npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Phys.: Sae Mulli 2023; 73: 324-329

Published online April 30, 2023

Copyright © New Physics: Sae Mulli.

Spin Clusters-Induced Electrical Transport Properties of Hexagonal and Orthorhombic Ni3Sn2

Beopgil Cho, Jaemun Park, Keeseong Park*

Department of Physics and Chemistry, Daegu Gyeongbuk Institute of Science and Technology, Daegu 42988, Korea

Correspondence to:*E-mail:

Received: January 3, 2023; Revised: February 21, 2023; Accepted: March 14, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Ni3Sn2 crystallizes into a hexagonal phase (HT-Ni3Sn2) at higher temperatures while it undergoes structural distortion and vacancy alignment to transform into an orthorhombic phase (LT-Ni3Sn2) at lower temperatures. LT-Ni3Sn2 has not been synthesized in a single-crystalline form, although spin heptamers of Ni atoms can constitute well-organized spin clusters and possibly influence various physical phenomena. This paper demonstrated a successful synthesis of both phases in single crystals using a flux method, and their electrical transport was measured. Both phases showed unusual metallic resistivity, which can be fitted via a power law. This power law behavior is frequently exhibited by compounds consisting of 3d transition metals because of their spin frustration. In magnetoresistance, LT-Ni3Sn2 showed an abrupt increase at a low temperature and weak magnetic field region, indicating an influence of the spin clusters or occurrence of a weak antilocalization due to a strong spin–orbit coupling.

Keywords: Single crystal, Ni3Sn2, Resistivity, Magnetoresistance

Topological materials have been researched extensively due to their exotic physical phenomena, and electrical transport is widely investigated for these materials for its use in observing the behavior of bands near the Fermi level[1, 2]. In particular, when combined with spin–orbit coupling, some spin states of topological materials could break the time reversal symmetry of the bands under the protection. Ferromagnetic Fe3Sn2 and antiferromagnetic Mn3Sn could be excellent examples because of their physical phenomena as magnetic topological materials, where Dirac and Weyl bands produce large anomalous Hall effects through interaction with their innate spin state[3, 4]. This is likely to be a case when a spin becomes unsettled by the nearest neighbors of the lattice[5]. Gerard Toulouse introduced this concept of geometrical frustration, and topics on crystals consisting of triangles and hexagons of 3d transition metals have been actively investigated.

Meanwhile, some crystals can possess topological properties from structural transformation. For instance, some IV–VI semiconducting crystals, such as SnTe, can transform from a cubic to a rhombohedral phase by decreasing the synthesis temperature[6]. Though symmetry is reduced for such crystals, they are still able to generate topological semimetallic properties such as nodal lines or Weyl points. However, although such method of distortion could break symmetry or produce new topological properties that can lead potentially intriguing research fields, it is difficult to find proper samples to be investigated.

It has been reported that many T–Sn binary phases can reduce symmetry via synthesis conditions. For instance, cubic Cu3Sn undergoes transformation to an orthorhombic phase around 650 °C. Here, orthorhombic Cu3Sn could generate large magnetoresistance because of the broken symmetry[7]. Likewise, Ni3Sn2 can have hexagonal (P63/mmc) and orthorhombic (Pnma) structures that are temperature dependent as shown in Table 1[8]. The hexagonal structure contains random vacancies at two sites of the unit cell, which should require high-activation energy of migration. In contrast, when synthesizing at lower temperatures, an orthorhombic distortion is permitted by assigning one site as fully filled while leaving others vacant; they have been named HT-Ni3Sn2 and LT-Ni3Sn2.

Table 1 Lattice parameters of HT-Ni3Sn2 and LT-Ni3Sn2, excerpted from [8].

Space groupP63/mmcPnma
a [Å]0.410458.1541
b [Å]0.410457.1247
c [Å]0.518315.1954

HT-Ni3Sn2 grown via chemical vapor transport (CVT) is known to exhibit anisotropic and enhanced paramagnetic behavior and unusual temperature dependence of resistivity that are proportional to the power law[9]. In fact, such dependence has frequently been observed in various materials consisting of 3d transition metals with geometrical frustration[10, 11]. What is fascinating is that Ni3Sn2 possesses such cusp from a relatively high temperature. In contrast, LT-Ni3Sn2 is less known as it has not been synthesized as a single-crystalline phase so far. Together with its ortho-rhombically distorted structure, the fully filled and other fully vacant sites could break structural symmetry enough.

Furthermore, spin heptamers may occur when the vacant site is filled, where hexagonal isostructural Fe1.3Sb exhibits a topological Hall effect via scalar spin chirality derived from the Dzyaloshinskii–Moriya interaction of the spin heptamer[12]. Similarly, stacked spin heptamers in LT-Ni3Sn2 function as spin clusters and exhibit intriguing physical properties, concerning geometrical frustration, when compared to HT-Ni3Sn2.

