Jun-Nan Sun(孫俊男) Bin-Bin Ruan(阮彬彬) Meng-Hu Zhou(周孟虎)Yin Chen(陳銀) Qing-Song Yang(楊清松) Lei Shan(單磊)Ming-Wei Ma(馬明偉) Gen-Fu Chen(陳根富) and Zhi-An Ren(任治安)

1Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education,Institutes of Physical Science and Information Technology,Anhui University,Hefei 230601,China

2Institute of Physics and Beijing National Laboratory for Condensed Matter Physics,Chinese Academy of Sciences,Beijing 100190,China

3Songshan Lake Materials Laboratory,Dongguan 523808,China

4School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

Keywords: Mo3-xRexAl2C,superconductivity,β-Mn structure,microwave synthesis

1. Introduction

The crystal structure of non-centrosymmetric superconductors has the potential to realize unconventional superconductivity,and has attracted much attention in recent years.[1-3]The Cooper pair wave function of superconductor is formed by two parts: the orbit (i.e., s-, p-, or d-wave) and the spin (single or triplet)parts. In a non-centrosymmetric superconductor

where space inversion symmetry is broken,the wave function could result in the mixing of spin singlet and spin triplet.[1,4]In 2004,a heavy fermion superconductor CePt3Si with a noncentrosymmetric crystal structure was reported to demonstrate intriguing physical properties,such as the extraordinarily large upper critical field and line nodes in the superconducting gap,which led to an upsurge of research on non-centrosymmetric superconductors,[5]such as CeRh3Si,[6]CeIrSi3,[7]UIr,[8]andA2Mo3As3(A=K,Rb,Cs).[9-11]

In 1963, Jeitschkoet al. reported several compounds of theM3Al2C (M=Mo, Nb, Ta, V, Ti) type, and discovered a new non-centrosymmetric superconductor Mo3Al2C which has aβ-Mn type structure.[12]Since then, a series of superconductors of the same structural family, such as Li2Pt3B,Cr2Re3B,[13]Rh2Mo3N,[14]Cu2Pt3B,[15]Al2W3C,[16]and Mg2Rh3P[17]have been discovered one after another. Among them,Mo3Al2C marks the highest superconducting transition temperature(Tc)～9 K.

In theβ-Mn type superconductors, doping has been a powerful way to modulate the structure, as well as the superconducting properties. A prominent example is the Li2(Pd1-xPtx)3B system with a space group ofP4332.[18-21]Being a conventional Bardeen-Cooper-Schrieffer (BCS) superconductor on the Li2Pd3B side,the system gradually transforms into a spin triplet on the Li2Pt3B side, together with dramatic changes in the band and gap structures.[22-27]The enhancement of spin-orbit coupling(SOC)by the substitution of 4d-Pd to the 5d-Pt plays an important role.

Despite Mo3Al2C has a relatively highTcand unconventional superconductivity, and shares a quite similar geometric configuration with Li2(Pd1-xPtx)3B, research in depth is to a large extent limited due to the difficulty of synthesis.Currently, Mo3Al2C synthesis methods include arc-melting method,high pressure synthesis method,hot pressing method,and spark plasma sintering(SPS)method.[18,26-28]Arc-melted samples contain many impurity phases such as Mo2C and Mo3Al8. The other three methods require special equipment and are resource-consuming. As a result, the doping effect of Mo3Al2C has not been extensively studied. Recently, Ramachandranet al.reported the evolutions of lattice parameters andTcfor Mo3-xNbxAl2C(0≤x ≤0.25)and Mo3-xRuxAl2C(0≤x ≤0.15) systems. Their results suggested that the superconductivity in Mo3Al2C was quickly suppressed with increasing content of Nb and Ru.[29]In this paper, to further understand the physical properties of Mo3Al2C,we choose to dope Re into the Mo sites in Mo3Al2C. As Re possesses one more valence electron compared to Mo,it is expected to introduce electrons into the system, which may modify the band structure as well as the physical properties. Moreover, we present a convenient method to synthesize Mo3Al2C for the first time. By applying the microwave method,[30]polycrystalline Mo3-xRexAl2C (0≤x ≤0.3) samples were successfully obtained. We also report the systematic study of Re doping effect in Mo3Al2C for the first time. Upon Re doping,the lattice shrinks monotonously,whileTcfirst increases and then decreases.

2. Experiment

Molybdenum powder (99.9%), rhenium powder(99.99%), aluminum powder (99.97%), and graphite sheet(99%)were obtained from Alfa Aesar. The starting materials were mixed in the Mo/Re/Al/C molar ratio of(3-x):x:2:1(the total mass of the sample was approximately 0.80 g),pressed into a pellet, and loaded into an alumina crucible(3 mL).All the above manipulations were carried out in an argon filled glove box(content of O2＜0.01 ppm). The crucible was buried in 3 g carbon black in a lager alumina crucible,and then shielded with another crucible to prevent the carbon black from splashing. The assembly was sintered in a domestic microwave oven at a power of 1000 W for 3 min. Our assembly resembled the one illustrated in Ref.[31]with some minor modifications. Likewise,the carbon black was directly contacted with air. This method is effective since the carbon black will generate a protective atmosphere at high temperature. The final products were dark grey, hard, and stable in air.

