Superconductivity of high-entropy-alloy-type transition-metal zirconide (Fe,Co,Ni,Cu,Ga)Zr₂

Transition-metal zirconides (TrZr₂) are superconductors with a wide range of transition temprature: T_c = 1.6, 5.5–6.0, 11.3, 7.5 K for Tr = Ni, Co, Rh, Ir, respectively [1]. The flexible solution at the Tr site is possible, and T_c is tuned by the Tr-site solution [2–4]. In addition, CoZr₂ exhibits a large enhancement of T_c under pressures, which suggests that the superconducting properties of TrZr₂ are sensitive to crystal-structure modification [5]. Recently, we reported synthesis and superconductivity of (Fe,Co,Ni,Rh,Ir)Zr₂ and (Co,Ni,Cu,Rh,Ir)Zr₂ [6, 7], in which the Tr site was designed based on the high-entropy-alloy (HEA) concept [8–12]. Due to the solution of five or more Tr elements at the Tr site, local structural disorders are expected, while investigation on local structural disorder has not been addressed in detail. Instead, from specific heat measurements on the superconducting transitions for the HEA-type TrZr₂, local (microscopic) inhomogeneity of the superconducting states were revealed from the broadening of the specific heat jump [13]. Because creation of local structural disorder and/or inhomogeneity of superconducting states would be useful for developing superconductivity application and creating novel superconducting states [14–19], further development of the examples of HEA-type superconductors with a high purity is desired. In this study, we synthesized an HEA-type TrZr₂ superconductor with 3d elements (Fe, Co, Ni, Cu, and Ga) and Zr, while we have investigated HEA-type TrZr₂ superconductors containing 4d and 5d elements [6, 7, 13]. The purity of the CuAl₂-type phase in the examined (Fe,Co,Ni,Cu,Ga)Zr₂ was the best among the HEA-type TrZr₂ samples studied so far. Therefore, we could reveal the effects of the HEA-type Tr site on the local disorder using neutron powder diffraction (NPD) at different temperatures. In addition, anomalous temperature evolution on the lattice constant c was revealed as well. Recently, we reported on the negative thermal expansion of the c-axis for CoZr₂ and alloyed phases [20]. The anomalous c-axis evolution in (Fe,Co,Ni,Cu,Ga)Zr₂ would be related to the negative thermal expansion of the c-axis observed in CoZr₂.

The Polycrystalline samples of (Fe,Co,Ni,Cu,Ga)Zr₂ was prepared by arc melting. Powders of Fe (99.9%), Co (99%), Ni (99.9%) and Cu (99.9%) and grains of Ga (99.9999%) were pelletized and melted together with Zr foils (99.2%) in an Ar atmosphere. The arc melting was repeated three times for homogenization. The actual composition of the obtained sample was examined by energy-dispersive x-ray spectroscopy (EDX, SwiftED, Oxford) on a scaning electron microscope (TM3030, Hitachi-hightech). From the obtained Tr-site composition, we calculated configurational entropy of mixing (ΔS_mix) at the Tr site using the formula of ΔS_mix = −RΣ_i c_i ln c_i , where c_i and R are the atomic fraction of component i and the gas constant, respectively.

The purity and crystal structure were investigated by NPD, and the Rietveld method was used for refining the crystal structure parameters. Low-temperature NPD experiments were performed with a HERMES diffractometer [21] installed at the T1-3 guide port in the JRR-3 of the Japan Atomic Energy Agency, Tokai. A thermal neutron beam was monochromatized to be 2.1972 Å with a vertically-focused Ge (331) monochromator. Typical instrumental parameters were determined by analyzing line positions and line shapes of a standard reference material (LaB₆, NIST660c) [22]. Powder samples were sealed in a vanadium cylinder cell with φ6 mm-diameter (thickness 0.1 mm) and ∼60 mm-length in a ⁴He gas atmosphere. A closed-cycle refrigerator was use to cool the samples and controlled from a base temperature (T ∼ 2 K) to room temperature. The obtained XRD and NPD patterns were refined by the Rietveld method using RIETAN-FP [23], and the schematic images of the refined crystal structure were depicted using VESTA [24].

