Large transverse magneto-thermoelectric effect in narrow-band-gap polycrystalline Ag_2−δTe

Abstract

To achieve practical applications of transverse thermoelectricity, it is essential to discover novel high-performance polycrystalline transverse magneto-thermoelectric materials. Herein, we find that polycrystalline Ag_2−δTe exhibits a peak Nernst thermopower of 625 μV K⁻¹ at 75 K under a magnetic field of 14 T. Such a high value might originate from the enhanced bipolar effect and the crossed linear band near the low-temperature N–P transition. Our studies suggest the promising potential of Ag₂Te-based materials for energy conversion utilizing the Nernst effect and open up a new avenue for the development of novel magneto-thermoelectric materials.

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Introduction

Thermoelectricity plays a crucial role in solid-state waste-heat harvesting and cooling, as it enables the direct conversion of electricity into heat and vice versa without mechanical components and greenhouse gas emissions.^1–3 In recent years, significant advancements have been made in traditional thermoelectric materials by band engineering, such as band convergence,^4–6 band flattening,⁷ or phonon engineering, including nano-inclusions^8,9 and grain boundaries.^10–12 Additionally, the application of an external magnetic field offers an additional strategy for optimizing thermoelectric performance.¹³ In general, magneto-thermoelectric (MTE) effects encompass both longitudinal and transverse components, depending on the orientations of the temperature gradient, magnetic field, and voltage. When the magnetic field is applied perpendicularly to the temperature gradient (along the x-axis), a voltage drop can be generated along the y-axis, known as the transverse-MTE or the Nernst effect. The hallmark of the Nernst effect is the involvement of both electrons and holes within a single material, making it feasible to manufacture a transverse-thermoelectric device using only one type of material.¹⁴

Previous studies on the Nernst effect have mainly focused on single-crystal materials, such as Cd₃As₂, PtSn₄, and Mg₂Pb,^14–16 due to their susceptibility to defects. However, compared to single-crystal materials, polycrystalline materials are easier to fabricate and more promising for practical applications. Consequently, studies on MTE effects in polycrystalline materials have attracted significant attention in recent years. For instance, Feng et al. reported that polycrystalline Mg_3+δBi₂:Mn_x exhibits a significant transverse thermopower of 617 μV K⁻¹ and a power factor of 20 393 μW m⁻¹ K⁻² under a 14 T magnetic field at 14 K.¹⁷ This remarkable performance is attributed to the modulation of chemical pressure through Mn doping, resulting in the transition from a topological insulator to a Dirac semimetal. Li et al. revealed that, due to the electron–hole compensation and phonon-drag effect, polycrystalline NbSb₂ achieves a high transverse thermopower of 396 μV K⁻¹ under a 9 T magnetic field at 21 K.¹⁸

These results indicate that MTE materials are predominantly topological semimetals, characterized by linearly dispersed low-energy excitations and unique topological surface states. The presence of massless Weyl and Dirac quasiparticles typically results in ultra-high carrier mobility, which is beneficial for MTE properties. Furthermore, there are also some narrow-band-gap semiconductors exhibiting high transverse thermoelectric performance, such as Bi₇₇Sb₂₃ (E_g = 4.4 meV)¹⁹ and Re₄Si₇ (E_g = 120 meV).²⁰ The change of Hall mobility induced by Te-doping in Bi₇₇Sb₂₃ and the coexistence of electrons and holes in different bands, which is called the multi-carrier mechanism, in the near-intrinsic semiconductor Re₄Si₇ result in the enhanced transverse thermoelectric performance. For the narrow-band-gap semiconductor Ag_2−δTe, on one hand, according to Abrikosov's theory, it exhibits a crossed linear band when doped near 100 K.²¹ On the other hand, Ag_2−δTe (E_g = 50 meV) exhibits an electronic mobility of approximately 8000 cm² V⁻¹ s⁻¹ at 300 K,²² which is related to the narrow-band-gap electronic structure near room temperature. In general, the Nernst effect is influenced by the carrier mobility and the band structure.²³ On one hand, the magnetic effect, including the Nernst effect, is influenced by the parameter eBτ/m* which can be enhanced by the high magnetic field B and high carrier mobility μ = eτ/m* simultaneously, where e is the electronic charge, τ is the relaxation time and m* is the effective mass, respectively.²⁴ On the other hand, in non-magnetic semimetal materials, electron–hole compensation, small Fermi surfaces, and high carrier mobility arising from the crossed linear band will be beneficial for enhancing the Nernst effect.^25,26 Consequently, the narrow-band-gap semiconductor Ag_2−δTe might exhibit promising MTE properties.

