Physical Properties of Cd Doped CeIrIn 5 under Pressure

We measured the electrical resistivity ρ of CeIr(In1-xCdx)5 under pressure for x = 0.05 and 0.10, which show the onset of superconductivity (SC) at Tsc ~ 0.9 K and antiferromagnetic transition at TN ~ 3.4 K. For x = 0.05, Tsc increases by applying pressure up to 2.8 GPa and zero resistivity is observed at Tsc above 2.4 GPa. For x = 0.10, the pressure dependence of TN shows peak at around 2 GPa and TN seems to be 0 K toward 3 GPa, where SC phase appears. The maximum value of Tsc is independent on amount of doped Cd, showing 1.35 K. We analyzed the temperature dependence of the electrical resistivity ρ for x = 0.05 and 0.10 under pressure using the following equation, ρ = ρ0 + AT . This analysis revealed that ρ shows the sublinear temperature dependence (n < 1) in the wide temperature region above Tsc, and ρ0 decreases abruptly in the pressure region where Tsc indicates a maximum.


Introduction
In the heavy-fermion (HF) compound, interesting physical phenomena are observed such as unconventional superconductivity (SC) or non-Fermi liquid (NFL) behavior in the vicinity of quantum critical point (QCP) where a magnetic phase transition temperature is suppressed to 0 K.These characteristic behaviors in f electron system are attributed to a competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect.The RKKY interaction enhances a long-range magnetic ordering.On the other hands, the Kondo effect quenches a magnetic moment of f electron.The RKKY interaction and the Kondo effect are expressed by the function of the strength of exchange interaction between f and conduction electrons, Jcf, which corresponds to the hybridization effect between them.The parameter of Jcf is tuned by external fields such as pressure, magnetic field, and chemical substitution.Thus, the pressure could be a powerful tool to study the electronic state of HF compounds in the vicinity of QCP.One of typical HF compounds CeTIn5 (T = Co, Rh, Ir) that crystallizes in the tetragonal HoCoGa5 type structure have provided knowledges of the relationship between unconventional SC and antiferromagnetic (AFM) transition in the vicinity of magnetic QCP.CeRhIn5 with AFM transition temperature TN = 3.8 K at ambient pressure shows the pressure induced SC phase dome centered at Pc ~ 2.1 GPa, where TN becomes 0 K [1], which is typical feature in the vicinity of the magnetic QCP.CeCoIn5 is a HF superconductor with SC transition temperature Tsc ~ 2.3 K [2].Substituting In for Cd in CeCoIn5, Tsc is suppressed and AFM order is induced [3].The Cd doped CeCoIn5 shows the similar phase diagram as CeRhIn5.In the magnetic QCP regime, theoretical study revealed that electrical resistivity ρ shows the NFL behavior, ρ ∝T n (n = 1 ~ 1.5) [4], which is in good agreement with experimental results of CeCoIn5 [5].
CeIrIn5 is a member of CeTIn5 family and shows the SC at Tsc ~ 0.4 K [6].With increasing pressure, Tsc increases and reaches a maximum value of 1 K at around 3 GPa [7,8].The mechanism of SC in CeIrIn5 has not been clear yet.Interestingly, the pressure study in CeRh1-xIrxIn5 reported that there are two SC phase [9].The SC phase at lower and higher x are called SC1 and SC2, respectively [9].The magnetic instability plays an important role in the SC1.On the other hand, the SC2 phase is far from the magnetic QCP, and non-magnetic fluctuation is considered to play an important role in the SC2 [7].Thus the origin of the SC of CeIrIn5 is expected to be the non-magnetic fluctuation.Nuclear quadrupole resonance (NQR) measurement of Cd doped CeIrIn5 suggests a valence instability contributes to the SC2 [10].On the other hands, nuclear magnetic resonance (NMR) and transport measurements suggest CeIrIn5 is in the vicinity of AFM QCP [11][12][13][14][15].In order to clarify the relationship between SC and magnetic instability in CeIrIn5, we measured the electrical resistivity of Cd doped CeIrIn5 under pressure.

