Ultralow temperature NMR of ${\mathrm{CeCoIn}}_5$

We have performed ${}^{59}\mathrm{Co}$ NMR measurements of ${\mathrm{CeCoIn}}_5$ down to ultralow temperatures. We find that the temperature dependence of the spin-echo intensity provides a good measure of the sample temperature, enabling us to determine a pulse condition not heating up the sample by the NMR pulses down to ultralow temperatures. From the longitudinal relaxation time ($T_1$) measurements at 5 T applied along the $c$ axis, a pronounced peak in $1/T_{1}T$ is observed at 20 mK, implying an appearance of magnetic order as suggested by the recent quantum oscillation measurements [H. Shishido et al., Phys. Rev. Lett. 120, 177201 (2018)]. On the other hand, the NMR spectrum shows no change below 20 mK. Moreover, the peak in $1/T_{1}T$ disappears at 6 and 8 T in contrast to the results of the quantum oscillation. We discuss that an antiferromagnetic state with a moment lying in the $a-b$ plane can be a possible origin for the peak in $1/T_{1}T$ at 5 T.

Figure 1

(a) A picture of the sample with a silver wire (100 $\mu \mathrm{m}$ diameter) soldered by indium. The sample size is 1.1 mm $\times$ 1.0 mm $\times$ 0.1 mm. (b) Cu wires were wound around the sample for NMR measurements. The silver wire was thermally anchored to the cryostat.

Figure 2

(a) Crystal structure of ${\mathrm{CeCoIn}}_5$. (b) NMR spectrum taken at 1.7 K and 8 T ($H\parallel c$). Seven absorption peaks corresponding to ${}^{59}\mathrm{Co}$ ($I=7/2$) were clearly observed. Note that a ${}^{115}\mathrm{In}$ NMR signal from the In(1) site is merged with the first quadrupole-satellite peak at the higher-frequency side. (c) The calculated temperature dependence of the spin-echo intensity of the center line at different fields. Each curve is normalized by the peak value.

Figure 3

The temperature dependence of the spin-echo intensity at 5, 8, and 12 T. The solid line shows the Boltzmann curve [Eq. (1)] for each temperature. The error bars represent $\pm \sigma$, where $\sigma$ is one standard deviation of the data.

Figure 4

(a) Recovery curve of the magnetization $M\left(t\right)$ divided by the saturation value $M_{\text{sat}}$ at 5 T and 10 mK. The solid line shows a fit for the central transition of the nuclear spin 7/2. (b) The temperature dependence of $1/T_{1}T$ at 5, 6, and 8 T. The data of the previous work are taken from Ref. [27] (5 T) and Ref. [22] (8 T). The error bars represent $\pm \sigma$, where $\sigma$ is one standard deviation of the fitting of the recovery curve by Eq. (3). To show the overlapped data points at 5 T, all the data at 5 T are listed in Table 1. (c) Comparison of recovery curves at 5 T at different temperatures. To compare $T_{1}T$, rather than $T_1$, at different temperatures, the data are plotted as a function of the product of the delay time ($t$) and the temperature.

Figure 5

The NMR spectrum of ${}^{59}\mathrm{Co}$ center peak at 5.0 and 30 mK.

Figure 6

Proposed magnetic structures of ${\mathrm{CeCoIn}}_5$ below 20 mK with an incommensurate $Q_{\text{IC}}$ (a) and a commensurate $Q_{\text{C}}$ (b) by reference to that of ${\mathrm{CeRhIn}}_5$ under pressure [30]. The magnetic moments are suggested to be in-plane. Inequivalent In(2) sites for $Q_{\text{C}}$ are marked by solid circles with different colors in (b).

Figure 7

(a) An illustration of the NMR pulse sequence consisting of the first and second pulses of the width of $t_{\text{1st}}$ and $t_{\text{2nd}}$, and the amplitude $V_{\text{pls}}$. A spin-echo signal is observed at $2\tau$ after the first pulse, where $\tau$ is the interval time between the first and the second pulses. This sequence is repeated with the repetition time ($t_{\text{rp}}$). The spin-echo decay by the transverse relaxation on the timescale of $T_2$ is illustrated by the dashed line. (b) The time dependencies of various temperatures; the temperature of the cryostat ($T_{\text{Cryostat}}$, gray), the electrons ($T_{\text{ele}}$, blue), and the nuclear spins ($T_{\text{Ncl}}$, pink) are shown. The solid (dashed) lines show the case that the sample is heated up (not heated up) by the NMR pulse. Timescales of the longitudinal relaxation of the nuclear spins ($T_1$) and the thermal relaxation of the electron system ($t_{\text{rlx}}$) are also indicated by the arrows. Because of the repetition sequence, the effective temperature of the nuclear spins ($T_{\text{eff}}$, filled circles), where the NMR signals are accumulated, is affected by $t_{\text{rp}}$. Spin-echo signal is observed at a higher $T_{\text{eff}}$ (thus with a smaller spin-echo intensity) for a shorter $t_{\text{rp}}$ when the $T_{\text{ele}}$ is increased (open circles on the solid line). On the other hand, there is no repetition time dependence when the heating is negligible (open circles on the dashed line).

Figure 8

Repetition time dependence of the spin-echo intensity at 21.8 mK and 5 T. The data are normalized by the intensity at the longest repetition time. The signal becomes smaller at a shorter repetition time when a large pulse power is applied to the NMR circuit.

Figure 9

(a) The dependence of the spin-echo intensity on the interval time between the first and the second pulses ($\tau$) at different temperatures. The data are normalized by the value at $\tau =0$. The data of ${}^{59}\mathrm{Co}$ and ${}^{115}\mathrm{In}$ NMR at the In(2) site are shown by circles and diamonds, respectively. Each solid line shows a fit by $I_{\text{SE}}(T,2\tau )=I_{\text{SE}}\left(T\right)exp\left\{-{(2\tau /T_2)}^2\right\}$. (b) The temperature dependence of $1/T_2$ of ${}^{59}\mathrm{Co}$ at 5, 8, and 12 T. The dashed lines show a guide to the eyes.

Figure 10

The temperature dependence of $I_{\text{SE}}$ at 5 T calculated for all NMR absorption in ${}^{59}\mathrm{Co}$ ($I=7/2$) by using Eq. (1). The data are normalized by $I_{\text{SE}}$ of the center peak.