Lattice, Magnetic, and Electronic Transport Properties in Antiperovskite M3AX Compounds
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Research Progress on NiBased Antiperovskite Compounds
Abstract
The superconductivity in antiperovskite compound MgCNi_{3} was discovered in 2001 following the discovery of the superconducting MgB_{2}. In spite of its lower superconducting transition temperature (8 K) than MgB_{2} (39 K), MgCNi_{3} has attracted considerable attention due to its high content of magnetic element Ni and the cubic structure analogous to the perovskite cuprates. After years of extensive investigations both theoretically and experimentally, however, it is still not clear whether the mechanism for superconductivity is conventional or not. The central issue is if and how the ferromagnetic spin fluctuations contribute to the cooper paring. Recently, the experimental results on the single crystals firstly reported in 2007 trend to indicate a conventional swave mechanism. Meanwhile many compounds neighboring to MgCNi_{3} were synthesized and the physical properties were investigated, which enriches the physics of the Nibased antiperovskite compounds and help understand the superconductivity in MgCNi_{3}. In this paper, we summarize the research progress in these two aspects. Moreover, a universal phase diagram of these compounds is presented, which suggests a phononmediated mechanism for the superconductivity, as well as a clue for searching new superconductors with the antiperovskite structure. Finally, a few possible scopes for future research are proposed.
1. Introduction
To explore new superconductors is one of the central issues of material science and condensed matter physics. The discovery of hightemperature (high) superconductivity in cuprates has attracted a lot of attention in the past decades [1]. In 2001, Professor R. J. Cava from the University of Princeton reported the superconductivity in antiperovskite compound MgCNi_{3} with the transition temperature K (Figure 1) [2]. The superconductivity in MgCNi_{3} is unusual in view of the large content of the magnetic element Ni, which often favors a magnetic ground state. A prominent feature of the electronic structure is an extended van Hove singularity as shown in Figure 2(a), giving rise to a large density of states (DOS) just below the Fermi level () [see Figure 2(b)] [3]. A similar feature has been observed in some high superconductors. Moreover, the DOS peak is mainly attributive to the Ni 3d states [4, 5]. Structurally, the cubic symmetry recalls the high cuprates superconductors with perovskite structures. Thus the central question was raised, whether the superconductivity in MgCNi_{3} is exotic. In other words, the answer to the question lies in clarifying the roles of the spin fluctuations or ferromagnetic (FM) correlations probably from the dominant Ni content in MgCNi_{3}. However, the experimental results based on polycrystalline samples by different techniques (such as NMR [6], London penetration depth [7, 8], critical current behavior [9], tunneling spectra [10, 11], carbon isotope effect [12],specific heat [13, 14], μSR [15] and so on) from different groups are controversial. A detailed summary on the experimental and theoretical results published before 2004 can be found in the review paper [16] written by Mollah. From then on, the researchers have been focusing on two main scopes in this field, namely, the experimental investigations on MgCNi_{3} single crystals and on the synthesis and physical properties of neighbor compounds of MgCNi_{3}, which have never been included in any review papers. In this paper, we focus on these two topics, as well as give a phase diagram based on the available data of the lattice constant, the Debye temperature and the density of state at the Fermi level, , for the Nibased antiperovskite compounds. The phase diagram supports that the superconductivity observed in the Nibased antiperovskite compounds is rather phononmediated than unconventional. The phase diagram also helps explore new superconductors in Nibased antiperovskite compounds. Some possible future research scopes were proposed in the end of this paper.
(a)
(b)
2. Experimental Results on Single Crystalline MgCNi_{3}
The experiments on single crystal are desirable for eliminating the discrepancies in the experimental results based on polycrystalline samples. However, the first, also the only successful synthesis of MgCNi_{3} single crystal up to date, was reported in 2007 [17] by Lee et al., five years after the discovery of superconductivity in polycrystalline MgCNi_{3}.
