# Research Progress on Ni-Based Antiperovskite Compounds

Authors: P. Tong; Y. P. Sun
Journal: Advances in Condensed Matter Physics
 (2012)

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## Abstract

The superconductivity in antiperovskite compound MgCNi3 was discovered in 2001 following the discovery of the superconducting MgB2. In spite of its lower superconducting transition temperature (8 K) than MgB2 (39 K), MgCNi3 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 s-wave mechanism. Meanwhile many compounds neighboring to MgCNi3 were synthesized and the physical properties were investigated, which enriches the physics of the Ni-based antiperovskite compounds and help understand the superconductivity in MgCNi3. 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 phonon-mediated 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.


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## Body

## 1. Introduction

To explore new superconductors is one of the central issues of material science and condensed matter physics. The discovery of high-temperature (high-TC) 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 MgCNi3 with the transition temperature TC~8 K (Figure 1) [2]. The superconductivity in MgCNi3 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 (EF) [see Figure 2(b)] [3]. A similar feature has been observed in some high-TC superconductors. Moreover, the DOS peak is mainly attributive to the Ni 3d states [4, 5]. Structurally, the cubic symmetry recalls the high-TC cuprates superconductors with perovskite structures. Thus the central question was raised, whether the superconductivity in MgCNi3 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 MgCNi3. 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 MgCNi3 single crystals and on the synthesis and physical properties of neighbor compounds of MgCNi3, 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, N(EF), for the Ni-based antiperovskite compounds. The phase diagram supports that the superconductivity observed in the Ni-based antiperovskite compounds is rather phonon-mediated than unconventional. The phase diagram also helps explore new superconductors in Ni-based antiperovskite compounds. Some possible future research scopes were proposed in the end of this paper.Figure 1
The temperature-dependent resistivity for polycrystalline MgCNi3 [Adapted by permission from Macmillan Publishers Ltd: Nature. He et al., Nature, 411, 6833 (2001), copyright 2001]. The up and low insets show the antiperovskite crystal structure and superconducting transition, respectively.(a) Surface plot (and contour plot below) of the van Hove singularity inεk (relative to EF) in the G-M-X plane, with M at the right-hand corner (planar coordinates are given in units of 2π/a) [Reprinted with permission from H. Rosner et al., Phys. Rev. Lett. 88, 027001 (2002)]. (b) The peak structure in the electronic density of state around EF [Reprinted with permission from D. J. Singh et al., Phys. Rev. B 64, 140507 (2001)].
(a)
(b)


## 2. Experimental Results on Single Crystalline MgCNi3

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 MgCNi3 single crystal up to date, was reported in 2007 [17] by Lee et al., five years after the discovery of superconductivity in polycrystalline MgCNi3.In [17], Lee et al. employed a self-flux 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 MgCNi3 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 MgCNi2.8±0.05. As displayed in Figure 3, the transition temperature is found to be 6.7 K, slightly lower than the TC for polycrystalline MgCNi3. 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 high-resolution transmission electron microscopy (TEM) images for polycrystalline samples [17].Figure 3
(Color online) Temperature-dependent resistivity of MgCNi2.8 [Reprinted with permission from H. -S. Lee et al., Adv. Mater. 19, 1807-1809 (2007)]. The sample with four metallic leads is shown in the upper inset. The lower inset shows a magnified view of ρ(T) near the superconducting transition.In order to clarify the nature of the superconductivity in single crystal MgCNi3, 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 electron-phonon (e-p) scattering mechanism, indicating a conventional BCS behavior [18]. It is further supported by the linear behavior of HC2(T) near TC. The low-temperature electronic specific heat Cp(T) in superconducting state shows a classical exponential decrease confirming s-wave pairing with a moderate e-p coupling in this material [19, 20]. However, the Cp(T) at normal state cannot be well described by the usual T3 term of phonon contribution. A higher phonon-term 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 high-precision 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/kBTC≈4 and high specific-heat jump at TC in zero field, ΔC(TC)/γnTC≈1.96, indicating a strong-coupling mechanism. This scenario is supported by the direct gap measurements via the point-contact spectroscopy [20]. The reported superconducting parameters are summarized in Table 1. The availability of single crystal specimens also allows a detailed phonon-dispersion mapping which is closely related to the superconducting mechanism. By applying inelastic X-ray 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 MgCNi3. 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 well-studied NbSe2. Also, the PE in MgCNi3 was suggested be a dynamic phenomenon.Table 1
The lattice constanta, superconducting transition temperature TC, low critical field HC1(0), up critical field HC2(0), coherence length ξ(0), penetration depth λ(0), Ginzgurg-Landau parameter κ(0), electronic specific heat coefficient (Sommerfeld constant) γ, Debye temperature ΘD, coupling ratio 2Δ/kBTC, and the density of state at the Fermi level EF, N(EF), for the Ni-based antiperovskite superconductors. The parameters are mainly from [41]. The parameters under the “/” are for MgCNi3 single crystal from [17–20]. The values of N(EF) are from theoretical calculations reported in [4, 28, 42].
MgCNi3
CdCNi3
ZnNNi3
a (Å)
3.812/3.8125
3.844
3.756
T
C (K)
7.6/7.3
3.2
3
H
C
1
(
0
) (mT)
10
8.6
6.9
H
C
2
(
0
) (T)
14.4/12.8
2.2
0.96
ξ(0)
46/51
122
185
λ(0) (Å)
2480/2300
2767
3089
κ(0)
54/44
23
17
γ (mJ·mol−1 K−2)
30.1
18
13
Θ
D (K)
284/132
352
336
2Δ/kBTC
(3.75–5)/4
—
—
N(EF) (states eV−1/f·u)
4.99
3.82
2.813Although the experimental results measured on the single crystal samples suggest that MgCNi3 is a conventional BCS-type superconductor with mediate or strong e-p 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 Ni-deficient [17] though its superconducting parameters are close to those determined on polycrystalline samples (see Table 1). Theoretically, for another Ni-based antiperovskite compound InCNi3, 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 spin-fluctuations given a perfectly stoichiometric MgCNi3 single crystal. Therefore, a theoretical comparison between the Ni-deficient MgCNi3-δ and perfect MgCNi3 would resolve the problem. Moreover, growth of single crystals without Ni deficiencies is needed to end the ten-year debate on whether MgCNi3 is unconventional superconductor.


