Sign change in c-axis thermal expansion constant and lattice collapse by Ni substitution in transition-metal zirconide superconductor Co1−xNixZr2

Recently, c-axis negative thermal expansion (NTE) was observed in a CoZr2 superconductor and related transition-metal zirconides. Here, we investigated the structural, electronic, and superconducting properties of Co1−xNixZr2 to achieve systematic control of c-axis NTE and switching from NTE to positive thermal expansion (PTE) by Ni substitution. At x ≤ 0.3, c-axis NTE was observed, and the thermal expansion constant αc approached zero with increasing x. At x = 0.4–0.6, c-axis thermal expansion close to zero thermal expansion (ZTE) was observed, and PTE appeared for x ≥ 0.7. On the superconducting properties, we observed bulk superconductivity for x ≤ 0.6, and bulk nature of superconductivity is suppressed by Ni heavy doping (x ≥ 0.7). For x ≤ 0.6, the evolution of the electronic density of states well explains the change in the superconducting transition temperature (Tc), which suggests conventional phonon-mediated superconductivity in the system. By analyzing the c/a ratio, we observed a possible collapsed transition in the tetragonal lattice at around x = 0.6–0.8. The lattice collapse would be the cause of the suppression of superconductivity in Ni-rich Co1−xNixZr2 and the switching from NTE to PTE.


Introduction
Thermal expansions are structural properties of materials.In the case of normal (positive) thermal expansion (PTE), an axis and/or volume expand with increasing temperature.In contrast, materials with negative thermal expansion (NTE), those contract with increasing temperature.Importantly, zero thermal expansion (ZTE) can be achieved by fabricating a composite using PTE and NTE materials, and the ZTE materials have been used in various structural materials and devices in which ultraprecision of positions is required [1][2][3][4][5].However, achievement of ZTE in a single material is quite rare [6] but has potential merits for development of ZTE application.Development of ZTE in a superconductor is particularly interesting because it will be available in superconducting devices like Josephson junctions with a strength to temperature cycle.
Recently, we reported anomalous axis thermal expansion in CuAl2-type (tetragonal) transition-metal zirconide superconductors TrZr2 (Tr: transition metal) [7][8][9].In CoZr2, for example, the c-axis shows NTE in a wide temperature range, while the a-axis exhibits PTE.Owing to the contrasting axis thermal expansion, CoZr2 and similar TrZr2 show volume ZTE in a limited temperature range.In addition, we revealed that the axis ratio c/a is the potential factor for switching the character of the c-axis expansion [9].In this study, we focus on CoZr2 and NiZr2 with a large and small c/a ratio, respectively.CoZr2 exhibits a c-axis NTE and is a superconductor with a transition temperature (Tc) of ~6 K [7,10,11].NiZr2 exhibits PTE in both a and c axes.
In previous works [12][13][14], synthesis and physical properties of a solid solution system of Co1-xNixZr2 were reported with its superconducting properties.Here, we show that the c-axis thermal expansion character in Co1-xNixZr2 is systematically changed from NTE, ZTE, and PTE with increasing Ni concentration x.