In [17], Lee et al. employed a selfflux method with the aid of high pressure. The mixtures of Mg, C, and Ni powders with the ratio 1 : 1 : 3 were ground, pressed into a pellet, and then loaded into a high pressure cell. Then the sample was heated at 1200°C under 4.25 GPa for 12 hours. The resulted sample is a mixture of single crystalline MgCNi_{3} with the size of hundreds of micrometers and some fluxes. Unlike the polycrystalline samples, the single crystal does not contain C or Mg deficiencies. Instead, Ni is found to be deficient. The real composition turns out to be . As displayed in Figure 3, the transition temperature is found to be 6.7 K, slightly lower than the for polycrystalline MgCNi_{3}. Even so, the entire sample quality was greatly improved compared with the crystalline samples. For example, the residual resistivity ratio is 2.7, larger than the values ever reported for the crystalline samples. Moreover, the single crystal was homogeneous and free of microscopic regular arrays observed in the highresolution transmission electron microscopy (TEM) images for polycrystalline samples [17].
In order to clarify the nature of the superconductivity in single crystal MgCNi_{3}, further measurements have been performed on the samples from Lee’s group. Based on the resistance measured as functions of the temperature and the applied magnetic field, it is found that the normal state resistivity can be explained by using only electronphonon (ep) scattering mechanism, indicating a conventional BCS behavior [18]. It is further supported by the linear behavior of near . The lowtemperature electronic specific heat in superconducting state shows a classical exponential decrease confirming swave pairing with a moderate ep coupling in this material [19, 20]. However, the at normal state cannot be well described by the usual term of phonon contribution. A higher phononterm probably due to the softening of the lowest acoustic Ni phonon modes is needed to interpret the deviation [20]. It is consistent with the magnetic penetration depth measured by highprecision tunnel diode oscillator technique and Hall probe magnetization, which shows that the superconducting gap is fully open over the whole Fermi surface [21]. Moreover, the ratio 2Δ/ and high specificheat jump at in zero field, ΔC, indicating a strongcoupling mechanism. This scenario is supported by the direct gap measurements via the pointcontact spectroscopy [20]. The reported superconducting parameters are summarized in Table 1. The availability of single crystal specimens also allows a detailed phonondispersion mapping which is closely related to the superconducting mechanism. By applying inelastic Xray scattering (IXS), the phonon mapping was reported by Hong et al. [22]. The IXS result implies that there are no phonon anomalies that could support any exotic mechanisms for superconductivity in MgCNi_{3}. This result was verified by a late ab initio calculation [23]. In addition, Jang et al. [24] observed the collapse of the peak effect (PE), namely a sudden increase in the critical current near the end of superconductivity. As the AC driving frequency increases, the PE was collapse and observable flux creep was developed in contrast to the result observed in the wellstudied NbSe_{2}. Also, the PE in MgCNi_{3} was suggested be a dynamic phenomenon.

Although the experimental results measured on the single crystal samples suggest that MgCNi_{3} is a conventional BCStype superconductor with mediate or strong ep coupling, it is yet arbitrary to exclude the contribution from spin fluctuations or FM instability. The reason is relative to the single crystalline sample itself. All the experiments were performed on the crystals prepared by the same group. Moreover, the crystal is Nideficient [17] though its superconducting parameters are close to those determined on polycrystalline samples (see Table 1). Theoretically, for another Nibased antiperovskite compound InCNi_{3}, it is proved that the excess of Ni, or say, deficiency of In can tune the system to the FM instability [25], even to a FM order [26]. It is natural to expect stronger spinfluctuations given a perfectly stoichiometric MgCNi_{3} single crystal. Therefore, a theoretical comparison between the Nideficient and perfect MgCNi_{3} would resolve the problem. Moreover, growth of single crystals without Ni deficiencies is needed to end the tenyear debate on whether MgCNi_{3} is unconventional superconductor.
3. Research Progress on NiBased Antiperovskite Compounds other than MgCNi_{3}
The purpose of investigating the materials which are closely related to MgCNi_{3}, that is, AXNi_{3} (A = Zn, Al, Ga, In, Cd and so on; X = C, N, B), is two sided to explore new superconductors and to shed light on the superconducting mechanisms for MgCNi_{3}. Up to date, there are more than ten compounds neighboring to MgCNi_{3} were synthesized and the physical properties investigated. These newly synthesized Nibased antiperovskite compounds can be grouped into three types, that is, carbides ACNi_{3}, nitrides ANNi_{3}, and borides ABNi_{3}.