Experimental method
Single crystals of CeIr(In1-xCdx)5 were grown by (In-Cd)-flux technique.Here, x is composition ratio of starting materials Ce : Ir : In : Cd = 1 : 1 : 20x : 20(1-x).The electrical resistivity was measured by four probe method from 0.7 to 300 K. We used Bridgman anvil cell (BAC) with Daphne oil 7373 as the pressure medium for electrical resistivity measurement under pressure.Pressure inside the pressure cell at low temperature was calibrated by the SC transition temperature of Pb.

x =0.05
Figure 1(a) shows the temperature dependence of ρ for x = 0.05 in the temperature range between 0 and 300 K.At ambient pressure, ρ shows a peak at Tρ max = 37 K.This peak is shifted to higher temperature by applying pressure, meaning that the hybridization effect between f electron and conduction electron becomes strong under pressure.At temperatures lower than Tρ max , ρ shows a hump just below T* in the pressure range between 2.4 and 3.2 GPa, as shown in the inset of Fig. 1(a).T* increases by applying pressure.As shown by the arrow in Fig. 1(b), a sudden drop in ρ is observed at Tsc onset ~ 0.9 K at ambient pressure, which corresponds to the onset of SC.In the previous specific heat measurement, any phase transition is not observed down to 0.2 K for x = 0.05 [3].This different experimental results between ρ and specific heat might be due not to the bulk SC but filamentary SC in CeIrIn5.With increasing pressure, Tsc onset increases and zero resistivity is observed at Tsc ρ=0 above 2.4 GPa.The difference between Tsc onset and Tsc ρ=0 shrinks by applying pressure.

x =0.10
We present the temperature dependence of ρ for x = 0.10 up to 300 K in Fig. 2(a).ρ shows peak at Tρ max = 28 K at ambient pressure, which is smaller than that for x = 0.05, meaning the suppression of the hybridization effect.The peak at Tρ max is shifted to higher temperatures by applying pressure, and a hump of ρ is also observed above the 3.1 GPa, as shown by the arrow in the inset of Fig. 2(a), which are similar behavior for x = 0.05.At low temperature, ρ shows a kink at TN = 3.4 K, which is consistent with the previous specific heat study [3].With increasing pressure, TN reaches the maximum at 2.1 GPa and rapidly decreases above 2.1 GPa.At 2.9 GPa, SC emerges below TN and zero resistivity is observed at 3.1 GPa with Tsc ρ=0 =1.1 K.

Phase diagram
From the experimental results of ρ under pressure, we constructed temperature (T)-pressure (P) phase diagram for x = 0.05 and 0.10, as shown in Figs.3(a) and 3(b), respectively.

x =0.05
Tsc onset indicates the maximum value of 1.6 K at 2.8 GPa.On the other hands, Tsc ρ=0 indicates the maximum value of 1.35 K at 3.2 GPa, which is higher than that of CeIrIn5 [8].T* appears above 2.4 GPa in the pressure region where zero resistivity emerges, and T* increases by applying pressure.We analyzed the temperature dependence of ρ in low temperatures above Tsc onset at several pressures using the following equation, ρ = ρ0 + AT n , where ρ0, A, and n are fitting parameters.ρ follows the equation up to about 20 K. Pressure dependences of power law exponent n (open circles on the left axis) and residual resistivity ρ0 (closed circle on the right axis) are shown in Fig. 3(c).The data of n shows almost constant value of 0.9 up to 2 GPa.Above 2 GPa, n decreases and indicates a saturation of 0.6.ρ0 shows the similar pressure dependence as n, that is, ρ0 indicates a constant value up to 2 GPa and decreases above 2 GPa, which corresponds to the pressure where the zero resistivity is observed.Sublinear dependence of ρ ∝ T n (n < 1) could not be explained by magnetic fluctuation theory and valence one [4,16].The sublinear temperature behavior of ρ is also observed in CeRhIn5, and which is considered to be the electrical scattering by coexistence of spin and charge fluctuation [17].However, the origin of sublinear temperature dependence in ρ is still an open question.

