Tuning the magnetic ground state of ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ by Yb valence fluctuations

We characterize the properties of ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ single crystals with $0\le x\le 1$ using measurements of powder x-ray diffraction, energy dispersive x-ray spectroscopy, electrical resistivity, magnetic susceptibility, specific heat, x-ray absorption near edge structure (XANES), and neutron diffraction. The Yb valence $v_{\text{Yb}}$, calculated from the magnetic susceptibility and measured using XANES, decreases from $3+$ at $x=0$ to $\sim 2.1+$ at $x_{\mathrm{act}}=0.2$, where $x_{\mathrm{act}}$ is the measured Yb concentration. A transition from incommensurate to commensurate antiferromagnetism is observed in neutron diffraction measurements along $Q=(0.5,0.5,l)$ between $0.2\le x_{\mathrm{act}}\le 0.27$; this narrative is supported by specific-heat measurements in which a second robust feature appears at a temperature $T_I\left(T_I<T_N\right)$ for the same concentration range. Magnetic susceptibility measurements also reveal features which provide additional evidence of magnetic ordering. The results of this study suggest that the evolution of the Yb valence plays a critical role in tuning the magnetic ground state of ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$.

Figure 1

A representative XRD pattern for the $x=0.17$ sample is plotted. The expected Bragg peak positions are indicated with small ticks above the labeled $2\theta$ axis. The calculated fit from Rietveld refinement is plotted as the top (red) curve and the deviation from the fit is shown as the bottom (black) curve above the Bragg peak indicators. The inset illustrates differences in the XRD patterns for different Yb concentrations over a narrow window of $2\theta$. The peaks shift slightly between $x=0.03$ and $0.17$, and then shift significantly for $x=0.9$.

Figure 2

(a) Unit-cell volumes, plotted as a function of $x_{\mathrm{nom}}$, calculated from XRD and neutron diffraction measurements on single-crystal and polycrystalline samples. A linear extrapolation representing Vegard's law between the two parent compounds is shown as a guide to the eye; the horizontal (black) arrow emphasizes the discrepancy between the measured behavior of $V\left(x\right)$ and the Vegard's law construction. Plotted in the inset are the lattice parameters $a$ and $c$ vs $x_{\mathrm{nom}}$. (b) Comparison between the nominal and actual Yb concentrations determined from EDS, TXAS, and XRD measurements. A dashed line is drawn with slope $x_{\mathrm{act}}=x_{\mathrm{nom}}/3$, which fits the single-crystal data well for concentrations $x_{\mathrm{nom}}<0.7$. For higher concentrations, the data deviate from this line and approach the $x_{\mathrm{act}}=x_{\mathrm{nom}}$ line. The results from EDS and XRD measurements on polycrystalline samples fit the expected relation shown by the line $x_{\mathrm{act}}=x_{\mathrm{nom}}$. Error bars where indicated represent one standard deviation throughout the paper. These analyses establish a relationship between $x_{\mathrm{act}}$ and $x_{\mathrm{nom}}$, ensuring that all subsequent discussions of Yb concentration can be limited to the actual concentration, such that $x=x_{\mathrm{act}}$, unless otherwise stated.

Figure 3

Un-normalized XANES data for Yb, Ce, and Rh. (a) Shows the Ce $L_{\mathrm{III}}$ XANES for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ where $x=0.03$ is the top black line, followed by $x=0.1$ as the red intermediate line, and $x=0.17$ as the lower blue line. (b) The Yb $L_{\mathrm{III}}$ XANES, and (c) the Rh $K$ XANES are shown for the same concentrations. All data were collected at $T=200$ K and the “pre-edge” has been subtracted from the data.

Figure 4

Measured Yb $L_{\mathrm{III}}$ edge data for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ are plotted as black circles. The fit to the two-edge model is shown as the red solid line, while the dashed green line represents the contribution from ${\mathrm{Yb}}^{2+}$, and the dashed blue line represents the contribution from ${\mathrm{Yb}}^{3+}$. The results are shown over the same energy ranges for $x=0.03$, 0.1, and 0.17 in panels (a), (b), and (c), respectively.