Crystal structure of the synthesized polycrystalline sample was examined at room temperature using a PAN-analytical x-ray diffractometer with Cu-Kαradiation. The magnetic properties of the samples were measured on the magnetic property measurement system (MPMS) of Quantum Design.The instrument uses a superconducting quantum interference device (SQUID) to measure the magnetic field and magnetization. The magnetic susceptibility of the samples was determined in the temperature range of 4 K to 12 K under an applied magnetic field of 10 Oe. The electrical resistivity was measured using a conventional dc four-probe method with a measuring current of 1 mA in the temperature range between 4 K and 300 K, using a physical property measurement system (PPMS, Quantum Design). The specific heat was also measured on PPMS,using a time-relaxation method between 4 K and 20 K under zero magnetic field.

3. Results and discussion

Figure 1(a)displays the powder x-ray diffraction(PXRD)patterns of the synthesized samples of Mo3-xRexAl2C (0≤x ≤0.3). The main diffraction peaks can be indexed with a cubic unit cell ofβ-Mn type Mo3Al2C with the space group ofP4132(No.213),and are in good agreement with the reference pattern for Mo3Al2C.[18,27,28]The residual minor peaks come from a small amount of impurity phase,which is identified asα-Mo2C. According to the Rietveld refinement of each sample, there is about 10%-15% (by weight) ofα-Mo2C as the impurity. As the Re doping content increases, the lattice parameterashrinks regularly,which is clearly evidenced by the shift of the (310) peak position toward higher 2θvalues (see Fig.1(b)). Figure 1(d)shows the evolution of lattice parameteraupon Re concentration. The lattice parameteragradually decreases from 6.868(1) ?A(for Mo3Al2C)to 6.846(2) ?A (for Mo2.7Re0.3Al2C),showing a linear decrease upon Re doping.This is consistent with the Vegard’s law since Re has a smaller atomic radius than Mo.[33]The result indicates a successful doping of Re into the Mo sites in Mo3Al2C.It should be mentioned that samples with higher Re doping levels (x ＞0.3)were also synthesized. However, impurities such asα-Mo2C and Mo3Al8became dominant phases, and the lattice parameterafor the Mo3-xRexAl2C phase did not show a regular change. Therefore,the doping limit for Mo3-xRexAl2C in our research was aroundx=0.3.

It should be emphasized that the phase purity of our sample is comparable with Mo3Al2C made by hot pressing method and spark plasma sintering method.Yet the microwave method described here is far more convenient and resource-saving by a synthesis process within minutes.

The relationship between the resistivity and temperature of the Mo3-xRexAl2C(0≤x ≤0.3)sample is shown in Fig.2.Each curve has been normalized by its value at 250 K for a clear presentation. The temperature dependence of the resistivity shows typical metallic behavior,the resistivity decreases with decreasing temperature. Nevertheless,the residual resistivity ratio(RRR)for each sample is small,suggesting the resistivity of Mo3-xRexAl2C is not sensitive to temperature. It should be noted that this kind of temperature dependence of resistivity is intrinsic to Mo3Al2C,and is not due to the impurity or grain boundary scattering,as demonstrated in high quality,compact samples made by the SPS method.[28,29]Small values ofRRRwere also observed in the isostructural superconductor Rh2Mo3N[14]and Al2W3C,[16]implying this phenomenon might be common in theβ-Mn type carbides and nitrides.

Fig.1. (a)Powder XRD diffraction pattern of Mo3-xRexAl2C(0 ≤x ≤0.3),where the diamond symbol marks the Mo2C phase. (b)Expanded view of the (310) peak in Mo3-xRexAl2C (0 ≤x ≤0.3). (c) Three-dimensional crystal structure of Mo3Al2C, produced using the VESTA software.[32] The yellow balls represent Mo/Re atoms, and the light blue balls represent Al atoms. The black line indicates a unit cell. (d)Evolution of lattice parameter a upon doping.

Resistivity for each sample shows a drop to zero at low temperature, indicating the occurrence of superconductivity.The inset of Fig. 2 is an enlarged view of the superconducting transition. We take the midpoint of the transition as the superconducting transition temperatureTc. From the figure,it can be seen that the undoped compound Mo3Al2C becomes superconducting below 9.00 K.Upon doping,the critical temperatureTcstarts to increase with Re doping and reaches a maximum of 9.14 K atx=0.09,thenTcrapidly decreases and drops below 8.41 K atx=0.3.

Fig.2. Normalized resistivity of the Mo3-xRexAl2C(0 ≤x ≤0.3)samples changing with temperature. The inset is an enlarged view near the superconducting transitions.