Methods
Polycrystalline samples of Co1-xNixZr2 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) were synthesized by arc melting in an Ar atmosphere.Powders of pure transition metals (Tr) of Co (99%, Kojundo Kagaku) and Ni (99.9%,Kojundo Kagaku) with a nominal composition were mixed and pelletized.The Tr pellet and plates of pure Zr (99.2%, Nilaco) were used as starting materials.The samples were melted five times and turned over after melting to homogenize the sample.X-ray diffraction (XRD) patterns were collected by θ-2θ method with Cu-Kα radiation on a Miniflex-600 (RIGAKU) diffractometer equipped with a high-resolution semiconductor detector D/tex-Ultra.For Hightemperature XRD on a Miniflex-600, the sample temperature was controlled by a BTS 500 attachment.The obtained XRD patterns were refined by the Rietveld method using RIETAN-FP [15], and the schematic images of the crystal structure were depicted using VESTA [16].The actual compositions of the samples were investigated using energy-dispersive x-ray spectrometry (EDX, Swift-ED, Oxford) on a scanning electron microscope (SEM, TM3030, Hitachi Hightech).
The temperature dependence of magnetization was measured both after zero-field cooling (ZFC) and field cooling (FC) using a superconducting quantum interference device (SQUID) on an MPMS3 (Quantum Design).
The first principles band calculations were performed using the WIEN2k package [17] within the PBE-GGA exchange-correlation functional [18].The virtual crystal approximation is adopted to take into account the effect of the elemental substitution of Ni for Co.We used the experimentally determined lattice parameters shown in Table 1.The atomic coordinates of Zr were theoretically optimized.RKmax and the k-mesh were set to 8 and 10×10×10, respectively.

3-1. Crystal structure analysis and axis thermal expansion
The obtained actual compositions at the Tr site are comparable to the nominal values and summarized in Table 1. Figure 1(a) shows the schematic images of crystal structure of Co1-xNixZr2.Figures S1(a)-S1(c) (supporting materials) are XRD patterns for x = 0-1.0.These compounds have a tetragonal CuAl2-type structure (I4/mcm), and the main peaks could be indexed with the structural model.Small impurity peaks of the orthorhombic TrZr3 phase are seen as indicated by asterisks as reported in Ref. 7, and the amount of the impurity decreased with increasing Ni concentration (x).We estimated lattice constants by Rietveld refinements, and the obtained parameters are plotted in Fig. 1(b) and summarized in Table 1.The obtained trend of lattice constants is consistent with a previous study [14].x.The turning point for the NTE and PTE is estimated between x = 0.4 and 0.6.Therefore, there is a possibility to synthesize the sample which exhibits the perfect ZTE along the c-axis by optimizing the Ni amount doped at the Co site.As well, materials that exhibit anisotropic thermal expansion have been reported, such as β-Eucryptite (LiAlSiO4) [19], Ag3[Co(CN)6] [20], and Ca2RuO4 [21].The mechanisms of NTE are diverse [1,22].
For example, the cause of the NTE on the monoclinic Ca2RuO4 is dxy orbital ordering and disordering [21].Not only electronic contributions but also structural properties contribute to the NTE mechanisms.In another study on α-(Cu2-xZnx)V2O7, the chemical substitution of Cu by Zr decreases the free space for the transverse vibrations, which suppresses NTE along the b-axis [23].Furthermore, Mn3Cu1-xGexN exhibits giant negative thermal expansion due to the local lattice distortion triggered by Ge dope [24].These facts will help us to understand the mechanisms of the anomalous (anisotropic) c-axis thermal expansion in the current system.Recently, we reported that the NTE along the c-axis for TrZr2 was caused by the robust Tr-Zr distance to the temperature change and the flexible bonding of the TrZr8 polyhedron units.In addition, the c/a ratio is found to be an essential parameter that determines the polyhedron shape and the thermal expansion characteristics [7,9].Therefore, further studies on electronic and/or orbital characteristics and local structures of Co1-xNixZr2 will be striking in determination of the mechanisms of the emergence of c-axis NTE in TrZr2.however, the samples with x = 0.1 and 0.2 have Tc slightly higher than that for x = 0. Figure 4(b) shows the enlarged view near the Tc for = 0, 0.1, 0.2, 0.3, 0.4.The highest Tc of 6.39 K was observed for x = 0.1.To discuss about the electronic origins on this behavior, we performed first-principles calculations for Co1-xNixZr2.Figure 5(a) shows the x dependence of density of states near Fermi level, DOS(EF).The x dependence of the calculated DOS(EF) looks consistent with the evolution of Tc if we assumed conventional phonon-mediated superconductivity [25], because a large DOS(EF) achieves a higher Tc in a conventional superconductor.Figure 5(b) shows the x dependence of Tc.As we mentioned above, the evolution of Tc at x = 0.1 is consistent to the DOS(EF) behavior where the x value is smaller than x = 0.7.However, we cannot explain the change in Tc with DOS(EF) behavior where x is larger than x = 0.7.As mentioned above, the samples with x ≥ 0.7 exhibit filamentary superconductivity; in Fig. 5(b), we indicated the boundary between bulk superconductivity (Bulk SC) and filamentary superconductivity (Filamentary SC).According the discussion above, we suggest that the bulk superconductivity observed for x ≤ 0.6 is positively linked to DOS(EF), which would suggest the importance of phonon in the superconductivity mechanism in TrZr2.
For x ≥ 0.7, bulk superconductivity is suppressed, while the DOS(EF) is comparable or higher than x = 0.6.To explore possible cause of the suppression of superconductivity, we estimated the c/a ratio of Co1-xNixZr2 using the data at 303 K and plotted in Fig. 5(c) as a function of x.Although c/a linearly decreases with increasing x for x ≤ 0.7, the slope clearly changes at around x = 0.6-0.8.For x = 0.7-1.0,another slope can guide the evolution of c/a.We propose that the change in the c/a ratio is a kind of transition to collapsed tetragonal phases as observed in iron-based superconductors CaFe2As2 and KFe2As2 and related layered compound [26][27][28][29][30].The electronic structure is generally affected by a collapsed tetragonal transition, which affects superconductivity as well [31,32], we assume that the disappearance of bulk superconductivity by Ni heavy doping is related to the collapsed transition.In our previous work, we suggested the trend that a higher Tc of TrZr2 is achieved with increasing lattice constant c [33].This fact is also consistent with the above scenario because the c-axis is largely compressed at around x = 0.7.To obtain further evidence on the collapsed transition and its relation to electronic structure, superconductivity, and axis thermal expansion, further investigations with different probes are needed.

