Amorphization Effect for Kondo Semiconductor CeRu?Al??

We measured the magnetic susceptibility 𝜒 , electrical resistivity 𝜌 , and specific heat 𝐶 𝑝 of a sputtered amorphous ( a -)CeRu 2 Al 10 alloy. 𝜒 value for a -CeRu 2 Al 10 alloy follows a Curie-Weiss paramagnetic behavior in the high-temperature region, and magnetic transition was not observed down to 2 K. The effective paramagnetic moment 𝑝 eff is 1.19 𝜇 𝐵 /Ce-atom. The resistivity shows a typical disordered alloy behavior, that is, small temperature dependence for the whole temperature range. We observed an enhancement of 𝜌 and 𝐶 𝑝 /𝑇 in the low-temperature region of 𝑇 < 10 K. The enhancement in 𝜌 is suppressed by applying a magnetic field. It is suggested that this behavior is caused by the Kondo effect.


Introduction
The ternary rare-earth compound, CeRu 2 Al 10 , exhibits an unusual antiferromagnetic phase transition at  0 ≈ 27K [1,2].The resistivity for CeRu 2 Al 10 exhibits a semiconducting behavior in the paramagnetic phase.However, this behavior is suppressed by substituting La in Ce-site of CeRu 2 Al 10 .In addition,  0 decreases rapidly with an increase in La concentration and disappears when about half of Ce is substituted by La.The resistivity for Ce dilute region of Lasubstituted CeRu 2 Al 10 exhibits a metallic behavior at high temperatures, and the resistivity exhibits a minimum in the low-temperature region.Tanida et al. proposed that the longrange magnetic order was suppressed randomly in Ce dilute region for La substitution of CeRu 2 Al 10 .The authors pointed out that the resistivity minimum can be explained by a typical impurity Kondo effect, where Ce exists as a magnetic impurity [3,4].Moreover, the semiconducting band gap of CeRu 2 Al 10 is broken by La substitution.
However, several studies on the Kondo effect of structural-disordered Ce-alloys such as bulk metallic glasses and amorphous alloys, where Ce-atom is arranged randomly, have been recently performed.For example, in Ce-Al bulk metallic glasses, the tunable competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction with the variation in Ce-concentration and the magnetic field [5] is suggested.We studied the low-temperature properties of several binary amorphous Ce-alloys.Amorphous (a-)Ce-Mn and a-Ce-Ru alloys in Ce highconcentration region exhibit a large electronic specific heat coefficient  (>200 mJ/molK 2 ) and  2 law with a large coefficient A (>0.02 Ωcm/K 2 ) in the low-temperature resistivity [6][7][8][9][10].From these results, we show that an itinerant heavyfermion state occurs at low temperatures as a Fermi-liquid ground state in the structure-disordered system after the formation of a dense Kondo state.
In this study, to investigate the influence of the structuraldisordered effect on the electrical resistivity and magnetic properties for CeRu 2 Al 10 , we prepared a-CeRu 2 Al 10 alloy and measured its magnetic susceptibility, resistivity, and specific heat.In addition, we prepared a-LaRu 2 Al 10 alloy that does not have 4f -electrons with a rare-earth element for comparison.

Experimental
Bulk ingots of CeRu 2 Al 10 and LaRu 2 Al 10 were prepared by using the arc-melting method with a stoichiometric composition of Ce 99.9%, La 99.9% (Nippon Yttrium Co., Ltd.), Ru 99.95% (Rare Metallic Co., Ltd.), and Al 99.99% (Mitsuwa Chemicals Co., Ltd.), in Ar atmosphere.The amorphous alloy was prepared using a dc high-rate sputtering method with arc-melt ingots on a water-cooled Cu substrate (30 mm).The sample thickness was ∼200 m.The structure of the obtained samples was confirmed using X-ray diffraction measurements.Measurements were performed with an as-sputtered film.The chemical compositions of the present amorphous alloys were determined using scanning electron microscope energy dispersive X-ray spectroscopy (SEM-EDS) to be Ce 10 Ru 15 Al 75 and La 8 Ru 17 Al 75 (suffixes represent at%).Thus, we will use the notations a-CeRu 2 Al 10 and a-LaRu 2 Al 10 for the samples, hereafter.The magnetic susceptibility was measured using a commercial SQUID magnetometer (Quantum Design MPMS) from 2 to 300 K.The electrical resistivity was measured by using a typical four-terminal method (Quantum Design PPMS) from 2 to 300 K.The resistivity measurements of a-CeRu 2 Al 10 alloy were performed in a magnetic field (0, 20 kOe, 40 kOe, and 60 kOe) and the temperature range was 2-60 K.The specific heat was measured by PPMS from 2 to 300 K.

