Role of $f-d$ exchange interaction and Kondo scattering in the Nd-doped pyrochlore iridate ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$

We report a study of magnetization, resistivity, magnetoresistance, and specific heat of the pyrochlore iridate ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ with $x=0.0$, 0.5 and 1.0, where spin-orbit coupling, electronic correlation, magnetic frustration, and Kondo scattering coexist. The metal insulator transition temperature ($T_{MI}$) decreases with increase in Nd content, but always coincides with the magnetic irreversibility temperature (field-induced moment). Resistivity below $T_{MI}$ does not fit with either activated (gap) or any power-law (gapless) dependence. The Curie constant shows the surprising result that Nd induces singlet correlation (reduction of paramoment) in the Ir sublattice. Magnetoresistance is negative at low temperatures below 10 K and increases strongly with increase in $x$, and varies quadratically with field switching over to a linear dependence above 50 kOe. Low-temperature specific heat shows a Schottky peak, coming from Nd moments, showing the existence of a doublet split in the Nd energy level, arising from the $f-d$ exchange interaction. All materials show the presence of a linear specific heat in the insulating region. The coefficient of linear specific heat for $x=0.0$ does not vary with the external magnetic field, but varies superlinearly for $x=1.0$ materials. We argue that linear specific heat probably rules out weakly correlated phases such as Weyl fermions. We propose that with the introduction of Nd at the Eu site, the system evolves from a chiral spin liquid with gapless spinon excitations with a very small charge gap to a Kondo-type interaction superposed on a chiral spin liquid coexisting with long-range antiferromagnetic ordering. A huge increase of magnetoresistance with increase in Nd concentrations shows the importance of Kondo scattering in the chiral spin-liquid material by rare-earth moments.

Figure 1

Room-temperature x-ray diffraction pattern for the sample ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=0$, 0.5, 1.0, and red, orange, and black stars indicate the impurity phase due to nonreacting ${\mathrm{IrO}}_2, {\mathrm{Eu}}_2{\mathrm{O}}_3$, and ${\mathrm{Nd}}_2{\mathrm{O}}_3$, respectively. Inset: Rietveld refinement for an $x=0.0$ compound, where scattered data are observed and the solid line is a fit to the data.

Figure 2

(a) Temperature-dependent resistivity measured with the temperature range 3.8–300 K. (b) Fitting of resistivity below the MIT for the compounds ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=0$, 0.5, and 1.0. Inset: Variation of the charge gap ($E$) with temperature for all the samples.

Figure 3

(a)–(c) Temperature-dependent magnetization measured at 1 kOe in the ZFC FC protocol for ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=0$, 0.5, 1.0, and the dotted line for the $x=0$ compound represents Van Vleck susceptibility ${\chi }_{VV}$ of the ${\mathrm{Eu}}^{3+}$ ion.

Figure 4

(a)–(c) Temperature-dependent inverse susceptibility and (d) isothermal magnetization at 3 K for ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=0$, 0.5, and 1.0.

Figure 5

(a) Magnetic field dependent MR for ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=0$, 0.5, and 1.0, at 3 K with field $-90$ to $+90$ kOe. Inset: close view of the field dependent MR for $x=0.0$. (b), (c) Magnetic field dependent MR for the $x=0.5$ and 1.0 compounds at different temperatures.

Figure 6

Different magnetic field cycling MR at 5 K for the compound ${\left({\mathrm{Eu}}_{1-x}{\mathrm{Nd}}_x\right)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where $x=1.0$.

Figure 7

(a)–(c) Zero field specific heat ($C/T$) as a function of temperature between different temperature ranges for the $x=0.0$, 0.5, and 1.0 compound, respectively, and the solid lines are the fitting data. The inset in (a) shows $C/T$ vs $T^2$ data at low temperature for the $x=0.0$ compound. (d) Variation of $\gamma$ with Nd doping.

Figure 8

(a) $C/T$ vs $T^2$ data with different field for the $x=0.0$ compound with fitting. (b) Magnetic field dependent specific heat as a function of temperature for the $x=1.0$ compound. Inset: Field dependent $\gamma$.