The superconducting properties were investigated by electrical resistivity, magnetic susceptibility, and specific heat experiments. The temperature dependence of electrical resistivity was measured by the DC four-probe method under magnetic fields on a Physical Property Measurement System (PPMS, Quantum Design). Au wire (φ25 μm) and Ag paste were used for fabricating the terminals. The temperature dependence of magnetic susceptibility was measured by a superocnducting intereference device magnetometor on a Magnetic Property Measurement System (MPMS3, Quantum Design) in both zero-field-cooling (ZFC) and field-cooling (FC) modes with an applied field of 10 Oe. The temperature dependence of specific heat was measured by the thermal relaxation method on a PPMS.

3.1. Structural characterization

The actual Tr composition estimated from EDX is Fe_0.17(1)Co_0.18(2)Ni_0.21(2)Cu_0.25(1)Ga_0.19(1), and the estimated ΔS_mix is 1.60 R for the examined sample. In this paper, we call the HEA-type TrZr₂ sample (Fe,Co,Ni,Cu,Ga)Zr₂. The EDX mapping (figure S1 of supplementary materials) suggests homogeneous distribution of Tr elements.

Figures 1(a) and (b) show the NPD pattern taken at T = 290 K and 2 K, respectively, and the Rietveld refinement results. The profile could be refined with the tetragonal CuAl₂-type (space group: #140) model. To obtain better fitting, a small amount of the impurity phase of TrZr₃ (7%) is included in the refinements. The reliability factor for T = 290 K is R_wp = 11.7%. By comparing NPD patterns at T = 290 and 2 K, we notice that there is no clear indication of the magnetic ordering in the examined sample.

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The refined crystal-structure parameters are summarized in figure 2. With decreasing temperature the lattice constant a decreases, but c exhibits almost constant value. Because the decrease in Zr-Tr-Zr angle with decreasing temperature (figure 2(e)) is common to CoZr₂ [20], the anomalous c-axis thermal expansion would be achieved by the flexible structure of the TrZr₈ polyhedron. Figure 2(d) shows the temperature dependences of isotropic displacement parameter U_iso for the Tr and Zr sites. Noticeably, the U_isos do not remarkably change with decreasing temperature for the present sample. To investigate the effects of the presence of the HEA-type Tr site on the temperature dependence of U_iso in TrZr₂, the data for CoZr₂ (ΔS_mix = 0) are plotted together in figure 3. The NPD results for CoZr₂ were reported in [20]. The U_iso for Co at T = 50 K was too small and could not be refined; hence, the U_iso for Co at T = 50 K was fixed to U_iso for the Tr site. For CoZr₂, U_isos clearly decrease with decreasing temperature, which is ordinary temperature dependence of atomic displacements with assumption of atomic vibrations. In the case of materials with anharmonic vibrations (as in caged materials) [25] and/or local disorders [26, 27], large U_iso with a weak temperature dependence has been observed. The large U_isos with a small temperature dependence in (Fe,Co,Ni,Cu,Ga)Zr₂ indicate the glassy phonon characteristics, which would be induced by the HEA-type Tr site.

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3.2. Superconducting properties

Figure 4(a) shows the temperature dependences of electrical resistivity (ρ) for CoZr₂ and (Fe,Co,Ni,Cu,Ga)Zr₂. It is clear that the residual resistivity ratio RRR∼ 1 for (Fe,Co,Ni,Cu,Ga)Zr₂ is larger than that for CoZr₂, which is common feature in HEA-type compounds [12] and a clear indication of the local disorder introduced onto the HEA-type Tr site. Figures 4(b) and (c) show the ρ-T and the upper critical fields (B_c2) estimated from the $T_{\text{c}}^{\,{\text{onset}}}$ and $T_{\text{c}}^{\,{\text{zero}}}$; to estimate B_c2(0), we used the Werthamer–Helfand–Hohenberg model [28] and the fitting results are displayed in figure 4(c). The estimated B_c2s from $T_{\text{c}}^{\,{\text{zero}}}$ and $T_{\text{c}}^{\,{\text{onset}}}$ are 1.5 T and 3.5 T, respectively.

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Figure 5 shows the temperature dependence of magnetic susceptibility measured after ZFC and FC. A large diamagnetic signals were observed below 2.9 K, which indicates the emergence of bulk superconductivity below T_c = 2.9 K. Figure 6 shows the temperature dependence of electronic specific heat (C_el/T), where C_el was calculated by subtracting phonon contribution (βT³) estimated from the low-temperature-limit formula of C = γT + βT³. γ is electronic-specific-heat coefficient and was estimated as 19.03(4) mJ K⁻²mol. The jump of C_el at T_c was estimated by considering the entropy balance as shown with blue lines in figure 6. The estimated C_el/γT_c is 1.35 with T_c (specific heat) = 2.78 K, which is almost consistent with the weak-coupling BCS model [29]. From both magnetic susceptibility and specific heat, bulk nature of superconductivity was confirmed.

