Fulde-Ferrell-Larkin-Ovchinnikov State in a Perpendicular Field of Quasi-Two-Dimensional ${\mathrm{CeCoIn}}_5$

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion ${\mathrm{CeCoIn}}_5$ when a magnetic field was applied parallel to the $ab$ plane. Here, we conduct ${}^{115}\mathrm{In}$ NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the $H\mathrm{\text{−}}T$ phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to $H\parallel ab$, the FFLO phase for $H\perp ab$ is confined in a much narrower region at the low-$T$–high-$H$ corner in the $H\mathrm{\text{−}}T$ plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing $H\perp ab$ results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.

Figure 1

${}^{115}\mathrm{In}$-NMR spectra of ${\mathrm{CeCoIn}}_5$ (samples 1 and 2) as a function of the Knight shift when going from a normal state (black lines) to a superconducting state (red or gray lines) at (a) $H=4.8\mathrm{T}$ (sample 2), (b) 4.60 T (sample 1), (c) 4.80 T (sample 1), and (d) 4.85 T (sample 1). The intensity is normalized by the largest peak intensity.

Figure 2

The $T$ dependence of the Knight shift, ${}^{115}\mathrm{K}$, at $H=4.8$ (●), 4.85 (⋄), and 4.90 T (◀) for sample 1, and also at $H=4.8\mathrm{T}$ (○) for sample 2. $T_c(H)=0.48$, 0.4, and 0.22 K at $H=4.8$, 4.85, and 4.9 T, respectively. The inset shows the detail of the low field region below $H=4.7\mathrm{T}$ for sample 1. The solid and dotted lines are guide for eyes.

Figure 3

$H\mathrm{\text{−}}T$ phase diagrams at low temperatures and high fields for $\mathit{H}\perp ab$ (left panel) and $H\parallel ab$ (right panel). The colored portions display the FFLO and BCS regions. The open circles are $H_{c2}^{\perp }$ determined by the NMR experiments. The black and green (gray) lines represent the upper critical fields which are in the first and the second order, respectively. The red or dark gray dashed and solid lines represent the phase boundary separating the FFLO and BCS states. For $\mathit{H}\perp ab$, precise determination of the phase boundary between the FFLO and the BCS states is difficult in the present experiments.