Negative magnetoresistance in the antiferromagnetic semimetal V_1/3TaS₂

The recent discoveries of both long-range magnetic ordering in the atomically thin layers of Cr₂Ge₂Te₆,^[1] CrI₃,^[2] and Fe₃GeTe₂,^[3,4] and the chiral solitons in Cr_1/3NbS₂^[5,6] and Fe_1/4TaS₂^[7] rekindle interest in the intercalated transition metal dichalcogenides (TMDCs). TMDCs are a class of layered materials, whose structure can be classified into 1H (triangular prismatic), 1T (octahedral), 2H (hexagonal), 3R (rhombic), and so on, depending on the local coordination of atoms around the central transition metal atoms. The intercalation (or doping) of atoms (or molecules) can modulate the physical properties of materials,^[8–10] such as, the Cu intercalation in TiSe₂, leads to superconductivity,^[11] the Fe, Cr intercalations of TaS₂ or NbS₂ result in long-range magnetic order.^[12,13] More interestingly, the Cr intercalation in NbS₂ leads to the chiral soliton lattice formation due to the antisymmetric Dzyaloshinskii–Moriya (DM) interactions. TMDCs become a material platform for exploring various exotic physical properties.

In these TMDCs, the M_xTS₂ (M = 3d transition metal, T = Ta, Nb) family^[14] with x = 1/3 exhibit unique properties, due to the inserted ionic arranging in a stacked 3×3 superlattice, reducing the crystal symmetry.^[15] For example, a chiral helical magnetic order was observed in Cr_1/3NbS₂,^[5] a large anomalous Hall effect occurs in Co_1/3NbS₂.^[16] In this article, on the basis of growing successfully high-quality V_1/3TaS₂ crystals, we carried out the magnetization, longitudinal, and Hall resistivity measurements, combined with the electronic band structure calculations. It was found that V_1/3TaS₂ is an A-type antiferromagnet (AFM) with the Neel temperature T_N = 6.20 K, a single magnetic transition, which is different from the multi-transitions due to the existence of impurities or disorder, reported in the previous literature.^[17] We also observed the negative magnetoresistance (MR) occurring near T_N, resulting from the suppression of spin-scattering by an external magnetic field. It is interesting that both band structure calculations and Hall resistivity measurements demonstrate it is a magnetic semimetal.

V_1/3TaS₂ single crystals were grown by a chemical vapor transport method with two steps. First, polycrystalline samples were prepared by using a stoichiometric of V (99.9%), Ta (99.9%), and S (99.99%) powders, whose mixtures were sealed in an evacuated silica tube and heated at 1073 K for a week. Second, the evacuated silica tube containing the polycrystalline powders with iodine as transport agent (10 mg/cm³) was placed in a tube furnace, and heated for 7 days with a temperature gradient from 1223 K to 1123 K. The hexagonal crystals were obtained at the cold end, whose typical dimensions are 2 mm × 1 mm × 0.2 mm (see the inset of Fig. 1(d)). The composition of crystals was determined by the energy-dispersive x-ray (EDX) technique, as shown in Fig. 1(c), to be of V:Ta: S = 1:3:6. The crystal structure was checked by both polycrystalline (not shown) and single crystal x-ray diffraction (XRD), as shown in Fig. 1(d). The (00l) peaks with a small width at half maximum were observed, indicating that the obtained crystals have high quality. The length of the c-axis was estimated to be 11.19 Å, which is similar to that reported previously.^[17]

The longitudinal and Hall resistivity and magnetization measurements were carried out on the quantum design physical property measurement system (PPMS-9T) and magnetic property measurement system (MPMS-7T), respectively. To calculate the electronic band structure, and Fermi surface of bulk V_1/3TaS₂, the Vienna ab initio simulation package (VASP)^[18,19] with the generalized gradient approximation of Perdew, Burke, and Ernzerhof for the exchange–correlation potential^[20] was employed to perform the first-principles calculations based on the density functional theory (DFT). The projector-augmented wave (PAW) potentials were adopted for the inner electrons^[21] and the cores of S:(Ne, 3s²3p⁴), Ta:(Xe, 6s¹5d⁴), and V:(Ar, 4s¹3d⁴) have been used in the calculations. The kinetic energy cut off was chosen as 360 eV for the wave function, and the Γ-centered mesh 6 × 6 × 4 was used to calculate the electronic structures. The tolerance of energy convergence was chosen to be 10⁻⁶ eV.

Figures 1(a) and 1(b) show the crystal structure of V_1/3TaS₂, a hexagonal non-centrosymmetric structure, where the V³⁺ ions occupy the octahedral position and intercalate between the triangular prismatic layers of the parent 2H-TaS₂, forming a superlattice of 3×3 structure with lower symmetry. The host TaS₂ layer provides conduction electrons, while the orbital moment of V³⁺ is usually quenched due to the octahedral crystal fields of neighboring S²⁻, and the localized moment of V³⁺ mainly originates from the spins of the unpaired electrons.

In order to understand well the physical properties of V_1/3TaS₂ compound, we calculate its electronic band structure. Figure 2(a) shows the band structure of the A-type AFM phase with considering spin–orbit coupling (SOC). It is clear that the Fermi energy level (E_F) locates in the conduction band, indicating a metallic behavior, there are three hole pockets (the left, near the Γ and A points) and one electron pocket (near the K point), and the results reveal that it is antiferromagnetic out-of-plane and ferromagnetic in-plane. These results demonstrate that V_1/3TaS₂ is a magnetic semimetal.