Figure 5

Electrical resistivity data for selected samples of ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$, normalized by electrical resistivity values measured at 200 K. The Kondo coherence feature for samples is observed near 25 K. (Inset) Example of $T^{*}$ being calculated for the $x=0.2$ sample.

Figure 6

The characteristic Kondo coherence temperature $T^{*}$ and $\rho \left(T^{*}\right)/\rho$(200 K) vs Yb concentration $x$. The Yb valence is indicated by the false (color) background $(3+$ on the green side at $x=0$ and $\sim 2.1+$ for $x>0.2)$. The Yb valence crossover at $x=0.2$ is indicated by a vertical dashed (green) line that acts as a guide to the eye. A blue dashed curve shows the progression of both $T^{*}$ and $\rho \left(T^{*}\right)/\rho$(200 K) as a function of $x$.

Figure 7

Calculated RRR values from $\rho \left(T\right)$ plotted vs $x_{\mathrm{nom}}$ for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$. At $x_{\mathrm{nom}}=0$, the RRR $\approx 150$. As Yb is introduced, the RRR drops precipitously. For the pure ${\mathrm{YbRhIn}}_5$ compound, the RRR increases to above 110, suggesting that substituted samples are likely to yield low RRR values, potentially related to the issues raised regarding synthesis in the range $x_{\mathrm{nom}}>0.8$ discussed in the text.

Figure 8

(a) Magnetic susceptibility measured in an applied magnetic field of ${\mu }_{0}H=0.5$ T along the $ab$ plane is plotted from 0 to 300 K. The inset shows data for $0\le T\le 20$ K where a black, dotted line is drawn through an inflection point, which is a signature of the AFM transition. The maximum value of magnetic susceptibility decreases with $x$. The temperature of the maximum is denoted $T_M$ and is shown by the dashed-dotted line. Due to a low-$T$ upturn in the magnetic susceptibility for $x=0.27,T_N$ is difficult to define, and thus not indicated with the dashed line. (b) Magnetic susceptibility data measured with magnetic field applied along the $c$ axis are plotted from 0 to 300 K. For this orientation, only some concentrations exhibit a clear feature at low temperature associated with AFM ordering; other concentrations are dominated by an upturn in this temperature range. The inset shows the ratio ${\chi }_{ab}/{\chi }_c$ at 10 K, which is above the AFM transition but below the temperature range exhibiting Curie-Weiss behavior. The values of ${\chi }_{ab}/{\chi }_c$ are scattered about 0.5 over the range of concentrations measured.

Figure 9

(a) Inverse magnetic susceptibility ${\chi }_{ab}^{-1}$, plotted for temperatures up to 300 K, exhibits linear Curie-Weiss behavior at high temperatures. (b) The effective magnetic moment ${\mu }_{\mathrm{eff}}$ for $x<0.33$ was calculated from the $c$-axis measurements and is plotted as a function of $x$. Dashed curves indicate theoretical calculations for ${\mu }_{\mathrm{eff}}$ in ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ assuming Yb valences of ${\mathrm{Yb}}^{2+}$ and ${\mathrm{Yb}}^{3+}$.

Figure 10

(a) Specific heat divided by temperature $C/T$, plotted as a function of temperature $T$. (b) $C/T$ plotted as a function of $T^2$ for selected concentrations; the linear region of data in the temperature range $T>T_N$ obeys the relationship $C/T\simeq \gamma +\beta T^2$. Best-fit results are plotted as functions of actual Yb concentration $x_{\mathrm{act}}$ for (c) the Sommerfeld coefficient $\gamma$ and (d) the Debye temperature ${\mathrm{\Theta }}_D$.

