Magnetic and transport properties of Zr_1−xNb_xCo₂Sn

The refinement of the single-crystal XRD study illustrates that Zr_0.725Nb_0.275Co₂Sn crystallizes in a cubic structure with space group Fm-3m (#225) and the lattice parameter a  =  6.097 50 Å. The further details are summarized in table 1. A schematic drawing of the crystal structure is shown in figure 1(a), where the Zr/Nb and Sn atoms form a NaCl-type frame with a simple cube of Co atoms inserted. The position of the Zr atoms (shown as green spheres) are partly occupied by Nb atoms (shown as gray spheres). The proportion of Nb atoms is approximately 30%, slightly higher than expected.

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The powder XRD patterns of the grounded single crystals for the five samples are presented in figure 1(b). The sharp diffraction peaks indicate the high crystalline quality, and the several additional low-density peaks marked with red asterisks correspond to the impurity of the Sn flux. The consistent peaks imply that the crystal structure remains in the Heusler phase of space group Fm-3m with Nb doping. The diffraction peaks shift to high degree with increasing x, obviously at a high degree, suggesting a change in the lattice parameter. The lattice constant a, refined from the powder XRD data, as a function of the doping concentration of Nb x, is plotted in figure 1(c). The value of a decreases monotonously as x increases, which may be related to the smaller atomic radius of the Nb atom (1.46 Å) compared to the Zr atom (1.6 Å). It must be noted that the nonstoichiometry of the Co atoms in these compounds is less than 2 (~1.83) and the vacancies of Co atoms are on the same level in all Zr_1−xNb_xCo₂Sn samples. As a result, the lattice parameter for x  =  0 is 6.200 78 Å smaller than that found in previous reports [30, 32].

Figure 2(a) shows temperature-dependent magnetic susceptibility (χ) from 2 K to 300 K with an applied field of H  =  1 kOe for all samples. Only the results of the ZFC mode are presented because the data overlap with those obtained with the FC mode. The χ–T curves exhibit similar characteristics, indicating a ferromagnetic to paramagnetic phase transition for each of samples. The sharp drop in χ near the transition allows for a reliable extraction of the Curie temperature [33]. T_C shifts a lower temperature with increasing x, which is accompanied with the reduction of the lattice constant. The magnitude of magnetic susceptibility at 2 K also drops considerably as the Nb concentration increases, further suggesting the weakening ferromagnetism with increasing Nb-doping. According to a previous theoretical work [14], the ferromagnetism in ZrCo₂Sn originates from a short-range ferromagnetic exchange interaction between Co atoms. Even though in many materials the reduction in the lattice constant enhances in the ferromagnetic exchange interaction and thus the Curie temperature. Our data, namely the stronger ferromagnetism at large lattice constant, rather suggest that mechanism of ferromagnetic exchange interaction is more complicated.

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In the previous reports, the T_C of polycrystalline samples ZrCo₂Sn is approximately 468 K [32], 352 K higher than that of NbCo₂Sn polycrystals [28]. In our experiment, the ZrCo₂Sn single-crystals exhibit a much lower T_C (~220 K), and the T_C of Zr_1−xNb_xCo₂Sn single crystals is lower than that of NbCo₂Sn polycrystals when x  ⩾  0.275. Kushwaha et al [29] have recently proposed that the Co vacancies may be account for the change in T_C of ZrCo₂Sn single crystals.

Figure 2(b) illustrates the inverse susceptibility (χ⁻¹) as a function of temperature. The data above the phase-transition temperature was fitted by the Curie–Weiss law via the formula ${{\chi}^{-1}}=T/C-{{T}_{\theta}}/C$, where T_θ and C are the Weiss temperature and Curie constant, respectively. A deviation between the χ⁻¹  −  T curves and fitted lines (dashed line in figure 2(b)) are observed. This deviation is fairly similar to that of HgCr₂Se₄ [34, 35], in which the spin correlations play an important role.

Figure 3(a) shows the isothermal magnetization as a function of the applied fields at T  =  2 K for different amounts of Nb doping. All samples exhibit very narrow hysteresis loops with a coercivity field of about 50 Oe. The magnetization reaches saturation at a field lower than H ~ 1 kOe. The value of the saturated magnetization (M_sat) decreases monotonously from 0.87 to 0.45 µ_B as x is increased from 0 to 0.5. It is noteworthy that M_sat of the ZrCo₂Sn sample is only 0.87 µ_B, much lower than 1.56 µ_B, reported for a polycrystalline sample [36]. This suggests that the magnetic properties of (Zr,Nb)Co₂Sn are very sensitive to the microscopic details of the samples, which deserve further investigation.

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Figure 3(b) displays the M–H curves for the sample with x  =  0.275 at several temperatures (2–200 K). At 2 K, the magnetization reaches the maximum value of 0.68 µ_B/F.U. Above 140 K, the magnetization is almost linear with the applied fields, consistent with a transition to the paramagnetic phase at T  =  110 K. The overall behavior is very similar to HgCr₂Se₄ [34, 35], which is also a soft ferromagnet.

