Evolution of Paramagnetic Quasiparticle Excitations Emerged in the High-Field Superconducting Phase of ${\mathrm{CeCoIn}}_5$

We present ${}^{115}\mathrm{In}$ NMR measurements in a novel thermodynamic phase of ${\mathrm{CeCoIn}}_5$ in a high magnetic field, where exotic superconductivity exists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.

Figure 1

(a) $H\mathrm{\text{−}}T$ phase diagram of ${\mathrm{CeCoIn}}_5$ for $\mathit{H}\parallel ab$. (b) Crystal structure of ${\mathrm{CeCoIn}}_5$. (c) A top view of the In(2) plane and directions of the largest principal axis of electric field gradient (arrows toward the center, blue) and of hyperfine fields (sharp arrows, red) on the In(2a) and the In(2b) sites transferred from the magnetic Ce moments parallel to the $c$ axis. (d) Field evolution of the NMR spectra at the In(2b) site as a function of $K_{\mathrm{spin}}$ at $T=0.05\mathrm{K}$ in the normal (11.8–12.0 T), HL (10.1–11.75 T), and BCS (8.2–9.7 T) states. $K_{\mathrm{spin}}=K-K_{\mathrm{orb}}$ is estimated by using $K_{\mathrm{orb}}=2.1\%$. Inset: Field dependence of the internal field $H_{\mathrm{int}}=\delta f/2{\gamma }_N$ obtained by the difference of the resonance frequency $\delta f$ of the two peaks (double-headed arrow in the main panel).

Figure 2

Field evolution of the NMR spectra at the In(2a) site at $T=0.05\mathrm{K}$ in the normal (12.0 T), HL (10.0–11.5 T), and BCS (8.2–9.9 T) states. The integrated intensity of each spectrum below $H_{c2}$ is normalized. The spin susceptibility (lower scale) is obtained by ${\chi }_{\mathrm{spin}}=K_{\mathrm{spin}}/A_{\mathrm{hf}}$ with $K_{\mathrm{orb}}=1.95\%$. The (green) shaded region indicates the quasiparticle spectrum emerged in the HL phase. Inset: Zoom of spectra near the edge structure at ${\mu }_{0}H=9.5$ (black), 10.2 (blue), 11.1 (green), and 11.2 T (red) from bottom to top. Dotted lines indicate the peak position in the normal state.

Figure 3

Temperature evolution of the In(2a) spectrum in HL (0.05–0.18 K) and BCS (0.21 K) phases at ${\mu }_{0}H=11.1\mathrm{T}$. The peak intensity of each spectrum is normalized. Thin black lines indicate the spectrum at $T=0.21\mathrm{K}$ just above $T^{*}$. The (green) shaded regions in the low-temperature data indicate the quasiparticle spectrum formed in the HL phase.

Figure 4

(a) Field dependence of the paramagnetic magnetization $M_p$ of the In(2a) (filled circles) and the In(1) (open circles) sites. Inset: Schematic quasiparticle structure in the FFLO state. The nodal planes with period of $2\pi /q$ appear perpendicular to the Abrikosov vortex lattice. (b) Field dependence of the DOS of the paramagnetic quasiparticles, $n_{qp}$ and $I_N$, extracted from the In(2a) spectra. The solid line is a fit to $\sqrt{H-H^{*}}$ dependence.