Universal scaling behavior under pressure in the heavy-fermion antiferromagnet ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$: ${}^{29}\mathrm{Si}$ NMR study

The microscopic origin of a magnetic phase diagram under pressure in the heavy-fermion antiferromagnet ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ was investigated using the ${}^{29}\mathrm{Si}$ nuclear magnetic resonance (NMR) technique. Owing to the characteristics of the hyperfine form factor at the Si site, which filters specific $\mathit{q}$-dependent fluctuations around antiferromagnetic $\mathit{q}$ vectors, we investigated the temperature and pressure dependences of $\mathit{q}$-independent local fluctuations caused by the single-site Kondo effect. A universal scaling behavior observed on the energy scale of the local fluctuations in the entire pressure region demonstrates that the characteristic energy scale $T_0$ of Kondo interactions monotonically increases by applying pressure without a critical anomaly around the quantum critical pressure $P_{\mathrm{c}}$ of antiferromagnetism. Our NMR result agrees with the Doniach picture of the heavy-fermion phase diagram, where the progressive delocalization of the $f$ electrons occurs across $P_{\mathrm{c}}$, accompanied by the development of antiferromagnetic correlations among the $f$ electrons.

Figure 1

(a) Crystal structure of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$. (b) Two types of local environments of the Si sites in the $4\mathit{q}$-magnetic structure, where the Rh atoms are excluded for simplicity.

Figure 2

Temperature dependence of ${}^{29}\mathrm{Si}$ NMR shifts in ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under various applied pressures for (a) $H_0\parallel c$ and (b) $H_0\parallel a$.

Figure 3

${}^{29}\mathrm{Si}$ NMR spectra of a single crystal of ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ enriched with 50% ${}^{29}\mathrm{Si}$ at a constant field of $H_0\sim$ 72.1 kOe along (a) the $c$ axis and (b) $a$ axis at temperatures of 40 K (above $T_{\mathrm{N}1}$), 30 K (below $T_{\mathrm{N}1}$), and 4.5 K (below $T_{\mathrm{N}2}$).

Figure 4

Pressure dependence of transferred hyperfine coupling constants $A_i$ ($i=c$ and $a$) for ${}^{29}\mathrm{Si}$ in ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$.

Figure 5

(a) ${}^{29}\mathrm{Si}$ NMR spectra with an external field of $H_0=38.2$ kOe at $T=15$, 12, and 1.52 K under $P=1.08$ GPa and at $T=1.52$ K under $P=1.25$ GPa. (b) Temperature dependence of the NMR line split $\mathrm{\Delta }{\nu }_{\mathrm{A}}$ under various pressures. The solid curves are drawn to guide the eyes. (c) $T\text{−}P$ phase diagram for ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$. The open and solid circles represent $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ determined using the NMR experiment. The pressure dependence of the NMR line split $\mathrm{\Delta }{\nu }_{\mathrm{A}}$ at 1.5 K is also plotted. The AFM transition temperatures of $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ (open and solid squares) determined using neutron diffraction in Ref. [23] and resistivity (open and solid triangles) in Ref. [12] are also plotted.

Figure 6

(a) Temperature dependence of ${\left(T_{1}T\right)}^{-1}$ for ${}^{29}\mathrm{Si}$ NMR in ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ at ambient pressure when applying an external field of 72.1 kOe parallel to the respective crystallographic axis of $c$ and $a$. Pressure variations of ${\left(T_{1}T\right)}^{-1}$ in the PM state are shown for (b) $H_0\parallel c$ and (c) $H_0\parallel a$.

Figure 7

(a) $R_c/{\left({\gamma }_n{A}_c\right)}^2$ vs $T$ and (b) $R_a/{\left({\gamma }_n{A}_a\right)}^2$ vs $T$ plots for several pressures determined from ${}^{29}\mathrm{Si}$ NMR relaxation rates in ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$.

Figure 8

$\frac{1}{2}{\mathrm{\Gamma }}_{0,c}\left(T\right)/T_0$ vs $T/T_0$ plot for the data in ${\mathrm{CeRh}}_2{\mathrm{Si}}_2$ under various pressures. The dotted curve represents the universal curve calculated for independently screened local moments based on a single Kondo impurity model [39]. The inset shows the temperature dependence of ${\mathrm{\Gamma }}_{0,c}$ at various pressures. The solid curve represents the $\sqrt{T}$ dependence. The legend for the symbols is the same for the inset and main panel.

Figure 9

Pressure dependence of $T_0$ and $T_{\mathrm{FL}}$ in the $T\text{−}P$ phase diagram. $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ (open and solid squares) determined using neutron diffraction in Ref. [23] and resistivity (open and solid triangles) in Ref. [12] are also plotted.