CdCNi_{3} with the same number of valence electrons as MgCNi_{3} is another superconductor in the carbides ACNi_{3}. As shown in Figures 4(a) and 4(b), the transition temperature is around 3.2 K, varying with fabrication conditions [27]. The superconducting parameters are listed in Table 1. The specific heat Sommerfeld constant is 18 mJ/(mol K^{2}), smaller than that of MgCNi_{3}. However, the theoretical calculation shows the value is slightly larger than MgCNi_{3}, while the calculated ep coupling coefficient (0.8) is nearly half that of the corresponding value of 1.5 for MgCNi_{3} [28]. This is argued to be associated with a softening behavior of the lowest acoustic phonon branch along the XR symmetry direction [28]. The large Wilson ratio and the well suppressed upper critical field T, compared with the Pauli limit (14 T) indicate the existence of strong FM correlations. Surprisingly, ZnCNi_{3} with the same number of valence electrons, as MgCNi_{3} and CdCNi_{3}, is found to be a Pauli paramagnetic (PM) metal without signals of superconductivity down to 2 K [29]. The value of is only 6.77 mJ/(mol K^{2}), much smaller than those of MgCNi_{3} and CdCNi_{3} (see Table 1), indicating a very weak ep coupling that explains the disappearance of superconductivity. However, it was theoretically suggested that the experimental ZnCNi_{3} is carbon deficient, while the stoichiometric compound should be superconducting [30].
(a)
(b)
(c)
(d)
The polycrystalline ACNi_{3} (A = Al, Ga, In) series with one more valence electron than MgCNi_{3} were prepared by solid state reaction and detailed studies of their basic properties were performed. For GaCNi_{3}, a temperature dependence of resistivity was observed. The large values of the Kadowakiwoods ratio (μΩ cm/K^{2}) and the Wilson ratio suggest a highly correlated Fermi liquid behavior [31]. The large electronelectron correlation was suggested to be caused by the proximity of FM order from the side of exchangeenhanced Pauli paramagnet, evidenced by the remarkable enhancements in both the specific heat Sommerfeld constant and the temperatureindependent magnetic susceptibility . As to AlCNi_{3} compound, the magnetic properties also show it is a strongly exchangeenhanced Pauli paramagnet in the very vicinity of FM order [32]. However, the lowtemperature resistivity is nearly linear temperaturedependent, indicating a possible nonFermiliquid behavior which is in sharp contrast with GaCNi_{3}. The lowtemperature electronic specific heat reveals that the spin fluctuations in AlCNi_{3} are strongly enhanced when compared with the superconducting MgCNi_{3}, while the ep couplings are comparable in both compounds. The Wilson ratio is about 2.4 and the dimensionless ratio that connects the lowtemperature Seebeck coefficient with the Sommerfeld specific heat constant indicate that AlCNi_{3} can be considered as a modest electroncorrelated material. Consistently, the enhanced spin fluctuations were confirmed using ^{27}Al NMR measurement in with where the FM order was suppressed and the system is in the vicinity of FM order [33, 34]. On the contrary, an early experimental report shows AlCNi_{3} is a weak ferromagnet with the FMPM transition at 300 K [35]. The nonmagnetic ground state for AlCNi_{3} and GaCNi_{3} was confirmed by many theoretical reports [36–39], though the predicted FM correlations or spin fluctuations are weaker than experimentally measured [37]. The existence of carbon deficiencies to various extents may account for this divergence, as suggested by Sieberer et al. [37]. As to the InCNi_{3}, it was found that the reduction of Indium ratio in the mixture of the raw powders helps make pure antiperovskite type compound [26]. The resulted composition from the optimum synthesis is In_{0.95}CNi_{3}. It behaves as a FM metal below the Curie temperature (577 K) [26]. It was suggested that the appearance of ferromagnetism originates from the deviation of the Ni/In atomic ratio from the ideal case. Theoretically, it is found the ideally stoichiometric InCNi_{3} is a nonmagnetic metal and far away from a longrange magnetic order [25, 40]. Both In vacancies and substitutional Ni on In site were found to be able to lead to a spinpolarized ground state. Energetically, the latter scenario is more preferable to generate a FM ground state [25].