Figure 3 shows the magnetic susceptibility of the Mo3-xRexAl2C(0≤x ≤0.3)doped samples under an applied magnetic field of 10 Oe. The measurements were carried out on warming after zero-field cooling (ZFC process) and then on cooling in a field(FC process). The magnetic susceptibility data exhibit marked drops,in both ZFC and FC processes,suggesting the occurrence of superconductivity. A small amount of Re doping (x ≤0.09) at the Mo site can improve the superconductivity of the sample. But as the doping amount further increases, the superconducting transition temperatureTcof the sample begins to decrease. For each sample,Tcobtained from the magnetic measurement is consistent withTcfrom the resistivity measurement. For all these samples, the diamagnetic signals in FC curves are significantly smaller than those in the ZFC runs, indicating a strong pinning effect in Mo3-xRexAl2C.Unlike the Nb or Ru doping in Mo3Al2C,[29]

where the superconducting volume fraction(SVF)was quickly suppressed, all the samples of Mo3-xRexAl2C show strong diamagnetic signals,validating the bulk superconductivity.

Fig. 3. Magnetic susceptibility of Mo3-xRexAl2C (0 ≤x ≤0.3) samples under an applied 10 Oe magnetic field.

It is worth noting that theα-Mo2C impurity is also a superconductor. However,Tcofα-Mo2C is not higher than 4.5 K.[34]Therefore, the impurity phase in the samples does not affect the conclusions from the resistivity and magnetization measurements.

whereμ*is the Coulomb repulsion constant. In our study,we takeμ*=0.13. We further estimate the density of states(DOS)at the Fermi level byN(EF)=3γ/[π2k2B(1+λep)].

Fig. 4. (a) Low temperature heat capacity of Mo3-xRexAl2C (0 ≤x ≤0.3) under zero magnetic field. The normal state data is fitted with Cp/T =γ+βT2,shown as the dash lines. (b)-(d)Evolution of Tc,γ,and λep respectively upon Re doping content x. Tc is determined by both the resistivity and the specific heat measurements.

All the thermodynamic and superconducting parameters mentioned above are summarized in Table 1. Notice that the normalized specific heat changes ΔCe/γTcof all samples are between 2.0 and 2.5(except for the sample ofx=0.15,whose small ΔCe/γTcpossibly comes from the existence of nonsuperconducting components and/or a poor crystallization,as revealed in the broad transition in Fig.3),andλepis between 0.7 and 0.8. These values are comparable with those in the references,[18,27]and are well beyond the BCS weak coupling limit.

Table 1. Thermodynamic and superconducting parameters of Mo3-xRexAl2C. Tc is determined as the midpoint of the superconducting transition in the resistivity measurement.

As shown in Fig. 4(a), at the superconducting state,the behavior ofCpfollows a relation ofCp～T3. As the phonon contribution ofCpisβT3,the electronic contribution of heat capacity (Ce) also follows a power-law behavior ofT3. Although the manners ofCpat lower temperatures were not measured in our study, this kind of power-law behavior is consistent with that of the previously reported Mo3Al2C samples.[18,27]Our results reveal that there might be point nodes at the superconducting gap. However, since there are considerable amounts ofα-Mo2C impurity and the measuring temperature is not low enough, we are not able to draw a conclusion on the gap symmetry with merely theCpresults.Further studies on single crystals are needed to answer this question.

Figure 4(b)summarizes the change ofTc(determined by both the resistivity measurements and the specific heat measurements) of Mo3Al2C upon Re doping.Tcis enhanced by a small amount of Re doping before it decreases, reaching a maximum when the Re doping concentration is about 3%.

The trends ofγandλepcorrespond well with the changing ofTc, as illustrated in Figs. 4(c) and 4(d). Most surprisingly,theγof Mo2.91Re0.09Al2C is significantly larger than that of the other samples,indicating a much largerN(EF)(～150%of the undoped sample). According to McMillan’s relation,λepis positively correlated withN(EF). Therefore, the enhancement ofN(EF) should be responsible for the increase ofTc.The dramatic increase inN(EF) with such a small amount of Re doping is possibly due to the modification of Fermi surface upon electron doping introduced by Re. In this respect,a detailed study of band structure calculation of Mo3-xRexAl2C(0≤x ≤0.3)is definitely of interest.

4. Conclusion

In summary,we successfully prepared Mo3Al2C,as well as the Re-doped samples Mo3-xRexAl2C (0≤x ≤0.3) by a microwave method for the first time. We systematically studied the crystal structure and the basic superconducting parameters. With the increase of Re contentx,the lattice parameteradecreases linearly, whileTcis enhanced by a small amount of Re doping up tox=0.09 before it decreases. The increase ofTcis possibly due to the enhancement ofN(EF),which may result from the modification of band structure upon electron doping. Our results not only provide a new convenient way to produce Mo3Al2C within minutes,they also shed lights on the study of the unconventional superconducting mechanism in Mo3Al2C.