Impurity-induced magnetic droplet in unconventional superconductors near magnetic instability: Application to Nd doped $\mathbf{CeCoIn_5}$

摘要

Beside the spin density wave (SDW) order inside the superconducting phase in$\mathrm{CeCoIn_5}$ at high magnetic fields, recent neutron scatteringmeasurements have found Bragg peaks in $5\%$ Nd doped $\mathrm{CeCoIn_5}$ atlow fields. The intensity of Bragg peaks in low fields is suppressed byincreasing field. Based on the phenomenological and microscopic modeling, weshow that for the Pauli limited $d$-wave superconductors in the vicinity of SDWinstability relevant for $\mathrm{CeCoIn_5}$, magnetic impurities locallyinduce droplets of SDW order. Because of the strong anisotropy in the momentumspace in the spin fluctuations guaranteed by the $d$-wave pairing symmetry,sharp peaks in spin structure factor at $\mathbf{Q}$s are produced by theimpurities, even when the droplets of SDW do not order. At zero field, the Ndimpurity spins are along the $c$ axis due to the coupling to the conductionelectrons with an easy $c$ axis, besides their own crystal field effect. Thein-plane magnetic field cants the impurity moments toward the $ab$ plane, whichsuppress the droplets of SDW order. At high fields, the long-range SDW insidethe superconducting phase is stabilized as a consequence of magnoncondensation. Our results are consistent with the recent neutron scattering andthermal conductivity measurements.