is triggered by an instability in the band structure [41,42]. In contrast, some theoretical models argue that local magnetic droplets play a decisive role [43,44]. In this scenario magnetism is mediated inside a d-wave superconducting background via strong magnetic fluctuations triggered by the nearby SDW critical point.…”

Multiple phases with intertwined magnetic and superconducting orders in Nd-doped CeCoIn5

“…An applied field has the opposite effect on these phases: magnetic field suppresses the low-field SDW phase but stabilizes the HFLT phase in both Ce 0.95 Nd 0.05 CoIn 5 and pure CeCoIn 5 . Suppression of the lowfield SDW by an applied in-plane magnetic field is understood to be due to field-induced tilting of Nd moments from out-ofplane to in-plane direction, which weakens the magnetization of impurity-induced droplets of local SDW correlations and, consequently, the temperature at which the long-range SDW order develops 24 . In contrast, a field-split excitation mode of the spin resonance softens and approaches zero for fields where the HFLT phase develops 9 .…”

“…In this zerofield phase, the four-fold symmetry of the d-wave superconducting order should be present. The SDW should appear with ordering wave vectors along the two perpendicular nodal directions with equal ordered moments in each domains 24 , and result in equal neutron-scattering intensities at these two Q's.…”

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

“…Theoretically, the ground state physics of the finite momentum paired phase of Pauli limited superconductors is well established based primarily on the quasi-classical and mean field theories (MFT) [32][33][34][35][36][37]. Moreover, attempts were made to access the impact of thermal fluctuations on these systems by pushing the MFT to higher temperatures [38][39][40][41], an approximation which in known to break down beyond the weak coupling regime. Based on the experimental outcomes it is now well established that the existing Pauli limited superconductors are, (i) materials with unconventional pairing state symmetry and (ii) short coherence length, typified by large superconducting gap to T c ratio and intermediate to strong superconducting coupling [17,25,[42][43][44].…”