Figure 11

(a) Specific heat divided by temperature $C/T$ for ${\mathrm{CeRhIn}}_5$ in applied magnetic fields ${\mu }_{0}H$ of up to 9 T; $H$ was applied parallel to both the $ab$ plane (filled circles) and along the $c$ axis (open circles). Note that data measured in different magnetic fields have been offset from one another by an amount $\delta C/T=1.0$ J/mol ${\mathrm{K}}^2$ for visual clarity. When $H\parallel c$, we observe a single feature at $T_N$ which is gradually suppressed to lower temperature with increasing $H$. When $H\parallel ab$ and ${\mu }_{0}H>3$ T, we observe a feature at $T_N$ and a magnetic-field-induced phase transition at $T_1\left(T_1<T_N\right)$. (b) $C/T$ data for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ are plotted in the vicinity of $T_N$. The data for different concentrations have been offset from one another by an amount $\delta C/T=0.5\mathrm{J}\mathrm{mol}/{\mathrm{K}}^2$ for visual clarity. A second feature emerges at temperatures $T_I<T_N$ for $x_{\mathrm{act}}>0.18$. Dashed lines are guides to the eye which emphasize the evolution of $T_N$ and $T_I$ with Yb concentration.

Figure 12

Specific-heat divided by temperature $C/T$ vs temperature $T$ for selected Yb concentrations in the system ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$: (a) $x=0$, (b) $x=0.07$, (c) $x=0.13$, and (d) $x=0.20$. For each concentration, measurements were performed in applied magnetic fields of ${\mu }_{0}H=0$, 1, 3, 5, 7, and 9 T (applied along the $ab$ plane). Data measured in different magnetic fields have been offset from one another by an amount $\delta C/T=0.5$–1 J/mol ${\mathrm{K}}^2$ for visual clarity. Two distinct features are observed in ${\mathrm{CeRhIn}}_5$ for ${\mu }_{0}H\ge 3$ T. At constant magnetic field, these features appear to merge with increasing $x$, such that a single broad feature is observed for $x=0.20$ in magnetic fields of up to 9 T.

Figure 13

Neutron diffraction measurements on the BT-4 and BT-7 triple-axis spectrometers at the NIST Center for Neutron Research. (a)–(c) The Néel temperature $T_N$ was determined for concentrations $x=0.17$, 0.2, and 0.27 by fitting the integrated intensity of a representative magnetic reflection at $Q=G+q$, where $G$ is reciprocal lattice vector, with a mean-field order-parameter function denoted by the solid line. Examples of curves for selected temperatures are shown in the inset of (a), where at the lowest temperature, the peaks were resolution limited. A shoulderlike feature is observed at a slightly lower $l$; however, no shoulder is observed in scans of the nuclear reflections which indicates a distribution of $q$ values. The inset of panel (c) demonstrates that no evidence for the incommensurate phase was observed for $x=0.27$ along the (0.5, 0.5, $l)$ direction. (d) A region of the $HHL$ zone in reciprocal space was mapped at 1.5 K for $x=0.17$. No additional magnetic reflections are present, which would suggest additional modifications to the magnetic structure. The inset of the panel (d), plotted using dave [42], shows that, in addition to the bright (110) and (002) nuclear reflections, we observed a series of peaks along (0.5, 0.5, $l)$, which are indexed using the same magnetic propagation vector, $q$.

Figure 14

(a) Yb valence vs Yb concentration $x$ over the same concentration range as the temperature $T$ vs $x$ phase diagram in the panel below. The valence was calculated from magnetic susceptibility measurements with the magnetic field in the $ab$ and $c$ orientations and from XANES measurements. (b) The $T$ vs $x$ phase diagram for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$. The Néel temperature $T_N$ is taken from measurements of the electrical resistivity, magnetic susceptibility, specific heat, and neutron diffraction. A linear fit, indicated by the dashed line, to the $T_N\left(x\right)$ data for ${\mathrm{Ce}}_{1-x}{\mathrm{Yb}}_x{\mathrm{RhIn}}_5$ extrapolates to 0 K at $x=1$. The orange region delineates incommensurate AFM order and the clear region represents commensurate AFM order.