Here, we report that the synthesis of HT-Ni3Sn2 and LT-Ni3Sn2 using the flux method is possible, and we discuss some distinguishable properties observed in LT-Ni3Sn2 from the perspective of resistivity measurements.

All Ni3Sn2 single crystals in the study were synthesized using the flux method. We determined synthesis conditions using the Ni–Sn binary phase diagram. Ni, Sn, and Bi elements were mixed and placed in an alumina crucible. The silica ampoule containing the crucible was then sealed under partial Ar atmosphere. They were initially heated up to 1000 °C to ensure completely melting, HT-Ni3Sn2 single crystals were obtained at 800 °C, whereas LT-Ni3Sn2 single crystals were obtained at 450 °C via annealing for 7 days. Unlike the HT-Ni3Sn2 single crystals that were grown as long hexagonal rods, the as-grown LT-Ni3Sn2 single crystals resembled needles.

X-ray diffraction (Empyrean, Malvern Panalytical, United Kingdom) was conducted to identify the Miller indices of the single crystals, and energy-dispersive X-ray spectroscopy (S-4800, Hitachi, Japan) was used to determine its nominal composition. Electrical transport was measured using a home-built 14-T magnet (Oxford Instruments, United Kingdom). Magnetoresistance was defined via the formula MR = 100 × [ρ(H)ρ(T=0)/ρ(T=0)] and corrected using the equation ρ(|H|)=[ρ(H)+ρ(H)]/2.

Figure 1(a) shows HT-Ni3Sn2 with one hexago-nal layer of a fully occupied Ni(I) site and another hexagonal layer of a half-filled Ni(II) and Sn sites. Meanwhile, lowering the synthesis temperature changes the unit cell orthorhombically by aligning the Ni(II) sites, as shown in Fig. 1(b). Here, the top-view schematics of Figs. 1(c) and 1(d) represent the emergence of spin clusters, as the ordered Ni(II) sites create a line of spin heptamers onto the b-axis (equivalent to the hexagonal c-axis). Considering the distorted trimers of Ni(I) nets arising in broken symmetry, this could produce interesting phenomena. As-grown single crystals are shown in Figs. 1(e) and 1(f).

Figure 1. (Color online) (a, b) Crystal structure of (a) HT-Ni3Sn2 and (b) LT-Ni3Sn2. Red, green, and black balls represent Ni(I), Ni(II) and Sn, respectively. (c, d) Top-view schematic of (c) HT-Ni3Sn2 and (d) LT- Ni3Sn2. (e, f) Optical image of HT-Ni3Sn2 and LT-Ni3Sn2.

Figure 2 displays the X-ray diffraction patterns analyzed to determine the orientation of the planes of HT-Ni3Sn2 and LT-Ni3Sn2, which are shown in Figs. 1(e) and 1(f), respectively. Their sharp peaks guaranteed the crystal’s growth. Still, since HT-Ni3Sn2 and LT-Ni3Sn2 were almost indiscernible during the analysis, we intentionally synthesized the Ni3Sn2 crystals by pulling the ampoule at 450 °C without annealing. As they showed a mixed phase where the peaks were separated, our observation strongly suggests that the HT-Ni3Sn2 and LT-Ni3Sn2 phases, grown under distinct temperatures, had not indented each other. The energy-dispersive spectroscopy (EDS) result for each sample was nominally Ni2.98Sn2 and Ni3.24Sn2. This implies that Ni3Sn2 crystals could have nonstoichiometric Ni3+δSn2 or Ni3-δSn2, which is consistent with the Ni–Sn binary phase diagram. The Bi element had not been identified, implying that the flux was not indented or contaminated the crystal.

Figure 2. (Color online) (from the top) XRD patterns of HT-Ni3Sn2, mixed Ni3Sn2 and LT-Ni3Sn2. The insets show zoomed-in graphs between 80° and 83°.

Figure 3 depicts resistivity as a function of temperature. We found that the residual resistivity (ρ5K) of HT-Ni3Sn2 was 73.5 μΩ cm. Since ρ300K was 88 μΩ cm, the residual resistivity ratio (RRR = ρ300K/ρ5K) achieved was 1.27. This defective property was previously reported in isostructural Fe5Sn3, which had ρ5K 60 μΩ cm and an RRR of <2[11]. It is comparable to the out-of-plane resistivity measured at CVT-grown HT-Ni3Sn2 that exhibited ρ2K reaching 450 μΩ cm[9]. This may suggest the presence of anisotropy in the resistivity. The isostructural Fe1.3Sb showed semiconducting behavior in the same out-of-plane direction measurement and metallic behavior in the in-plane direction measurement in the same way as our configuration[12].

