Field Evolution of Coexisting Superconducting and Magnetic Orders in ${\mathrm{CeCoIn}}_5$

We present nuclear magnetic resonance (NMR) measurements on the three distinct In sites of ${\mathrm{CeCoIn}}_5$ with a magnetic field applied in the [100] direction. We identify the microscopic nature of the long range magnetic order (LRO) stabilized at low temperatures in fields above 10.2 T while still in the superconducting (SC) state. We infer that the ordered moment is oriented along the $\widehat{c}$ axis and map its field evolution. The study of the field dependence of the NMR shift for the different In sites indicates that the LRO likely coexists with a modulated SC phase, possibly that predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. Furthermore, we discern a field region dominated by strong spin fluctuations where static LRO is absent and propose a revised phase diagram.

Figure 1

NMR spectra of (a) $\mathrm{In}(1),\mathrm{In}(2_{ac})$ and (b) $\mathrm{In}(2_{bc})$ at $T=70\mathrm{mK}$ for various ${\mathbf{H}}_0\parallel \widehat{a}$. The frequency scale is defined by subtracting ${\omega }_0$, the zero NMR shift frequency. N denotes the normal phase, IC the LRO phase, ESC the state with strong fluctuations, and LFSC the Abrikosov SC state. Solid lines in (a) are simulated spectra for the IC-SDW order described in the text.

Figure 2

Magnetic moment as a function of $H_0$ deduced from $\Delta f$ at $T\approx 70\mathrm{mK}$. The double arrow denotes the region of $H_0$ within which LRO is absent but spectra remain much broader than in the LFSC state.

Figure 3

NMR shift (spin part, $K_s$, and constant orbital part, $K_{\mathrm{orb}}$ [10]) of In(1), $\mathrm{In}(2_{ac})$, and $\mathrm{In}(2_{bc})$ at $T\approx 70\mathrm{mK}$ as a function of ${\mathbf{H}}_0\parallel \widehat{a}$. The solid lines indicate the values of $H^{*}$ and $H_{c2}$.

Figure 4

A sketch of an alternative phase diagram of ${\mathrm{CeCoIn}}_5$ (data points adopted from Ref. 9). The solid line and the dashed line indicate first and second order phase transitions, respectively.