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Here, we briefly discuss about the inhomogeneity of superconducting states seen by specific heat in TrZr₂. As reported in [13], HEA-type TrZr₂ containing Rh and/or Ir exhibited clear broadening of the superconducting jump in C_el near T_c; their T_cs were around 5 K. Since no clear phase separation was observed in those HEA-type TrZr₂, we concluded that the inhomogeneous superconducting transitions in HEA-type TrZr₂ containing Rh and/or Ir are caused by the local disorder introduced by the HEA-type Tr site. However, in the present sample, (Fe,Co,Ni,Cu,Ga)Zr₂, the transition is sharp. One of the differences between previous phases containing Rh and/or Ir and the present (Fe,Co,Ni,Cu,Ga)Zr₂ is T_c. T_c (specific heat) = 2.78 K is lower than 5 K for the samples examined in [13]. Another potential explanation is the difference in electronic structure. By alloying the Tr site in TrZr₂, the electronic structure should be affected and the band dispersion would be smeared, as observed in HEAs [30, 31]. Since electronic characters of 3d, 4d, and 5d orbitals are different, the influence of the HEA-type Tr site would be smaller in 3d-based (Fe,Co,Ni,Cu,Ga)Zr₂ than that in compositions containing 4d of Rh and 5d of Ir. To clarify the electronic structure of HEA-type TrZr₂, growth of single crystals and angle-resolved photoemission spectroscopy are desired. We enphasize, however, that the glassy phonon characteristics revealed in figure 3 are evidently induced by the introduction of high configurational entropy of mixing at the Tr site in TrZr₂. Therefore, the 3d-based (Fe,Co,Ni,Cu,Ga)Zr₂ superconductor reported in this paper will be useful to understand the electronic, phonon, and superconducting properties and their relations to local structural disorder and ΔS_mix at the Tr site in the TrZr₂ system.

We synthesized a HEA-type transition-metal zirconide superconductor (Fe,Co,Ni,Cu,Ga)Zr₂, which has been designed with 3d transition metals for the Tr site. NPD confirmed the tetragonal CuAl₂-type crystal structure and the absence of long-range magnetic ordering in (Fe,Co,Ni,Cu,Ga)Zr₂. Although the a-axis exhibits normal positive thermal expansion, the lattice constant c does not remarkably change at T = 2–290 K, which would be related to the recently-discovered anomalous axes thermal expansion in CoZr₂. From electrical resistivity, magnetic susceptibility, and specific heat, the emergence of bulk superconductivity with a T_c of 2.9 K was confirmed. Comparing the experimental data for HEA-type (Fe,Co,Ni,Cu,Ga)Zr₂ and zero-entropy CoZr₂, we found the temperature dependence of U_isos for (Fe,Co,Ni,Cu,Ga)Zr₂ are clearly larger than those for CoZr₂ at low temperatures. The difference would be caused by the unique phonon characteristics induced by the local disorder in the HEA-type sample. Evidently, the temperature dependence of electrical resistivity exhibits clear difference: large RRR for CoZr₂ and small RRR∼ 1 for the HEA-type sample. The (Fe,Co,Ni,Cu,Ga)Zr₂ superconductor would be a model system useful to study the effects of local disorder introduced by the HEA-type site on superconducting properties and to explore exotic superconducting states.

The authors thank M Fujita, Y Goto, and O Miura for their supports in experiments and discussion. This work was performed under the GIMRT Program of the Institute for Materials Research, Tohoku University (CN: Center of Neutron Science for Advanced Materials: Proposal No. 202112-CNKXX-0001). This work was carried out by the JRR-3 program managed by the Institute for Solid State Physics, the University of Tokyo (the T1-3 HERMES IRT program: Proposal No. 22410). This work was partly supported by Grant-in-Aid for Scientific Research (KAKENHI) (Proposal Nos. 21K18834, 21H00151, 19H05164 and 21H00139) and Tokyo Government Advanced Research (H31-1).

The data that support the findings of this study are available upon reasonable request from the authors.