Herein, we observe that polycrystalline Ag_2−δTe exhibits a peak transverse-MTE value of 625 μV K⁻¹ at 75 K, along with a peak transverse power factor of 532 μW m⁻¹ K⁻² at 300 K. Consequently, Ag_2−δTe exhibits an average Z_N value of 2.9 × 10⁻⁴ K⁻¹ over a wide temperature range of 80–300 K. These results highlight the promising potential of Ag₂Te-based materials for thermoelectric conversion applications utilizing the Nernst effect. These findings also provide a new pathway for discovering novel MTE polycrystalline materials.

Experimental section

Material synthesis

Polycrystalline Ag_2−δTe samples were prepared by melting high purity Ag shots (99.99 wt%, Beijing ZhongNuo Advanced Materials) and Te lumps (99.999 wt%, Beijing ZhongNuo Advanced Materials) together in vacuum-sealed quartz ampoules at a temperature of 1273 K for a duration of 10 hours. Stoichiometric amounts of Ag and Te were weighed according to the nominal compositions of Ag_2−δTe (δ = 0, 0.005, 0.01, 0.02). The as-cast ingots were subjected to a quenching process in cold water, followed by annealing at a temperature of 700 K for 3 days. The annealed ingots were then ground into fine powders using an agate mortar. Spark plasma sintering (SPS) was employed to consolidate the powders at 700 K under 50 MPa for 10 minutes. The resulting SPS bulks had a diameter of 10 mm and a thickness of 4 mm. To facilitate subsequent characterization, the sintered compacts were cut into various geometries using a diamond wire cutting machine. The relative densities of the sintered samples exceeded 97%.

Material characterization

The phase structure was determined using X-ray diffraction (XRD) with Cu Kα radiation (λ = 1.5406 Å) at room temperature. XRD measurements were performed on a SmartLab instrument. The temperature-dependent thermal conductivity was measured using the thermal transport option (TTO) on a Quantum Design Physical Property Measurement System (PPMS 14 T). The measurement configuration involved a one-heater and two-thermometer setup. Simultaneous measurements of the transverse and longitudinal thermopower were carried out using a custom sample geometry on the same PPMS system. The heat flow occurred between the hot and cold thermometers which were attached to the lower side of the sample. The transverse voltage leads were deliberately offset to allow for the measurement of both the longitudinal (Seebeck) and transverse (Nernst) voltages. It should be emphasized that, considering the inhomogeneous distribution of the sample temperature due to the voltage offset and the thermal hall effect, the inaccuracies of Seebeck and Nernst coefficients are about 20% and 10%, respectively. The longitudinal and Hall resistivities were determined using the four-probe alternating current transport option (ACT) on the PPMS system.

