Probing the localized to itinerant behavior of the $4f$ electron in CeIn${}_{3-x}$Sn${}_x$ by Gd${}^{3+}$ electron spin resonance

The CeIn${}_{3-x}$Sn${}_x$ cubic heavy fermion system presents an antiferromagnetic transition at $T_N=10$ K, for $x=0$, that decreases continuously down to 0 K upon Sn substitution at a critical concentration of $x_c\approx 0.65$. In the vicinity of $T_N\to 0$ the system shows non-Fermi liquid behavior due to antiferromagnetic critical fluctuations. For a high Sn content, $x\gtrsim 2.2$, intermediate valence effects are present. In this work we show that Gd${}^{3+}$-doped electron spin resonance (ESR) probes a change in the character of the Ce 4$f$ electron, as a function of Sn substitution. The Gd${}^{3+}$ ESR results indicate a transition of the Ce 4$f$ spin behavior from localized to itinerant. Near the quantum critical point, on the antiferromagnetic side of the magnetic phase diagram, both localized and itinerant behaviors coexist.

Figure 1

Gd${}^{3+}$ in Ce${}_{1-y}$Gd${}_y$In${}_{3-x}$Sn${}_x$. (a) Cubic lattice parameter $a$ dependance as a function of $x$. The dashed line represents the Vegard law.[5] For $x=3$ the departure of linear behavior is due to the Ce ion intermediate valence effects for $x\gtrsim 2.2$.[4] (b) Low-temperature dependence of $\chi \left(T\right)$ at $H=2.5$ kOe. Solid lines are the Curie-Weiss fitting. Filled symbols identify single-crystalline samples; open circles, polycrystals.

Figure 2

Gd${}^{3+}$ ESR powder spectra in Ce${}_{1-y}$Gd${}_y$In${}_{3-x}$Sn${}_x$ for $y\sim 0.5$$\%$, at $T\approx 10$ K, emphasizing the resonance region. Solid lines are the single Dysonian line-shape analysis. For Ce${}_{0.996}$Gd${}_{0.004}$In${}_3$ the spin Hamiltonian model discussed in Ref. 14 for powder was used.[15] Background contribution is present for the $x=0.5$ and $x=0.7$ samples (see text). Filled symbols identify single-crystalline samples; open circles, polycrystals.

Figure 3

Temperature dependence of the Gd${}^{3+}$ ESR line width in Ce${}_{1-y}$Gd${}_y$In${}_{3-x}$Sn${}_x$. Solid lines are the best fit to $\Delta H-\Delta H_0=bT$. A deviation from the linear dependence of $\Delta H$ at low temperatures is seen for $x=1.5$, which is related to short-range Gd-Gd interaction. Filled symbols identify single-crystalline samples; open circles, polycrystals.

Figure 4

Gd${}^{3+}$ ESR in Ce${}_{1-y}$Gd${}_y$In${}_{3-x}$Sn${}_x$. (a) Line-width thermal broadening $b$ and $g$ shift evolution. The dash-dotted line marks $\Delta g=0$. (b) Sommerfeld coefficient $\gamma$ and residual line-width $\Delta H_0$ evolution. For comparison, the Gd${}^{3+}$ ESR in La${}_{1-y}$Gd${}_y$In${}_{3-x}$Sn${}_x$ data are also shown.[12] Dashed and dotted spline lines are guides for the eye.

Figure 5

(a) Gd${}^{3+}$ ESR powder spectra in Ce${}_{0.990}$Gd${}_{0.010}$In${}_{2.5}$Sn${}_{0.5}$, at $T\approx 10$ K. Solid lines are the single Dysonian line-shape analysis for two field range fittings. (b) Temperature dependence of the Gd${}^{3+}$ ESR line width for the two field ranges shown in (a). Solid lines are the best fit to $\Delta H=\Delta H_0+bT$. (c) $g$-value temperature dependence of the Gd${}^{3+}$ ESR for the two field ranges shown in (a). The dashed line is the $g$ value for Gd${}^{3+}$ ESR in insulators.

Figure 6

(a) Gd${}^{3+}$ ESR powder spectra in Ce${}_{0.995}$Gd${}_{0.005}$In${}_{2.3}$Sn${}_{0.7}$, at $T\approx 10$ K, for three samples with the same Sn concentration. Solid lines are the single Dysonian line-shape analysis. (b) Temperature dependence of the Gd${}^{3+}$ ESR line width for the three samples shown in (a). Solid lines are the best fit to $\Delta H=\Delta H_0+bT$. Inset: Low-temperature $g$-value dependence of the Gd${}^{3+}$ ESR for the three samples shown in (a). The dashed line is the $g$ value for Gd${}^{3+}$ ESR in insulators.

Figure 7

Effective exchange interaction parameter evolution as a function of Sn substitution. Data for LaIn${}_{3-x}$Sn${}_x$ compounds are taken from Ref. 12. The AFM temperature transition $T_N$ evolution and the non-Fermi-liquid (NFL) region in the vicinity of the critical Sn concentration $x_c$ are also shown.[5] For CeIn${}_{3-x}$Sn${}_x$ one can identify the presence of only the localized (Loc.) spin behavior for $x=0$ and the itinerant (It.) character for $x⩾0.7$, since only a single-band effective exchange interaction is probed in each case. At $x=0.5$, near the quantum critical point, Gd${}^{3+}$ ESR probes both localized and itinerant components of the Ce 4$f$ electron. Shaded areas and spline lines are guides for the eye.