ZnNNi_{3} is the only superconductor observed so far in the nitrides ANNi_{3} [41]. The K, as shown in Figures 4(c) and 4(d), is close to that of CdCNi_{3}. The magnetic susceptibility shows a Paulilike behavior with the magnitude much smaller than that of CdCNi_{3}. It indicates the FM correlations in this material are not as enhanced as in CdCNi_{3}. The obtained specific heat Sommerfeld constant is 13 mJ/(mol K^{2}), smaller than the value of 18 mJ/(mol K^{2}) for CdCNi_{3}. Even so, the is close to CdCNi_{3} because the FM correlation which could suppress the is weak in ZnNNi_{3}. Compared with MgCNi_{3}, a significantly reduced was theoretically observed in ZnNNi_{3} [42], which accounts for the lower in ZnNNi_{3} than in MgCNi_{3}. The CdNNi_{3} and InNNi_{3} were also successfully synthesized by the same authors of [41] but neither is superconducting [43]. The value is 12 mJ/(mol K^{2}) and 8 mJ/(mol K^{2}) for CdNNi_{3} and InNNi_{3}, respectively, smaller than that for ZnNNi_{3}. However, the temperatureindependent magnetic susceptibility for CdNNi_{3} and InNNi_{3} is larger than that of ZnNNi_{3}, indicative of an enhanced contribution from the FM correlations in the former two compounds. It shows by theoretical calculations that the for CdNNi_{3} is comparable with that for ZnNNi_{3} [44], but the is much reduced in InNNi_{3} [45]. Assuming that the ep coupling is comparable in CdNNi_{3} and ZnNNi_{3}, it is possible to observe superconductivity in CdNNi_{3} in case the FM correlations can be well suppressed. Very recently, He et al. reported two series of doped CdNNi_{3}, that is, () and NNi_{3} () [46]. These compounds show metallic resistivity and exhibit a Fermi liquid behavior at low temperatures. No superconductivity was found down to 2 K. However, all samples exhibit very soft and weak ferromagnetism, in contrast to the PM behavior for CdNNi_{3 }reported previously by Uehara et al. [43].
Compared with the carbides ACNi_{3} and nitrides ANNi_{3}, little attention has been paid to the borides ABNi_{3}. To the best of our knowledge, ScB_{0.5}Ni_{3} [47] is the only boron based Nibased antiprovskite compound with its physical properties reported in the literatures. It shows a Pauli PM behavior without any superconducting signals observed down to 2 K. We tried to synthesize ABNi_{3} (A = Al, Ga, In, and so on) samples by solid state reaction [48]. The pure sample of InBNi_{3} with the antiperovskite structure (lattice constant Å) was successfully synthesized and structural, magnetic, transport properties, and specific heat measurements performed. No superconductivity appears down to the lowest temperature by electric and magnetic measurements (5 K) as shown in Figure 5(a). The magnetization takes a typical Pauli PM behavior with a very small contribution from the FM spin fluctuations. As shown in the inset of Figure 5(b), the lowtemperature specific heat data, plotted as versus , can be well fitted using the following formula, , where is the Sommerfeld constant for electronic contribution and the second term represents the phonon contribution according to the Debye approximation [31, 32]. The fitted values of and are equal to 11.33 mJ/(mol K^{2}) and 0.32 mJ/(mol K^{4}), respectively. The Debye temperature is estimated to be 311 K according to the formula, , where is the number of atoms in a unit cell. The Wilson ration is estimated to be 0.93, very close to the free electrons, indicating weak FM correlations or spin fluctuations in InBNi_{3}. The value of is smaller than the superconducting compounds in Table 1. So the ep coupling is weak in this compound, accounting for the disappearance of superconductivity. Theoretically, the is only 1.47 states eV^{−1}/f·u [49], consistent with the observed small . Besides, the authors predicted that introduction of holes into InBNi_{3} could make it superconducting, which has not been proved experimentally yet. Theoretically, it is predicted that AlBNi_{3} is candidate for studying unconventional superconductivity, which has not been tested experimentally either [50].
(a)
(b)
4. A Universal Phase Diagram
Thanks to the systematic studies in the past, it is possible to draw a uniform picture of the properties for the Nibased antiperovskite compounds, thus to shed light on the unique superconductivity in MgCNi_{3}. The Debye temperature obtained from specific heat measurements, the calculated density of state at Fermi level available in the published literatures are plotted as a function the lattice constant, as shown in Figure 6. Two main trends can be found, the increases approximately as the lattice constant is reduced. The shrinkage of lattice constant reduces the , which is more scattered than though.