Results and discussion

Ag₂Te has a monoclinic crystal structure and belongs to the space group P2₁/c.²⁷ Ag_2−δTe, with a slightly excessive Te content, has the same lattice structure as the stoichiometric Ag₂Te and exhibits significant magnetoresistance (MR = [ρ_xx(B) − ρ_xx(0 T)]/ρ_xx(0 T)) effect.²⁸ Since a positive correlation exists between MR and MTE effects,¹⁷ a series of Ag_2−δTe samples with nominal compositions of Ag_2−δTe (δ = 0, 0.005, 0.01, and 0.02) were synthesized to optimize the MR effect. Since the maximum MR value of Ag_2−δTe occurs around 100 K,²⁹Fig. 1a compares the maximum MR of polycrystalline Ag_2−δTe samples with different nominal compositions (δ = 0, 0.005, 0.01, and 0.02) around 100 K under a magnetic field of 9 T. Through the defect engineering strategy proposed by Feng et al.,³⁰ the MR of Ag_2−δTe at 100 K under 9 T increases from 317% to 741%, 822%, and 733% as the nominal Ag-deficient content δ increases from 0 to 0.005, 0.01, and 0.02, respectively. Moreover, as shown in Fig. 1b, the XRD patterns at room temperature confirm that the samples belong to the monoclinic phase and space group P2₁/c. However, with δ increasing to 0.02, the excessive Te in sample #4 results in the appearance of Ag₅Te₃ impurities. Therefore, the pure phase sample #3, with a nominal composition of Ag_1.99Te, exhibiting a maximum MR value of 822% at around 100 K under 9 T, is selected for the subsequent studies.

Fig. 1 (a) The MR measured under 9 T at 100 K, and (b) XRD patterns (at 300 K) of Ag_2−δTe samples [sample #1 (δ = 0), #2 (δ = 0.005), #3 (δ = 0.01), and #4 (δ = 0.02)].

Fig. 2a displays the temperature-dependent transverse-MTE properties of polycrystalline Ag_2−δTe (sample #3) with a nominal composition of Ag_1.99Te. The transverse thermopower was measured with the temperature gradient (dT/dx) along the x-axis, voltage (V) along the y-axis, and magnetic field (B) along the z-axis as illustrated in Fig. 2a. As shown in Fig. 2a, the transverse thermopower (S_xy) increases with the increase of the magnetic field and reaches a peak value of 625 μV K⁻¹ under 14 T at 75 K. This value is much higher compared to previously reported values for another silver chalcogenide, Ag₂Se, and is comparable to the S_xy values of other outstanding transverse thermoelectric materials,^{14–19,30–34} such as polycrystalline Mg_3+δBi₂:Mn_x (617 μV K⁻¹ under 14 T at 14 K) and single-crystal NbSb₂ (616 μV K⁻¹ under 9 T at 25 K) (Fig. 2b).

Fig. 2 Transverse thermopower properties of Ag_2−δTe. (a) Temperature dependent transverse thermopower under a magnetic field from 1 T to 14 T. (b) The comparation of the optimal transverse thermopower between our work (Ag_2−δTe) and other materials. Including some single-crystal materials (PtSn₄,¹⁵ Cd₃As₂,¹⁴ Pb_0.77Sn_0.23Se,³² Mg₂Pb,¹⁶ and NbSb₂ (ref. 31)) and some polycrystal materials (Ag₂Se,³³ Bi₇₇Sb₂₃,¹⁹ NbP,³⁴ Mg₃Bi₂,³⁰ NbSb₂,¹⁸ and Mg_3+δBi₂:Mn_0.1 (ref. 17)).