x =0.10
In Fig. 3(b), TN seems to become zero at Pc ~ 3.2 GPa, where SC phase emerges.The maximum value of Tsc ρ=0 is 1.35 K at 4.0 GPa, which is the same value as that for x = 0.05.In non s-wave superconductor, SC is sensitive to a sample quality, and Tsc is easily suppressed by disorder, as observed in CeRh2Si2 under pressure or UPt3 [18,19].However, the maximum value of Tsc ρ=0 is independent on amount of the doped Cd in CeIr(In1-xCdx)5.T* for x = 0.10 also appears in the pressure region where zero resistivity appears as x = 0.05 and increases by applying pressure.Figure 3(d) displays the pressure dependence of fitting parameters n and ρ0 for x = 0.10.ρ for x = 0.10 follows the power law up to TN below 2.9 GPa, and ρ shows Fermi liquid behavior (n = 2) up to 1.0 GPa.Above 3.1 GPa, ρ also follows the power law up to about 20 K as x = 0.05.At pressures higher than 1.0 GPa, n decreases to about 1 at 3.0 GPa.Sublinear temperature dependence of ρ is observed above 3.1 GPa.Although ρ0 for x = 0.10 is larger than that for x = 0.05, the pressure dependence of ρ0 for x = 0.10 is similar to that for x = 0.05.ρ0 monotonically decreases by applying pressure and shows a change of slope above 3.1 GPa, where Tsc ρ=0 reaches the maximum.The decreases of ρ0 at around Pc is different from the conventional pressure induced HF superconductor which shows the maximum of ρ0 at Pc [17,20].

Summary
We measured the electrical resistivity ρ of CeIr(In1-xCdx)5 for x = 0.05 and 0.10 under several  pressures.AFM QCP probably exists at Pc ~ 3.2 GPa for x = 0.10.Tsc ρ=0 reaches the maximum value of 1.35 K at 3.2 and 4.0 GPa for x = 0.05 and 0.10, respectively, which is higher than that of CeIrIn5.The maximum of Tsc ρ=0 in CeIr(In1-xCdx)5 is found to be independent of ρ0 and x, meaning that the SC in CeIrIn5 is insensitive to impurity.ρ shows a hump just below T * above 2.4 and 3.1 GPa for x = 0.05 and 0.10, respectively.Although T* appears in the pressure region where SC phase emerges, the relationship between T* and SC, and the origin of T* are not clear yet.Our analysis of ρ at low temperatures revealed that ρ shows the sublinear temperature dependence and ρ0 abruptly decreases in the pressure region where Tsc ρ=0 becomes the maximum for both of x = and 0.10.The impurityinsensitive behavior in SC and sublinear temperature dependence of ρ are not explained by the conventional magnetic QCP theory.Another fluctuations possibly contribute to the SC in CeIr(In1-xCdx)5.Experiments under high pressure and high magnetic field which suppresses the magnetic fluctuations are necessary in order to investigate the relationship between magnetic fluctuation and anomalous behaviors in CeIr(In1-xCdx)5.Specific heat measurement under pressures are also needed to discuss the bulk SC.

Fig. 1 .
Fig. 1.Temperature dependence of electrical resistivity ρ for x = 0.05 at several pressures in the temperature range up to (a) 300 K, inset of (a) 150 K, and (b) 3 K, respectively.The data of ρ in inset of (a) and (b) is properly shifted for clarity.

Fig. 2 .
Fig. 2. Temperature dependence for ρ for x = 0.10 at several pressures in the temperature range up to (a) 300 K, inset of (a) 200 K, and (c) 6 K, respectively .The data of ρ in the inset of (a) and (b) is properly shifted for clarity.