Next, we discuss the results of magnetization measurements. Figure 2(b) shows the temperature dependence of magnetic susceptibility, χ = M/H, measured at a magnetic field of H = 2000 Oe applied along the c-axis with zero-field-cooling (ZFC) and field-cooling (FC) processes. Although the χ(T) curves measured with ZFC and FC processes seem to overlap with each other, small differences at low temperatures can be recognized in the magnified χ(T) curves (not shown). With decreasing temperature, the susceptibility increases continuously for both processes. A sharp peak occurs at T_N = 6.2 K in the χ(T) curves, corresponding to an antiferromagnetic transition. The susceptibility above T_N follows the Curie–Weiss law

where C is the molar Curie constant and θ is the Weiss temperature. Figure 2(b) (the right axis) shows the temperature dependence of inverse susceptibility, χ⁻¹(T), exhibiting a linear temperature dependence. We obtained that C ≈ 0.11 cm³⋅K⋅mol⁻¹, corresponding to the effective moment μ_eff ≈ 2.7 μ_B/V³⁺, and θ ≈ 3.8 K, close to T_N value, by fitting the χ⁻¹(T) data between 10 K–300 K. Different from the observations that two magnetic transitions emerge in the polycrystalline or as-grown V_1/3TaS₂ single crystals, only one transition was observed in our crystals, implying our crystal has high quality (no impurities or disorders). Early, V_1/3TaS₂ was identified as a ferromagnet by Parkin et al.,^[22] similar to that suggested for other intercalated TMDCs, such as, Cr_1/3TaS₂, a soliton candidate;^[13] Mn_1/3NbS₂, a ferromagnet with a long period spin modulation.^[23] Recently, based on their magnetization and neutron diffraction results on a single crystal of V_1/3TaS₂, Lu et al.^[17] suggested that V_1/3TaS₂ is an A-type antiferromagnet, composed of a staggered stacking of ferromagnetic planes, with a small out-of-plane canted (2°) of XY spins and the Neel temperature T_N = 32 K. Although the T_N value here is different from that reported by Lu et al.,^[17] we believe that the magnetic structure at low temperatures is the same as that determined by their neutron diffraction and the exchange interaction analysis, i.e., an antiferromagnetic stacking of ferromagnetic planes with a small canting of V³⁺ spins (A-type AFM).

Third, we discuss the influence of magnetic transition on electronic transport properties. Figure 3(a) presents the temperature dependence of longitudinal resistivity, ρ_xx(T), measured at zero field. With decreasing temperature, the resistivity decreases at first, reaches a minimum at about 60 K, then increases before dropping again below T_N. The resistivity exhibiting a maximum at T_N is usually due to the scattering of local spins to the conduction electrons, which is also confirmed by the resistivity data measured at magnetic fields. As shown in the inset of Fig. 3(a), with increasing magnetic field, the resistivity around T_N is suppressed, and its maximum at T_N almost disappears. Figure 3(b) shows the magnetoresistance (MR) as a function of magnetic field measured at various temperatures, here MR is defined as

where ρ(H) and ρ(0) are the resistivities measured at a magnetic field H applied along the c-axis and zero-field, respectively. Below 50 K, the resistivity decreases with increasing magnetic field H, i.e., exhibiting a negative magnetoresistance behavior, and MR reaches −5%, at μ₀H = 8 T, T = 1.8 K, which can be ascribed to reducing spin scattering by the applied magnetic field.

Finally, as mentioned above, the band structure calculations demonstrate that V_1/3TaS₂ is a magnetic semimetal, which is also confirmed by the Hall resistivity measurements. Figure 4(a) shows the Hall resistivity as a function of the magnetic field applied along the c-axis, ρ_yx(H,T), measured at various temperatures (1.8 K–100 K). Both the nonlinear field dependence of ρ_yx(H,T) below 20 K and the change in the slope of ρ_yx(H,T) from a positive value below 10 K to negative one above 40 K imply the existence of multi-band structure. To parameterize the Hall data, we analyze the longitudinal and Hall resistivity using a two-carrier model, as we discuss for other semimetals.^[24–29] In this model, the conductivity tensor in its complex representation is given as^[30]

where n_e (n_h) and μ_e (μ_h) denote the carrier concentrations and mobilities of electrons (holes), e is the elementary charge, respectively. To appropriately evaluate the carrier densities and mobilities, we calculate the Hall conductivity σxy=ρyx/(ρxx2+ρyx2) using the original experimental ρ_yx(H,T) data. Then, as shown in Fig. 4(b), we fit σ_xy(H,T) data using the fitting parameters and the field dependence given by^[31]

The obtained n_e (n_h) and μ_e (μ_h) as a function of temperature are plotted in Fig. 5 and the inset. It is clear that both the n_e and n_h are almost independent of temperature below 20 K, such as n_e(1.8 K) = 0.22 × 10¹⁹ cm⁻³, n_e(20 K) = 0.34 × 10¹⁹ cm⁻³, n_h(1.8 K) = 0.21 × 10¹⁹ cm⁻³, n_h(20 K) = 0.54 × 10¹⁹ cm⁻³, and enhance markedly with increasing temperature, such as n_e(100 K) = 8.2 × 10¹⁹ cm⁻³, n_h(100 K) = 3.6 × 10¹⁹ cm⁻³. On the contrary, the mobility of the hole, μ_h, increases rapidly with decreasing temperature and is much larger than the μ_e at lower temperatures, although they are almost the same at higher temperatures. These behaviors are similar to those occurring in many other semimetals.^[27,32]

We performed electronic structure calculations and measured the longitudinal resistivity, Hall resistivity, and susceptibility on V_1/3TaS₂ crystals with a hexagonal non-centrosymmetric structure (space group P6₃22). It was found that V_1/3TaS₂ is an A-type antiferromagnet with T_N = 6.20 K, and exhibits a negative MR near T_N. Both band structure calculation and Hall resistivity measurement demonstrated it is a magnetic semimetal.