Magnetic-Field-Induced Lattice Anomaly inside the Superconducting State of ${\mathrm{CeCoIn}}_5$: Anisotropic Evidence of the Possible Fulde-Ferrell-Larkin-Ovchinnikov State

We report high magnetic field linear magnetostriction experiments on ${\mathrm{CeCoIn}}_5$ single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field $B_{c2}$ that becomes less pronounced as the temperature increases and (ii) a distinctive second orderlike feature observed only along the $c$ axis in the high field ($10\mathrm{T}\lesssim B\le B_{c2}$) low temperature ($T\lesssim 0.35\mathrm{K}$) region. This second order transition is observed only when the magnetic field lies within 20° of the $ab$ planes and there is no signature of it above $B_{c2}$, which raises questions regarding its interpretation as a field induced magnetically ordered phase. Good agreement with previous results suggests that this anomaly is related to the transition to a possible Fulde-Ferrel-Larkin-Ovchinnikov superconducting state.

Figure 1

(a) Linear $c$-axis magnetostriction vs field at $T\approx 30\mathrm{mK}$ for different directions of the applied magnetic field. The angle is measured from the $ab$ plane. Inset: $ab$-plane linear magnetostriction. (b) $c$-axis magnetostriction coefficient $\lambda =\frac{1}{L}(\frac{\partial L}{\partial B})$. The arrows denote the transition to a possible FFLO state. Inset: sketch of the experimental configuration. Curves have been vertically shifted.

Figure 2

(a) Linear $c$-axis magnetostriction vs field at different temperatures. The magnetic field lies along the $ab$ planes. (b) $c$-axis magnetostriction coefficient. Curves have been vertically shifted.

Figure 3

(a) Magnetic field vs temperature ($B\parallel ab$ planes) and (b) magnetic field vs angle $T\approx 30\mathrm{mK}$ phase diagrams. $B_{c2}$ is determined from the peak position and $B_{\mathrm{FFLO}}$ from the higher kink at which the slope of $\lambda$ changes. The lines are guides to the eye.