Figure 4(a) displays the temperature dependences of the zero-magnetic field longitudinal resistivities of the Zr_1−xNb_xCo₂Sn samples. The overall trend is that the increase in the Nb-concentration results in larger resistivity value, but the value of ρ rises by less than an order magnitude as x is varied from 0 to 0.5. A common feature of all ρ–T curves is that a hump-like feature appears the Curie temperature, which is marked with a downward arrow. The undoped sample (x  =  0) exhibits a metallic behavior at a wide temperature range below T_C (~220 K). The Nb-doping leads to the shrinking of temperature range for the metallic behavior, which can be attributed to the decreasing T_C in as well as the resistivity upturn at low temperatures. The resistivity upturn becomes more pronounced with increasing Nb-concentration. For the sample with x  =  0.5, the metallic behavior below T_C nearly vanishes. It is also noteworthy that for x  =  0.275, the resistivity upturn is terminated with a small, but sharp drop as the temperature is lowered to 3 K. This feature might be attributed to a small amount of Sn phases in the sample, since the superconductivity transition temperature is 3.7 K and the resistivity drop can be suppressed by applying magnetic field.

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Similar humps around T_C in the ρ–T curves have been observed in many colossal magnetoresistance (CMR) materials (Ti₂Mn₂O₇, HgCr₂Se₄) and Heusler compounds (Fe₃Si, Fe₂Val, Ru₂CrSi) [37–44, 35]. In the CMR materials, the nanoscale phase separation or the formation of the magnetic polarons has been widely accepted as the origin of the resistivity hump around T_C [37–39]. The strong scattering caused by these spin in homogeneities can be suppressed by applying magnetic field, leading to the CMR effect observed in large variety of materials. Figures 4(b)–(e) show that similar phenomena also takes place in Zr_1−xNb_xCo₂Sn samples. The resistivity upturn at low temperatures may also be attributed to spin disorder due to the weakening ferromagnetism with increasing Nb concentration. Only for undoped samples, the strong ferromagnetism allows for a truly metallic ground state. This situation is quite different from (Ti,Sc)₂Mn₂O₇ samples, in which Sc-doping only weakly influence the magnetic order but can vary the resistivity by several orders of magnitude [41]. The low-T resistivity upturn observed in the (Ti,Sc)₂Mn₂O₇ samples with large Sc concentration (e.g. x  =  0.4) can be attributed to Anderson localization. In Zr_1−xNb_xCo₂Sn, The Nb-doping only results in modest increase in the resistivity, so the resistivity upturn is unlikely to be caused by the localization of charge carriers.

The MR curves of four samples are depicted in figures 5(a)–(c). At low temperatures, MR is mostly positive and shows no sign of saturation up to 5 T. Such a MR is a property of the metallic phase, which has been observed in many materials, both magnetic and non-magnetic. At high temperatures (above 30–50 K, which varies the Nb-doping level), the MR becomes negative. This can be attributed to the reduced spin-dependent scattering in applied magnetic fields. The crossover from positive to negative MR can be seen more clearly in figure 4(d), in which a crossover temperature of ~30 K can be determined from the detailed measurements between 15 and 35 K for the sample with x  =  0.275. At such a temperature, the sample is still in the ferromagnetic phase.

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Figure 6(a) shows the Hall resistivity (−ρ_xy) as a function of magnetic field µ₀H for x  =0.275 at various temperatures. A large AHE signal is found for T below 200 K, with a sharp increase at low temperatures near zero field. With T increasing, the AHE weakens and the sharp increase no long exist. In general, the Hall resistivity of a magnetic compound mainly comes from two parts: normal Hall resistivity ($\rho _{xy}^{0}$) and anomalous Hall resistivity ($\rho _{xy}^{{\rm AHE}}$) due to the magnetism in the sample,${{\rho}_{xy}}=\rho _{xy}^{0}+\rho _{xy}^{{\rm AHE}}={{R}_{{\rm H}}}\times B+{{\mu}_{0}}{{R}_{{\rm S}}}\times M$, in which ${{R}_{{\rm H}}}$ and ${{R}_{{\rm S}}}$ are respectively the normal and anomalous Hall coefficients, ${{\mu}_{0}}$ is the vacuum permeability, and M is the magnetization of the sample [45, 46]. $\rho _{xy}^{{\rm AHE}}$ increases rapidly and is dominant in ρ_xy at low fields. When the magnetization is saturated, $\rho _{xy}^{0}$ is responsible for the linear behavior of ρ_xy at high fields. Based on this, an electron density n  =  ~1.26  ×  10²² cm⁻³ can be extracted for the sample (x  =  0.275) at 2 K. Figure 6(b) further shows the normalized  −ρ_xy plotted as a function of normalized M at 50 K to 150 K. The data at all temperatures collapse nicely onto a single curve. This suggests that the Hall signal is dominated by the AHE and a unified description of magnetic and electronic structures can be developed for this wide temperature range.

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