Results and Discussion
Figure 1 shows the X-ray diffraction patterns for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys.The diffraction patterns for both alloys exhibit two broad peaks at the center at about 25 ∘ and 42 ∘ , and definite Bragg peaks are not observed.Therefore, the samples are identified as amorphous materials.
Figure 2 shows the temperature dependence of the magnetic susceptibility  (left axis) and the inverse susceptibility 1/(− 0 ) (right axis) for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys at H = 10 kOe.We calculated  using the composition ratio of Ce 10 Ru 15 Al 75 obtained by SEM-EDS as 1 mol. value for a-CeRu 2 Al 10 alloy increases monotonically with decreasing temperature, and a magnetic transition is not observed in the measurement temperature region.However,  value for a-LaRu 2 Al 10 alloy is almost independent of the temperature and is very small value (<10 −6 emu/mol).1/( −  0 ) value for a-CeRu 2 Al 10 alloy exhibits a linear behavior in the hightemperature region of  > 30 K following the Curie-Weiss law, where  0 is a constant for the independence of temperature,  is the Curie constant, and  is the Weiss temperature. 0 value for a-CeRu 2 Al 10 alloy obtained from (1) was ∼1.0 × 10 −6 emu/mol.The value of  is −20 K.  is obtained as where  Ce is the number of Ce atoms,  eff is the paramagnetic effective magnetic moment, and   is the Boltzmann constant.Here,  eff is calculated from Ce-concentration (10 at%) of composition ratio Ce 10 Ru 15 Al 75 obtained from SEM-EDS.The estimated  eff obtained using (  Figure 3 shows the temperature dependence of the resistivity  for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys.The value of  at 300 K for a-CeRu 2 Al 10 alloy is about 2 times greater than that of a-LaRu 2 Al 10 alloy. value for both alloys exhibits small temperature dependence less than 10% in the whole temperature region, and it increases with decreasing temperature.Such temperature dependence is one of the characteristics of disordered alloys.In contrast to  value of a-LaRu 2 Al 10 alloy, which increases monotonically with decreasing temperature,  value of a-CeRu 2 Al 10 alloy exhibits an increase in the low-temperature region.Generally, in the case of disordered alloys, the resistivity is larger than that for the crystalline counterparts owing to the random arrangement of atoms.However, the absolute value of the low-temperature  in a-CeRu 2 Al 10 alloy is on about the same order as that for the polycrystalline CeRu 2 Al 10 .In addition, although  value of a-CeRu 2 Al 10 alloy increases with decreasing temperature, a small temperature dependence similar to that for the typical disordered alloy was observed.Therefore, it is considered that the semiconductor band for crystalline CeRu 2 Al 10 exhibited a metallic behavior as a result of amorphization.
Figure 4 shows the low-temperature specific heat   over  versus  2 plots for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys.The inset shows the temperature dependence of   for the alloys.  values of both alloys are almost in agreement in the whole temperature region, as shown in the inset.The lowtemperature specific heat of a usual metal can be expressed by where  is the electronic specific heat term and  3 is the phonon specific heat term.This relation can also be applied to amorphous alloys [11].As shown in Figure 4  of  2 below 50 K 2 .However,   / of a-CeRu 2 Al 10 alloy increases rapidly with decreasing  2 below 100 K 2 .The value of   / at the lowest temperature is ∼54 mJ/molK 2 .The temperature region where the enhancement in   / occurs agrees with the temperature region of the upturn for .Such enhancement in   / and  at low-temperature does not occur for a-LaRu 2 Al 10 .Therefore, it is considered to be due to the magnetic contribution of the 4f -electron of Ce.In order to clarify the magnetic contribution of the 4f -electron of Ce for a-CeRu 2 Al 10 , we measured the magnetoresistance of a-CeRu 2 Al 10 .Figure 5 shows the magnetic field dependence of the transverse magnetoresistance Δ/ at 2 K, 10 K, and 60 K for a-CeRu 2 Al 10 alloy.We calculated Δ/ as follows: where () is the resistivity in the magnetic field and (0) is the resistivity at zero field.Δ/ increases negative with increasing magnetic field strength.Δ/ at 2 K exhibits a large negative enhancement compared with that at other temperatures.Figure 6 shows the temperature dependence of Δ/ at 20 kOe, 40 kOe, and 60 kOe for a-CeRu 2 Al 10 alloy.The Δ/ in the high-temperature region ( > 10 K) is almost independent of the temperature for all the magnetic fields.However, Δ/ in the low-temperature region increases rapidly with decreasing temperature at  < 10 K for all the fields.Thus, the enhancement of  at low temperatures is suppressed by the applied magnetic field.The present a-CeRu 2 Al 10 alloy seems reasonable that the magnetic order of the crystalline counterpart have disappeared because they lose a long-range crystallographic order by amorphization.However, the local structure of the amorphous alloy is generally considered to be similar to that of the crystalline counterpart.Even in a-CeRu 2 Al 10 alloy, a local structure similar to that of the crystalline CeRu 2 Al 10 is expected to be realized.In addition, based on  eff , we have shown that half of Ce in a-CeRu 2 Al 10 alloy is in the trivalent state.Ce 3+ ions in a-CeRu 2 Al 10 alloy are distributed randomly in the amorphous sample.
In this case, it is considered that the random distribution of Ce 3+ in the disordered structure realizes the impurity Kondo effect at low temperatures.Thus, the enhancement of  and   / is observed in the low-temperature region for a-CeRu 2 Al 10 alloy.Since the Kondo scattering is suppressed by the applying a magnetic field, Δ/ increases negatively.Therefore, the negative increase of Δ/ for a-CeRu 2 Al 10 alloy at low temperatures and high magnetic fields indicates that the scattering center of the resistivity is due to Kondo scattering.

2
,   / of a-LaRu 2 Al 10 alloy follows a linear relation as a function Al 10 a-LaRu 2 Al 10

Figure 4 :
Figure 4:   / versus  2 plot for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys.The inset shows the temperature dependence of the specific heat   for a-CeRu 2 Al 10 and a-LaRu 2 Al 10 alloys.