In order to understand the mechanism of magnetic-field enhanced S_xy in polycrystalline Ag_2−δTe, Hall resistivities and Seebeck coefficients were measured. The temperature-dependent Hall resistivity (ρ_xy) (Fig. S1a†) and Seebeck coefficient (S_xx) (Fig. S1b†) approach zero near 75 K, where the N–P transition occurs,³⁵ indicating nearly symmetrical electron and hole transport. Furthermore, as a narrow-gap semiconductor (∼50 meV, about 2k_BT at 300 K),³⁶ the bipolar effect is inherent in Ag_2−δTe.¹⁶ In the longitudinal mode, the bipolar effect induces the decrease of the Seebeck coefficient. However, in the transverse mode, the electrons and holes are driven towards opposite directions under the magnetic field, which can enhance the Nernst effect. According to the simplified bipolar transport model with a single conduction band and a single valence band,¹⁶ the transverse thermopower S_xy increases with increasing the magnetic field. Additionally, at a specific magnetic field, when the conductivities of electrons and holes are equal, the value of S_xy is maximized.¹⁶ As a result, S_xy reaches its peak value near the N–P transition temperature (∼75 K) (Fig. 2a), which is attributed to the nearly symmetric transport of electrons and holes. The peak position of S_xy shifts towards higher temperature with increasing the magnetic field, which is consistent with the behavior of the N–P transition, as shown in Fig. S1a and b.† As temperature increases, Ag_2−δTe changes to an N-type semiconductor (Fig. S1a†) with electrons as the majority carrier. In the range of 75–200 K, the resistivity decreases with temperature (Fig. 3a), which is a general behavior of a narrow-gap semiconductor. Due to the increased electron concentration from thermal excitation, the contribution of electrons to the conductivity gradually exceeds that of holes. The partial conductivity ratio (σ_e/σ_h) gradually departs from 1 as temperature increases. As a result, the enhancement of the Nernst effect via the bipolar effect gradually disappears in the range from 75 to 200 K (Fig. 2a). When the temperature reaches 200 K, due to the narrow bandgap (∼50 meV) of Ag_2−δTe, the holes as minority carriers can be excited,²⁴ leading to a turning point in the temperature-dependent resistivity (Fig. 3a). At the same time, the transverse thermopower also shows a turning point near 200 K, followed by a slow increase in the range of 200 to 300 K as the temperature increases (Fig. 2a). This may be attributed to the change of mobility and the thermally excited hole carriers. The simplified bipolar transport model can explain the change of S_xy above 200 K.¹⁶ In the high-field limit (μB > 1), assuming an ideal intrinsic semiconductor model where the concentrations and conductivities of electrons and holes are equal, the S_xy can be expressed as:¹⁶

where S_e,xy and S_h,xy are the transverse thermopower of electrons and holes, and S_e,xx and S_h,xx are the longitudinal thermopower of electrons and holes, respectively. The transverse thermopower under a magnetic field is primarily influenced by the last term, which increases in proportion in the total transverse thermopower as the magnetic field increases. According to the Boltzmann transport model, S_h,xx increases with the temperature.³⁷ Due to the opposite signs of S_h,xx and S_e,xx, the value of (S_h,xx–S_e,xx) gradually increases with temperature. Additionally, when the temperature is above 200 K, though the minority holes can be excited, the magnetic-field-dependent Hall resistivity shows a nearly linear behavior (Fig. S2a†), suggesting a predominantly single-carrier behavior. Hence, the Hall carrier concentration and Hall mobility can be derived using the following formulae.

Fig. 3 The electrical properties and the corresponding transverse power factors of Ag_2−δTe. The temperature dependence of (a) the resistivity ρ_xx, (b) the MR and (d) the transverse power factor PF_N under various magnetic fields. (c) The magnetic field dependence of the MR at 2–300 K.

R _H, n_H, μ_H, e and ρ_xx represent the Hall coefficient, Hall carrier concentration, Hall mobility, elementary charge, and resistivity along the temperature gradient direction, respectively. The results are shown in Fig. S2b.† The Hall carrier mobility decreases from 6944 cm² V⁻¹ s⁻¹ at 200 K to 3932 cm² V⁻¹ s⁻¹ at 300 K. Finally, along with the gradual increase of the value of (S_h,xx–S_e,xx) with temperature as mentioned before, the transverse thermopower shows a slow increase in the range of 200 to 300 K as the temperature increases.

Additionally, based on the magnetic-field-dependent transverse thermopower values shown in Fig. S3a,† the magnetic-field-dependent Nernst coefficients are displayed in Fig. S3b† by utilizing the relationship N_xy = S_xy/μ₀H.³⁸ The Nernst coefficient (N_xy) decreases gradually as the magnetic field increases below 100 K. This behavior is also observed in other transverse-MTE materials.³⁰ However, when the temperature is above 100 K, the N_xy initially increases and then gradually decreases with increasing the magnetic field (Fig. S3b†). There are two possible reasons for such behavior of N_xy. On one hand, Ag_2−δTe exhibits electron-dominated extrinsic semiconductor properties within this temperature range (Fig. S2a†), which allows the N_xy to reach the maximum value when μB = 1.³⁹ On the other hand, Ag_2−δTe also has semi-metallic characteristics, such as a narrow bandgap (tens of meV) and relatively large carrier mobility (thousands of cm² V⁻¹ S⁻¹, as shown in Fig. S2b†), which lead to a constant value of N_xy when μB > 1.³⁹