## 3. Research Progress on Ni-Based Antiperovskite Compounds other than MgCNi3

The purpose of investigating the materials which are closely related to MgCNi3, that is, AXNi3 (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 MgCNi3. Up to date, there are more than ten compounds neighboring to MgCNi3 were synthesized and the physical properties investigated. These newly synthesized Ni-based antiperovskite compounds can be grouped into three types, that is, carbides ACNi3, nitrides ANNi3, and borides ABNi3.CdCNi3 with the same number of valence electrons as MgCNi3 is another superconductor in the carbides ACNi3. As shown in Figures 4(a) and 4(b), the transition temperature TC is around 3.2 K, varying with fabrication conditions [27]. The superconducting parameters are listed in Table 1. The specific heat Sommerfeld constant γ is 18 mJ/(mol K2), smaller than that of MgCNi3. However, the theoretical calculation shows the N(EF) value is slightly larger than MgCNi3, while the calculated e-p coupling coefficient (0.8) is nearly half that of the corresponding value of 1.5 for MgCNi3 [28]. This is argued to be associated with a softening behavior of the lowest acoustic phonon branch along the X-R symmetry direction [28]. The large Wilson ratio RW=(π2κB2/3μB2)(χ0/γ)~12 and the well suppressed upper critical field Hc2(0)~2.2 T, compared with the Pauli limit (14 T) indicate the existence of strong FM correlations. Surprisingly, ZnCNi3 with the same number of valence electrons, as MgCNi3 and CdCNi3, is found to be a Pauli paramagnetic (PM) metal without signals of superconductivity down to 2 K [29]. The value of γ is only 6.77 mJ/(mol K2), much smaller than those of MgCNi3 and CdCNi3 (see Table 1), indicating a very weak e-p coupling that explains the disappearance of superconductivity. However, it was theoretically suggested that the experimental ZnCNi3 is carbon deficient, while the stoichiometric compound should be superconducting [30].Temperature dependence of magnetic susceptibility (a) and electrical resistivity (b) for different CdCNi3 samples [Reproduced with permission from M. Uehara et al., J. Phys. Soc. Jpn. 76, 034714 (2007)]. Temperature dependence of electrical resistivity (c) and magnetic susceptibility (d) for ZnNyNi3 [Reproduced with permission from M. Uehara et al., J. Phys. Soc. Jpn. 78, 033702 (2009)].
(a)
(b)
(c)
(d)The polycrystalline ACNi3 (A = Al, Ga, In) series with one more valence electron than MgCNi3 were prepared by solid state reaction and detailed studies of their basic properties were performed. For GaCNi3, a T2 temperature dependence of resistivity was observed. The large values of the Kadowaki-woods ratio A/γ2~7.2 (μΩ cm/K2) and the Wilson ratio RW~9.2 suggest a highly correlated Fermi liquid behavior [31]. The large electron-electron correlation was suggested to be caused by the proximity of FM order from the side of exchange-enhanced Pauli paramagnet, evidenced by the remarkable enhancements in both the specific heat Sommerfeld constant γ and the temperature-independent magnetic susceptibility χ0. As to AlCNi3 compound, the magnetic properties also show it is a strongly exchange-enhanced Pauli paramagnet in the very vicinity of FM order [32]. However, the low-temperature resistivity is nearly linear temperature-dependent, indicating a possible non-Fermi-liquid behavior which is in sharp contrast with GaCNi3. The low-temperature electronic specific heat reveals that the spin fluctuations in AlCNi3 are strongly enhanced when compared with the superconducting MgCNi3, while the e-p couplings are comparable in both compounds. The Wilson ratio RW is about 2.4 and the dimensionless ratio that connects the low-temperature Seebeck coefficient with the Sommerfeld specific heat constant indicate that AlCNi3 can be considered as a modest electron-correlated material. Consistently, the enhanced spin fluctuations were confirmed using 27Al NMR measurement in ACxNi3 with x≥0.1 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 AlCNi3 is a weak ferromagnet with the FM-PM transition at 300 K [35]. The nonmagnetic ground state for AlCNi3 and GaCNi3 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 InCNi3, 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 In0.95CNi3. 