Nonlocal Magnetic Field-Tuned Quantum Criticality in Cubic ${\mathrm{CeIn}}_{3-x}{\mathrm{Sn}}_x$ ($x=0.25$)

We show that antiferromagnetism in lightly ($\approx 8\%$) Sn-doped ${\mathrm{CeIn}}_3$ terminates at a critical field ${\mu }_0{H}_{\mathrm{c}}=42\pm 2\mathrm{T}$. Electrical transport and thermodynamic measurements reveal the effective mass $m^{*}$ not to diverge, suggesting that cubic ${\mathrm{CeIn}}_3$ is representative of a critical spin-density wave (SDW) scenario, unlike the local quantum critical points reported in anisotropic systems such as ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ and ${\mathrm{YbRh}}_2{\mathrm{Si}}_{2-x}{\mathrm{Ge}}_x$. The existence of a maximum in $m^{*}$ at a lower field ${\mu }_0{H}_{\mathrm{x}}=30\pm 1\mathrm{T}$ may be interpreted as a field-induced crossover from local moment to SDW behavior as the Néel temperature falls below the Fermi temperature.

Figure 1

Temperature scale schematic of antiferromagnetic quantum criticality tuned at $g=g_{\mathrm{c}}$ according to (a) the locally critical scenario and (b) the SDW scenario. The dotted line at $g_{\mathrm{x}}$ in (b) separates regions where the antiferromagnetism is predominantly local momentlike and SDW-like. The parameter $g$ may correspond to $p$, $H$, or $x$.

Figure 2

(a) $T$, $H$ phase diagram of ${\mathrm{CeIn}}_{2.75}{\mathrm{Sn}}_{0.25}$ extracted from $C_p(T)$ (○ symbols) and $\rho (T)$ data (□ symbols) as described in the text. Grey shaded regions represent the antiferromagnetic (AFM) phase under the fitted $T_{\mathrm{N}}=T_{\mathrm{N},0}(1-(H/H_{\mathrm{c}}{)}^2)$ curve. △ symbols delineate maxima in $\partial \rho /\partial T$ which approximately delineate the Fermi temperature $T^{*}$ in the paramagnetic region. Green circles show the fitted $A^{-1/2}$ values for $n=2$ and $T\ll T^{*}$. The red dashed line represents $H_{\mathrm{c}}$, while the blue dotted line is $1/{\chi }^{\prime }=\partial H/\partial M$ approximately determined from $M_z(H)$ after smoothing and rescaling. All other lines are spline fits between data points. (b) The equivalent phase diagram versus $p$ using the available data of Knebel et al. [12]. Here the △ symbols represent $T^{*}$ of Kawasaki et al. [13].

Figure 3

(a) $C_p(T)/T$ raw data at selected magnetic fields $H$. (b) $\rho (T)$ data at selected magnetic fields. (c) The differential resistivity $\partial \rho (T)/\partial T$ obtained after polynomial smoothing the raw $\rho (T)$ data. (d) Magnetization of ${\mathrm{CeIn}}_{2.75}{\mathrm{Sn}}_{0.75}$ at 450 mK. The inset shows $\rho (T)$ at 30 T plotted versus $T^{1.4}$.

Figure 4

Coefficient $A$ for ${\mathrm{CeIn}}_{3-x}{\mathrm{Sn}}_x$ estimated from $\partial \rho (T)/\partial T$. (a) shows $A$ (filled green circles) estimated as a function of $H$ for $x=0.25$ and $n=2$ with open circles showing estimates of $A_n$ where $n$ (open blue squares) is allowed to vary in order to facilitate a comparison with similar measurements under $p$. Spline fits are draw to guide the eye. An actual plot of $\rho (T)$ versus $T^{1.4}$ at 30 T is shown in the inset of Fig. 3. (b) shows similar $A$ data for $x=0$ as a function of $p$ obtained by Knebel et al. [12].