Fig. 3a shows the electrical transport properties of Ag_2−δTe in the temperature range from 2 to 300 K. Notably, a nearly flat resistivity plateau is observed at temperatures below 50 K in Fig. 3a, and the Hall resistivity (ρ_xy) follows a similar trend to the resistivity (Fig. S1a†). Such behavior can be attributed to the presence of a degenerate low-temperature hole gas.³⁵ Furthermore, in the N–P transition region (50–100 K), the inflection points of these resistivity curves that reflect the N–P transition shift to higher temperatures with increasing magnetic fields. The electron to hole mobility ratio, which varies with the magnetic field, can account for the shift in inflection points.²⁹ Subsequently, in the temperature range of 100 to 200 K, a general semiconductor behavior appears due to carrier activation, resulting in a decreasing trend in resistivity. Furthermore, once the temperature surpasses 200 K, the resistivity at zero-field reaches a plateau again, due to the degeneracy of the electron gas.³⁵

We further investigate the dependence of MR on temperature and the magnetic field. As shown in Fig. 3b, the positive MR is observed across the entire temperature range, and the MR increases with the applied magnetic field. Such behavior is consistent with the previous report for polycrystalline Ag_2−δTe.²⁹ In addition, the peak MR is observed near the N–P transition temperature at various magnetic fields. Similarly, the temperature of the peak MR shifts to higher temperature with increasing the magnetic field. The maximum MR reaches 1162% at 97 K under 14 T. As shown in Fig. 3c, the field-dependent MR exhibits three distinct types of curves. At low temperatures (2, 30, and 75 K), it exhibits a sublinear field-dependent behavior. At 100 K, a nearly linear field dependence is observed, with the maximum MR occurring at this temperature (Fig. 3b). Then, at high temperatures (150, 200, 250, and 300 K), a superlinear field dependence is observed. Such field-dependent behavior is consistent with the previous report.⁴⁰ The chemical potential (φ) influenced by both the magnetic field and temperature may explain the different MR behaviors near the N–P transition temperature.⁴⁰ Based on Abrikosov's theories,²¹ the φ may lie at the crossing point of the crossed linear bands at 100 K, with the electron–hole symmetry occurring. As a result, the MR-B curve exhibits almost linear behavior in Fig. 3c. Both increasing magnetic field or decreasing temperature would lower the chemical potential, and vice versa. At temperatures below 100 K, the chemical potential shifts towards the hole-doped region.⁴⁰ When applying a magnetic field, as a P-type semiconductor, the further reduction of chemical potential leads to an increase in hole concentration. Compared to the linear MR, the additional increase in the carrier concentration leads to an extra reduction in resistance, resulting in the sublinear behavior. In contrast, when the temperature exceeds 100 K, as an N-type semiconductor, the lower chemical potential in the electron-doped region caused by the magnetic field would decrease the electron concentration, leading to an extra increase in resistance and a superlinear MR behavior.

Combining the transverse thermopower and resistivity, the transverse power factor (PF_N) can be calculated using the equation⁴¹

PF_N = S_xy²/ρ_yy (5)

The transverse thermopower, which is perpendicular to the temperature gradient, and the electrical resistivity along the y-axis, which is also perpendicular to the temperature gradient, are denoted by S_xy and ρ_yy, respectively. Considering the isotropic electrical resistivity of polycrystalline Ag_2−δTe, ρ_yy is expected to be equal to ρ_xx. The calculated PF_N values under various magnetic fields are presented in Fig. 3d. When the temperature is between 75 K and 200 K, the transverse power factors of Ag_2−δTe increase with increasing magnetic fields. When the temperature is above 200 K, they gradually saturate with the magnetic field. The highest PF_N of 532 μW m⁻¹ K⁻² at 300 K under 12 T and a peak PF_N of 222 μW m⁻¹ K⁻² at 85 K under 14 T are attributed to relatively low resistivity and high transverse thermopower, respectively. As shown in Fig. S4,† PF_N almost saturates at 3 T below 100 K, and the saturation magnetic field can reach 9 T above 150 K. Hence, the polycrystalline Ag_2−δTe can achieve a saturated PF_N under relatively low magnetic fields at low temperatures, and it can also attain higher PF_N under relatively high magnetic fields at high temperatures.