Figure 3. (Color online) Temperature dependence of resistivities and power-law fittings of HT-Ni3Sn2 and LT-Ni3Sn2. Red solid lines are results of the power law fitting for each crystal.

Fascinatingly, the order of the resistivity was similar in LT-Ni3Sn2, where ρ5K and ρ300K were 98.3 and 124 μΩ cm, respectively. The RRR achieved 1.20, indicating that the bad metal-like properties still existed. Therefore, although LT-Ni3Sn2 arranges randomly occupied Ni atoms, the resistivity was in a similar order against HT-Ni3Sn2. This is analogous to the Cu6Sn5, which also has hexagonal isostructural Cu6Sn5 and the monoclinic distortion η8-Cu5Sn4[13]. Thus, randomly distributed vacancy protects the structural symmetry, and its alignment may not enhance the metallic behavior.

The resistivity of metals is usually described using Matthiessen’s rule, ρ=ρd+ρp, where ρd is from the electron–defect scattering and ρp is from the electron–phonon scattering[14]. ρd is independent of temperature while ρp is linearly dependent on temperature. Therefore, the power law model ρ=a+bTn is applicable to describe the behavior of normal metals with n = 1. However, for magnetic metals with long-range ordering, n is greater than 1[15,16], whereas for metals with short-range ordering caused by geometrical frustration, n is less than 1[9,10].

We used the power law model to analyze HT-Ni3Sn2 over a temperature range between 50 and 300 K and found that n of HT-Ni3Sn2 was 0.89. When the fitting range became restricted to the intervals of 80 and 200 K, n was modified to 0.85. The measured value of n along the c-axis in Fig. 1(a) exhibits a substantial deviation from n = 0.07 that was previously measured for the CVT-grown crystal perpendicular to the c-axis[9]. Both measurements resulted in n < 1, which suggests that the crystal exhibits a short-range ordering that is different in each direction. The spin heptamer from the occupancy of Ni(II) atoms would make a spin cluster, which induces the anisotropic short-range ordering. The same analysis can be applied to LT-Ni3Sn2, which resulted in a value of 0.79 for n along the b-axis in Fig. 1(b), which is equivalent to the c-axis in HT-Ni3Sn2. By narrowing the fitting range from 80 to 200 K, n changed to 0.75. The smaller value of n observed for LT-Ni3Sn2 may indicate the presence of stronger short-range excitations in the crystal. It can be because of the ordered spin clusters via stacked heptamers, in contrast to the HT-Ni3Sn2, which can possess randomly distributed heptamers and clusters.

Notably, HT-Ni3Sn2 and LT-Ni3Sn2 also exhibited different behaviors in magnetoresistance, as depicted in Fig. 4. In Fig. 4(a), we found no clear dependence of magnetoresistance against the magnetic field for the HT-Ni3Sn2, in contrast to the reference[9]. This could be interpreted that our flux-grown HT-Ni3Sn2 may contain fewer Ni atoms or it has highly anisotropic transport behavior.

Figure 4. (Color online) (a, b) Transverse magnetoresistance graph of (a) HT-Ni3Sn2. and (b) LT-Ni3Sn2. Magnetic field was applied in ab-plane in HT-Ni3Sn2, and in ac-plane in LT-Ni3Sn2. Current was applied parallel to c-axis in HT-Ni3Sn2 and to b-axis in LT-Ni3Sn2.

In contrast, Fig. 4(b) shows the magnetoresistance of LT-Ni3Sn2, which is related to the increase in the magnetic field. It increased abruptly under 1 T with decreasing temperature and achieved 1.18% at 14 T and 5 K. Such a dip might imply fast short-range spin correlations via the occurrence of spin clusters in LT-Ni3Sn2. It could simply be a signal of the weak antilocalization derived from strong spin–orbit coupling, as demonstrated using several topological materials[17]. This behavior should be investigated further to elucidate the issue.

We successfully synthesized both single crystals of HT-Ni3Sn2 and LT-Ni3Sn2 using the flux method. The observed X-ray diffraction peaks imply that the phases are not merged and that each crystal shows that, as with the EDS results, they are not contaminated by flux. We found that both crystals are metallic with similar resistivity orders of magnitude. However, our analysis using the power law suggests LT-Ni3Sn2 may have stronger short-range excitations than HT-Ni3Sn2. In magnetoresistance, while HT-Ni3Sn2 was almost independent against the applied magnetic field, LT-Ni3Sn2 showed a strong dip at lower temperatures and weaker magnetic fields. This phenomenon might have something to do with its hidden nature in innate spin clusters. We hence conclude that LT-Ni3Sn2 could possess unusual physical properties, and further investigation would be required to elucidate speculations.

This work was supported by the DGIST institution specific program (21-BRP-07) and the faculty startup funds from DGIST.

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