Impurity-induced antiferromagnetic order in Pauli-limited nodal superconductors: Application to heavy-fermionCeCoIn5

Abstract

We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal d-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes d-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the Q-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field, dilute magnetic impurities cooperate via RKKY-like exchange interactions to generate a longrange ordered coexistence state identical to the Q-phase. This result is in agreement with recent neutron scattering measurements [S. Raymond et al., J. Phys. Soc. Jpn. 83, 013707 (2014)].

Intertwined Orders in Heavy-Fermion Superconductor CeCoIn5

“…Subsequent NMR [11] and neutron scattering measurements [12,13] revealed the presence of a magnetic spin-densitywave (SDW) order in the Q phase. A number of theories were proposed for its origin [14][15][16][17][18][19][20], many of them involving additional orders, distinct from the d-wave superconductivity [21,22] and the SDW. The issue of intertwined orders (magnetic, multiple, and inhomogeneous superconductivity, etc.)…”

Evolution of Magnetic Order from the Localized to the Itinerant Limit

“…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.…”

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

“…Meanwhile several theoretical proposals have been put forward to understand the origin of high field SDW phase. These theories highlight the importance of vortex lattice [11], Pauli pair breaking effect [12,13], the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, superconducting pairing density wave [14][15][16][17], and improved Fermi surface nesting by magnetic field [18][19][20], in stabilizing the SDW phase. Using the tight-binding parameters obtained by density functional calculations with renormalized bandwidth, it was shown that the in-plane magnetic field enhances the transverse magnetic susceptibility, χ(q, ω) in the Pauli-limited d-wave superconductors [21].…”

“…Assuming that the 5% Nd doping has negligible effect on the Fermi surface, and the Nd atoms serve as magnetic impurities in the d-wave superconductivity, a minimal model based on a quasi-nested Fermi surface was proposed to understand arXiv:1705.07174v1 [cond-mat.supr-con] 19 May 2017 these experiments, where the magnetic impurity induces a locally SDW pattern at low field [20]. It is argued that these local SDW patterns cooperate to form a long-range SDW order, as a consequence of the Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction between magnetic impurities.…”

“…1 (c-e). Because the system is close to the SDW instability, the induced SDW droplets decay slowly in space, which may be helpful to achieve a longrange order of the SDW droplets [20,35,36]. The low-field phase can overlap with the long-range SDW phase or they can separate, or accidentally touch the SDW phase at a point, depending on the saturation field for the impurities.…”