Magnetic-Field-Induced Enhancements of Nuclear Spin-Lattice Relaxation Rates in the Heavy-Fermion Superconductor ${\mathrm{CeCoIn}}_5$ Using ${}^{59}\mathrm{Co}$ Nuclear Magnetic Resonance

${}^{59}\mathrm{Co}$ nuclear spin-lattice relaxation has been measured for the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ in a range of applied fields directed parallel to the $c$ axis. An enhanced normal-state relaxation rate, observed at low temperatures and fields just above $H_{c2}(0)$, is taken as a direct measure of the dynamical susceptibility and provides microscopic evidence for an antiferromagnetic instability. The results are well described using the self-consistent renormalized theory for two-dimensional antiferromagnetic spin fluctuations, and parameters obtained in the analysis are applied to previously reported specific heat and thermal expansion data with good agreement.

Figure 1

$(T_{1}T{)}^{-1}$ for ${}^{59}\mathrm{Co}$ NMR at several fields along the $c$ axis of ${\mathrm{CeCoIn}}_5$. The broken lines are the data under $H_0=50\mathrm{kOe}$ along the $a$ axis. The results for 11 kOe along the $c$ axis are taken from Ref. 19. The inset shows the temperature dependence of Knight shifts ($K$) for ${}^{59}\mathrm{Co}$ NMR at several fields along the $c$ axis of ${\mathrm{CeCoIn}}_5$.

Figure 2

Field dependence of (a) $y_0$, (b) $y_1$, (c) $T_0$ and $T_A$ obtained from the SCR analysis of ${}^{59}\mathrm{Co}$ NMR and the specific heat for ${\mathrm{CeCoIn}}_5$ in the case of $H_0\parallel c$. The schematic phase diagram for ${\mathrm{CeCoIn}}_5$ is superimposed in the top-left panel, where a field-induced ($H\mathrm{\text{−}}I$) phase is apparent just below $H_{c2}(0)$ [6]. To show the fitting results, the data and fitted curves are plotted for (d) the normalized nuclear relaxation rates $(T_{1}T{)}^{-1}$ by $({\gamma }_{n}A{)}^2$ which are subtracted by the values for ${\mathrm{LaCoIn}}_5$ [19] and (e) the magnetic specific heat $C_m/T$ under several fields along $c$ axis. The data for specific heat are taken from Ref. 13. (f) The linear thermal expansion coefficient $\alpha$, from Ref. 14, and SCR curves drawn by using the same parameters obtained from NMR data at 50 and 80 kOe.

Figure 3

Temperature dependence of (a) magnetic correlation length $\xi /a$ and (b) spin fluctuation energy ${\Gamma }_Q$ derived from a SCR analysis of ${\mathrm{CeCoIn}}_5$ at 50, 64, and 80 kOe. The broken line in (a) indicates an estimate from inelastic neutron scattering (INS) at zero field. The closed circles in (b) are $\Gamma$ at $\mathit{Q}=(1/2,1/2,1/2)$ obtained by INS at zero field. These data are divided by $\sqrt{3}$ to compare the in-plane component.