Figure 1

(Color online) Crystal and magnetic structures of ${\text{CeRhIn}}_5$. (a) The incommensurate helical structure along the $c$ axis with $Q_i=\left(1/2,1/2,0.297\right)$ at $P=0$. (b) The commensurate antiferromagnetic structure starts to appear under $P$. In this magnetic structure, there are two magnetically different In(2) sites, as shown in this figure. One of these sites considers $H_{\text{int}}$ with a “$+$” or a “$-$” sign against the direction of $M_Q$ and the other site considers $H_{\text{int}}=0$. As discussed in Ref. 15 the $H_{\text{int}}$ at the In(2) site also originates from the direct dipolar field from the Ce magnetic moments and from the indirect “pseudodipolar” anisotropic field via the supertransferred hyperfine interaction due to the hybridization between the In-$5p$ and Ce-$4f$ orbits.Reuse & Permissions

Figure 2

(Color online) (a) The $P$ dependence of the NQR spectrum on the magnetically ordered state in ${\text{CeRhIn}}_5$ at the In(2) site (the $3{\nu }_Q$ transition). It was measured at $T=1.5\text{K}$, well below $T_N$. The dashed line at $P=0$ indicates the NQR spectra of the paramagnetic spectrum measured at $T=4.2\text{K}$. At $P=1.67\text{GPa}$, the dashed and the dotted-dashed lines indicate the simulated spectra for the commensurate AFM and the incommensurate helical order, respectively. The solid line represents the convolution of them with fractions of 0.6 and 0.4, respectively. At $P=1.86\text{GPa}$, the solid line represents a simulated spectrum for the commensurate AFM; the two peaks indicated by the dashed line represent the In(2) sites with $H_{\text{int}}=\pm 1.1\text{kG}$, which are indicated by “$+$” and “$-$” signs in Fig. 1b. The dotted line is the simulated spectrum for the In(2) site with $H_{\text{int}}=0$. (b) The spectrum of the $1{\nu }_Q$ transition at the In(1) site, $T=0.2\text{K}$, and $P=1.62\text{GPa}$. The spectrum is well simulated similar to that at In(2) at $P=1.67\text{GPa}$ in (a). (c) The spectrum of the $1{\nu }_Q$ transition at the In(1) site, $T=0.6\text{K}$, and $P=1.27\text{GPa}$. The spectrum in the paramagnetic state at 4.2 K is indicated by the dashed line.Reuse & Permissions

Figure 3

(Color online) (a) The phase diagram of ${\text{CeRhIn}}_5$. $T_N$ (triangles) and $T_c$ (solid circles and encircled crosses) are determined from the In-NQR-$1/T_1$ measurement. The encircled cross indicates $T_c$ for the incommensurate AFM. The $P$ dependence of $T_c$ (diamonds) is determined from the susceptibility measurement performed using a single crystal (Ref. 18). The open circle indicates $T_c$ obtained from the specific-heat measurements (Ref. 4). The solid lines are guides to the eyes. $P_{\text{tetra}}$ indicates the pressure at the tetracritical point separating AFM, $\text{AFM}+\text{S}$, SC, and PM phases. AFM-QCP points to the quantum critical point at which the AFM collapses. The commensurate AFM is completely realized at $P_m$. (b) The $P$ dependences of ${\text{VF}}_c$ (triangles) and the SC diamagnetism extrapolated to $T=0$ (circles). The open triangle at 1.62 GPa is estimated from the analysis of the spectrum at the In(1) site, as shown in Fig. 2b. The solid lines are guides to the eyes. (c) The $P$ dependences of $H_{\text{int}}$ on the In(2) sites for the incommensurate AFM (△) and the commensurate AFM (▲) along with those of $M_Q$ ($\ast$ and $☆$) obtained from neutron-scattering experiments (Refs 9, 11). $H_{\text{int}}$ and $M_Q$ data are normalized at $P=0$ [$H_{\text{int}}=2.5\text{kOe}$ and $M_Q\sim 0.8{\mu }_B$ $(*)$ or $0.6{\mu }_B$ $(☆)$]. The energy gap $2{\Delta }_0/k_B{T}_c$ as a function of $P$ is estimated from a decreasing rate in $1/T_1$ below $T_c\left(●\right)$ and the specific-heat jump at $T_c\left(○\right)$ using the relation $\Delta C=-D\left(E_F\right)\frac{d{\Delta }^2\left(T\right)}{dT}{\mid }_{T=T_c}$ (Ref. 4). Here, the values of $2{\Delta }_0/k_B{T}_c$ obtained from the specific-heat measurements are normalized as they fit the values obtained from the NQR measurements between 2.1 and 2.5 GPa. The solid lines are guides to the eyes.Reuse & Permissions

Figure 4

(Color online) The $T$ dependences of ${\left(T_{1}T\right)}^{-1}$ at pressures above 1.51 GPa. For clarity, note that the ${\left(T_{1}T\right)}^{-1}$ data at 1.82, 2.05, and 2.35 GPa are divided by 3, 9, and 18, respectively. The solid and the dashed arrows indicate $T_N$ and $T_c$, respectively. The solid curves represent fitting curves with parameters $2{\Delta }_0/k_B{T}_c$ and RDOS (see text).Reuse & Permissions

Figure 5

(Color online) (a) The $T$ dependences of ${\left(T_{1}T\right)}^{-1}$ on the In(1) site for $P=0$, 0.52, and 1.27 GPa. The inset shows the $T$ dependences of ${\left(T_{1}T\right)}^{-1}$ for $P=1.27$ and 1.51 GPa. (b) The $T$ dependences of the ac susceptibility between $P=0\text{GPa}$ and 2.05 GPa obtained by using the in situ NQR coil. The ac susceptibility is normalized by its value at 2.4 K for each pressure. The fact that the ac susceptibility at $T=0$ is saturated above $P_m$ suggests that the full SC diamagnetism is realized above $P_m$.Reuse & Permissions