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 InCNi3 is a nonmagnetic metal and far away from a long-range magnetic order [25, 40]. Both In vacancies and substitutional Ni on In site were found to be able to lead to a spin-polarized ground state. Energetically, the latter scenario is more preferable to generate a FM ground state [25].ZnNNi3 is the only superconductor observed so far in the nitrides ANNi3 [41]. The TC~3 K, as shown in Figures 4(c) and 4(d), is close to that of CdCNi3. The magnetic susceptibility shows a Pauli-like behavior with the magnitude much smaller than that of CdCNi3. It indicates the FM correlations in this material are not as enhanced as in CdCNi3. The obtained specific heat Sommerfeld constant γ is 13 mJ/(mol K2), smaller than the value of 18 mJ/(mol K2) for CdCNi3. Even so, the TC is close to CdCNi3 because the FM correlation which could suppress the TC is weak in ZnNNi3. Compared with MgCNi3, a significantly reduced N(EF) was theoretically observed in ZnNNi3 [42], which accounts for the lower TC in ZnNNi3 than in MgCNi3. The CdNNi3 and InNNi3 were also successfully synthesized by the same authors of [41] but neither is superconducting [43]. The γ value is 12 mJ/(mol K2) and 8 mJ/(mol K2) for CdNNi3 and InNNi3, respectively, smaller than that for ZnNNi3. However, the temperature-independent magnetic susceptibility χ0 for CdNNi3 and InNNi3 is larger than that of ZnNNi3, indicative of an enhanced contribution from the FM correlations in the former two compounds. It shows by theoretical calculations that the N(EF) for CdNNi3 is comparable with that for ZnNNi3 [44], but the N(EF) is much reduced in InNNi3 [45]. Assuming that the e-p coupling is comparable in CdNNi3 and ZnNNi3, it is possible to observe superconductivity in CdNNi3 in case the FM correlations can be well suppressed. Very recently, He et al. reported two series of doped CdNNi3, that is, Cd1-xInxNNi3 (0≤x≤0.2) and Cd1-xCuxNNi3 (0≤x≤0.2) [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 CdNNi3reported previously by Uehara et al. [43].Compared with the carbides ACNi3 and nitrides ANNi3, little attention has been paid to the borides ABNi3. To the best of our knowledge, ScB0.5Ni3 [47] is the only boron based Ni-based 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 ABNi3 (A = Al, Ga, In, and so on) samples by solid state reaction [48]. The pure sample of InBNi3 with the antiperovskite structure (lattice constant a=3.795 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 χ(T) 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 low-temperature specific heat data, plotted as C(T)/T versus T2, can be well fitted using the following formula, C(T)/T=γ+βT2,where γ 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 γ and β are equal to 11.33 mJ/(mol K2) and 0.32 mJ/(mol K4), respectively. The Debye temperature ΘD is estimated to be 311 K according to the formula, ΘD=(n×1.944×106/β)1/3, where n 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 InBNi3. The value of γ is smaller than the superconducting compounds in Table 1. So the e-p coupling is weak in this compound, accounting for the disappearance of superconductivity. Theoretically, the N(EF) is only 1.47 states eV−1/f·u [49], consistent with the observed small γ. Besides, the authors predicted that introduction of holes into InBNi3 could make it superconducting, which has not been proved experimentally yet. Theoretically, it is predicted that AlBNi3 is candidate for studying unconventional superconductivity, which has not been tested experimentally either [50].(Color online) The physical properties for InBNi3. (a) dc magnetic susceptibility χ(T) at H=1 kOe. Inset shows the temperature dependence of resistivity measure at zero field. (b) Specific heat as a function of temperature. Inset shows a linear fit of C(T)/T versus T2 below 15 K.