Conclusion
We investigated the crystal structure, axis thermal expansion, electronic structure, and superconducting properties of transition-metal zirconide superconductor Co1-xNixZr2.The samples were synthesized by arc melting and characterized by powder XRD and EDX.At x ≤ 0.3, c-axis NTE was observed, and the thermal expansion constant (αc) approached zero with increasing x.At x = 0.4-0.6,c-axis thermal expansion close to ZTE was observed, and PTE appeared for x ≥ 0.7.Those results confirm that the c-axis NTE can be controlled by Ni substitution (tuning c/a ratio) and switched to PTE.On the superconducting properties, we observed bulk superconductivity for x ≤ 0.6, and bulk nature of superconductivity is suppressed by Ni heavy doping.For x ≤ 0.6, the evolution of the electronic DOS(EF) well explains the change in Tc, but it cannot explain the disappearance of bulk superconductivity at x ≥ 0.7.By analyzing the c/a ratio, we revealed a possible transition to collapsed tetragonal phases with a boundary concentration of x = 0.6-0.8 by Ni heavy doping.The

Figure 1 .
Figure 1.(a) Schematic images of the crystal structure of Co1-xNixZr2.(b) Ni concentration (x) dependence of

Figure 1 a 1 V
Figure S2(d) (supporting materials) shows the typical high-temperature XRD patterns.The 002 peak shifts to

Figure 3
shows the x dependence of the linear thermal expansion coefficient along the c-axis, which shows a successful control of the switching of NTE and PTE along the c-axis by tuning

Figure 2 .
Figure 2. (a-i) Temperature dependence of the normalized rate of change of the lattice constants a, c, and V from

Figure 5 .
Figure 5. (a) The x dependence of DOS(EF) for Co1-xNixZr2.(b) The x dependence of superconducting transition

Table 1 .
Results of chemical analyses, evolutions of lattice constants and thermal expansion constants, and Tc in examined Co1-xNixZr2.Tc with bracket indicates filamentary superconductivity.