The evolution of derived from experimental specific heat data with lattice constant can be understood as follows: the lattice contraction leads to the hardening of phonon mode, thus an increase of Debye temperature [29]. There exists a strong hybridization between X 2p and Ni 3d orbitals [4, 5, 16, 25, 30, 36, 37], playing important roles in determining the physical properties. The decrease of lattice constant reduces the Ni–C bond length, thus enhances the hybridization, leading to a decreased . It is more general that the DOS is inversely proportional to the band width . for a cubic solid, the band width is related with the lattice constant by the expression [29]. Therefore, the decrease of lattice constant will increase the band width, leading to a reduction of . In addition, the theoretical calculations show there is a peak structure in the DOS below the for all Nibased antiperovskite compounds AXNi_{3}. For carbide compounds ACNi_{3} (A = Al, Ga, In) or ZnNNi_{3} that has more electrons than MgCNi_{3}, could be interpreted as electrondoped MgCNi_{3}, resulting in a downward shift of the position of the peak in the DOS from the , consequently a reduced [39]. In a word, the is expected to increase as the lattice expands. It is basically followed by many compounds as shown in Figure 6. However, the real case may be too complex to be attributed to the above models. One example is InBNi_{3} whose is extremely lower than expected. It is probably because the B 2p state in borides hybridizes with Ni 3d state more than the C 2p state in carbides ACNi_{3} [51].
For a BCS theory, the ep coupling constant can be estimated by the McMillan’s formula [32], , where is the averaged electronion matrix element squared, is an atomic mass, and the averaged phonon frequency proportional to Debye temperature . Therefore, a combination of a large and small will lead to a strong ep coupling, consequently a BCSlike superconductor. The Nibased antiperovskite compounds seem to obey this raw. All discovered superconductors locate on the right side of the map in Figure 6, where the is relatively small, but the is relatively large. For instance, MgCNi_{3} which shows the highest has the largest and smallest . Figure 6 also suggests that the superconductivity observed in the Nibased antiperovskite compounds is predominantly swave BCS type mediated by ep coupling, though the other contributions, for example, from spin fluctuations, may not be excluded. We note that the for MgCNi_{3} in the figure is from polycrystalline sample [27], while the value deduced from resistivity for single crystal MgCNi_{3} is surprisingly small (132 K) [18]. There is no clear trend for the relation between number of the valence electrons and or . Regardless of this, the phase diagram in Figure 6 provides a clue for searching new superconductors in Nibased antiperovskite compound AXNi_{3}, namely, the compounds with large lattice constant may be superconducting in terms of the BCS scenario.
5. Future Outlook
In the future, the following works are worthy to be done.a.New MgCNi_{3} single crystals with ideal 1 : 1 : 3 stoichiometry would finally close the longtime debate on the mechanism of superconductivity. b.In order to clarify the divergences among the experimental and theoretical results for the Nibased antiperovksite compounds other than MgCNi_{3}, more extensive investigations on single crystal samples are desirable. The growth of single crystal AXNi_{3} is a challenge. The successful growth of MgCNi_{3} single crystals would help, because the application of high pressure during heating can improve the solubility of carbon and suppresses the volatility of magnesium. c.The AXNi_{3} materials may serve as a platform for studying quantum critical phenomena (QCP) and quantum phase transitions (QPT) in simple material systems with threedimensional cubic structure and none “f” elements. Previously, the QCP and QPT have been extensively studied in some “unique” systems [52], such as heavy fermions with “f” elements, magnetic systems with spin frustration, and so on. Taking the advantages of the single crystal samples, the possible quantum phase transitions can be explored in some AXNi_{3}, such as AlCNi_{3}, GaCNi_{3}, and CdCNi_{3}, driven by chemical alloying, external pressure, or magnetic field. d.It is interesting to explore new superconductors with antiperovskite structure based the clues mentioned, for example, large lattice constant may favor BCS superconductivity. This clue may work for the antiperovskite compounds based on other 3d elements, such as Ti and Sc. The discovery of new superconductors can always cheer the superconductor society.
6. Conclusion
We summarized the recent progress for Nibased antiperovskite compounds closely related to the superconducting MgCNi_{3}. A universal phase diagram is presented based on the published data, which would help design new superconductors with the antiperovskite structure. The synthesis and characterization on single crystals are desirable for future study in order to eliminate the divergences made by different authors or between the theoretical and experimental result.
Acknowledgments
This work was supported by the National Key Basic Research under Contract no. 2011CBA00111 and the National Natural Science Foundation of China under Contract nos. 50701042, 11174295, 51001094, 51171177, and 91222109.
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Copyright © 2012 P. Tong and Y. P. Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.