(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 Ni-based antiperovskite compounds, thus to shed light on the unique superconductivity in MgCNi3. The Debye temperature ΘD obtained from specific heat measurements, the calculated density of state at Fermi level N(EF) available in the published literatures are plotted as a function the lattice constant, as shown in Figure 6. Two main trends can be found, (1) the ΘD increases approximately as the lattice constant is reduced. (2) The shrinkage of lattice constant reduces the N(EF), which is more scattered than ΘD though.Figure 6
(Color online) The Debye temperature,ΘD, and the DOS at EF, N(EF) as a function of the lattice parameter a for Ni-based antiperovskite compounds. The crossing dashed lines indicate the trends of ΘD (downwards) and N(EF) (upwards) with increasing the lattice constant a. The ΘD values are derived from specific heat data reported in [26, 29, 31, 32, 41]. The N(EF) values are from theoretical calculations where corresponding calculated lattice constant is the closet to the experimental ones [4, 28, 30, 37, 39, 40, 42].The evolution ofΘD 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 N(EF). It is more general that the DOS is inversely proportional to the band width W. for a cubic solid, the band width is related with the lattice constant a by the expression W~1/a3 [29]. Therefore, the decrease of lattice constant will increase the band width, leading to a reduction of N(EF). In addition, the theoretical calculations show there is a peak structure in the DOS below the EF for all Ni-based antiperovskite compounds AXNi3. For carbide compounds ACNi3 (A = Al, Ga, In) or ZnNNi3 that has more electrons than MgCNi3, could be interpreted as electron-doped MgCNi3, resulting in a downward shift of the position of the peak in the DOS from the EF, consequently a reduced N(EF) [39]. In a word, the N(EF) 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 InBNi3 whose N(EF) 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 ACNi3 [51].For a BCS theory, the e-p coupling constant can be estimated by the McMillan’s formula [32], λph=[N(EF)〈I2〉/M〈ω〉], where 〈I2〉 is the averaged electron-ion matrix element squared, M is an atomic mass, and 〈ω2〉 the averaged phonon frequency proportional to Debye temperature ΘD. Therefore, a combination of a large N(EF) and small ΘD will lead to a strong e-p coupling, consequently a BCS-like superconductor. The Ni-based antiperovskite compounds seem to obey this raw. All discovered superconductors locate on the right side of the map in Figure 6, where the ΘD is relatively small, but the N(EF) is relatively large. For instance, MgCNi3 which shows the highest TC has the largest N(EF) and smallest ΘD. Figure 6 also suggests that the superconductivity observed in the Ni-based antiperovskite compounds is predominantly s-wave BCS type mediated by e-p coupling, though the other contributions, for example, from spin fluctuations, may not be excluded. We note that the ΘD for MgCNi3 in the figure is from polycrystalline sample [27], while the value deduced from resistivity for single crystal MgCNi3 is surprisingly small (132 K) [18]. There is no clear trend for the relation between number of the valence electrons and N(EF) or ΘD. Regardless of this, the phase diagram in Figure 6 provides a clue for searching new superconductors in Ni-based antiperovskite compound AXNi3, 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 MgCNi3 single crystals with ideal 1 : 1 : 3 stoichiometry would finally close the long-time debate on the mechanism of superconductivity.b.
In order to clarify the divergences among the experimental and theoretical results for the Ni-based antiperovksite compounds other than MgCNi3, more extensive investigations on single crystal samples are desirable. The growth of single crystal AXNi3 is a challenge. The successful growth of MgCNi3 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 AXNi3 materials may serve as a platform for studying quantum critical phenomena (QCP) and quantum phase transitions (QPT) in simple material systems with three-dimensional 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 AXNi3, such as AlCNi3, GaCNi3, and CdCNi3, 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 Ni-based antiperovskite compounds closely related to the superconducting MgCNi3. 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.



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