[Paper Review] Texture in the Superconducting Order Parameter of CeCoIn_5 Revealed by Nuclear Magnetic Resonance

Kakuyanagi, K., Saito, M.+5 more|arXiv (Cornell University)|May 28, 2004

Rare-earth and actinide compounds3 citations

TL;DR

This study presents the first microscopic evidence for a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in the heavy-fermion superconductor CeCoIn5 using 115In nuclear magnetic resonance (NMR). Below T*(H), a new NMR resonance line emerges at higher frequency, indicating spatially modulated superconducting order parameter and localized quasiparticle states, with spectral evolution consistent with a FFLO state featuring oscillating order parameter wave length that decreases with temperature.

ABSTRACT

We present a ^{115}In NMR study of the quasi two-dimensional heavy-fermion superconductor CeCoIn_5 believed to host a Fulde-Ferrel-Larkin-Ovchinnkov (FFLO) state. In the vicinity of the upper critical field and with a magnetic field applied parallel to the ab-plane, the NMR spectrum exhibits a dramatic change below T*(H) which well coincides with the position of reported anomalies in specific heat and ultrasound velocity. We argue that our results provide the first microscopic evidence for the occurrence of a spatially modulated superconducting order parameter expected in a FFLO state. The NMR spectrum also implies an anomalous electronic structure of vortex cores.

Motivation & Objective

• To provide direct microscopic evidence for the existence of a spatially inhomogeneous superconducting state in CeCoIn5 under high magnetic fields.
• To investigate the quasiparticle excitation spectrum in the high-field superconducting phase near Hc2∥ab, particularly below T*(H).
• To determine whether the observed NMR spectral changes correlate with the proposed FFLO state and vortex core anomalies.
• To probe the electronic structure of vortex cores in CeCoIn5, contrasting it with conventional superconductors.

Proposed method

• Performed 115In NMR measurements on single-crystal CeCoIn5 under magnetic fields aligned parallel to the ab-plane, near Hc2∥ab.
• Measured temperature-dependent NMR spectra in the superconducting state at fields just below Hc2∥ab, focusing on the region below T*(H).
• Used a theoretical model of a d-wave superconductor with a spatially oscillating order parameter (q ∼ 2μBH/ℏvF) to simulate the NMR spectrum.
• Fitted the experimental NMR spectra using a formula incorporating the ratio of coherence length to modulation wave vector (Λ/λ) and T/Δ0, with Lorentzian broadening for inhomogeneous effects.
• Analyzed Knight shift and line shape to infer quasiparticle density and spatial inhomogeneity in the superconducting state.
• Compared spectral features with predictions for FFLO states and conventional superconductors to identify deviations in vortex core structure.

Experimental results

Research questions

• RQ1 Does the NMR spectrum in CeCoIn5 near Hc2∥ab show signatures of a spatially modulated superconducting order parameter as predicted by the FFLO state?
• RQ2 What is the nature of quasiparticle excitation in the high-field superconducting phase below T*(H), and how does it differ from conventional superconductors?
• RQ3 How does the vortex core structure in CeCoIn5 differ from that in conventional superconductors, based on NMR line shape and Knight shift?
• RQ4 Is the observed spectral evolution with temperature consistent with the theoretical expectations of a FFLO state in a d-wave superconductor?
• RQ5 What is the role of strong electron correlations and antiferromagnetic fluctuations in shaping the vortex core and quasiparticle spectrum?

Key findings

• A new NMR resonance line appears at higher frequency below T*(H), indicating the formation of a distinct normal-like quasiparticle region within the superconducting state.
• The NMR spectrum evolution with temperature is well reproduced by a model assuming a spatially oscillating superconducting order parameter with wave vector q ∼ 2μBH/ℏvF, consistent with the FFLO state.
• The ratio Λ/λ (coherence length over modulation wave vector) increases from 4.7 at 240 mK to 7.5 at 260 mK, indicating a decreasing spatial period of the order parameter oscillation with decreasing temperature.
• The intensity of the higher-frequency NMR line suggests that only a few percent of the volume is occupied by the newly formed normal quasiparticle sheets, indicating spatial localization.
• The two well-separated NMR lines imply that quasiparticle excitations near planar nodes are spatially localized, suggesting a Bloch wall-like or rectangular spatial dependence of the order parameter rather than sinusoidal oscillation.
• The vortex core structure is anomalous: the Knight shift within the core deviates from the normal-state value, indicating a distinct electronic state unlike conventional superconductors, likely due to strong antiferromagnetic correlations and reduced quasiparticle density of states.