Fig. 4a illustrates the temperature-dependent thermal conductivity (κ_xx) of polycrystalline Ag_2−δTe. These measurements were carried out by employing the four-probe method. It is worth noting that the κ_xx exhibits similar behavior under different magnetic fields. Specifically, κ_xx increases first with the temperature, reaching a maximum value of approximately 10 W m⁻¹ K⁻¹ at 10 K. Subsequently, it declines as the temperature increases to about 150 K. Finally, a gradual upward trend is observed until the temperature reaches 300 K. As shown in Fig. 4a, when the temperature is below 50 K, the κ_xx remains almost constant with varying magnetic fields, indicating that the thermal conductivity is primarily governed by the lattice thermal conductivity (κ_l) in this temperature range. The κ_l is mainly influenced by the heat capacity, which follows a T³ dependence according to the Einstein model. As the temperature increases, the κ_l exhibits a T⁻¹ dependence due to the enhanced phonon–phonon scattering. Consequently, the thermal conductivities change from a κ_l–T³ dependence at low temperatures to a κ_l–T⁻¹ dependence at high temperatures.³¹ At 300 K, the κ_xx is approximately 1.3 W m⁻¹ K⁻¹, which is comparable with the thermal conductivity of conventional thermoelectric materials like Bi₂Te₃ (1.1 W m⁻¹ K⁻¹)⁴² and Cu₂Se (1.0 W m⁻¹ K⁻¹).⁴³ Furthermore, the κ_xx remains at around 1 W m⁻¹ K⁻¹ within the range of 75–300 K. Such relatively low thermal conductivity of polycrystalline Ag_2−δTe benefits the value of Z_N. When a magnetic field is applied, the κ_xx of polycrystalline Ag_2−δTe above 150 K decreases. As shown in Fig. 4b, the κ_xx at 150 K decreases from 0.99 W m⁻¹ K⁻¹ to 0.75 W m⁻¹ K⁻¹ with the magnetic field increasing up to 5 T. Then it saturates under higher magnetic fields. When a magnetic field is applied, it can affect the motion and scattering of charge carriers, resulting in a decrease of the thermal conductivity.³¹ However, when the temperature is lower than 150 K, the higher field over 5 T enhances the κ_xx again (Fig. 4b). The thermal conductivity of polycrystalline Ag_2−δTe predominantly consists of two components: the lattice part (κ_l) and the electronic part (κ_e).⁴⁴ The magnetic field has a minor influence on the lattice part (κ_l). Therefore, the variations in the thermal conductivity under the magnetic field are solely attributed to the change of the electronic part (κ_e). As previously mentioned, in the crossed linear bands of doped Ag₂Te, the chemical potential (φ) is influenced by both the magnetic field and temperature. Both decreasing the temperature and enhancing the magnetic field would lower the φ and vice versa. When the temperature is around 100 K, increasing the magnetic field significantly suppresses the contribution of charge carriers at a low magnetic field. As the magnetic field continues to increase, this effect saturates, as is observed at high temperatures. In addition, the further reduced chemical potential due to the increasing magnetic field shifts towards the hole-doped region, increasing the concentration of carriers involved in the thermal conductivity. As a result, the thermal conductivity exhibits a slight increase at high magnetic fields below 150 K.

Fig. 4 The thermal conductivity κ_xx (a), the transverse thermoelectric figure of merit Z_N (c) and Z_NT (d) under various magnetic fields over the investigate temperature range. The magnetic-field-dependent thermal conductivity (b) at different temperatures.

The Nernst figure-of-merit (Z_N) can be expressed by Z_N = S²_xy/(ρ_yy·κ_xx). The Z_N and corresponding Z_NT of polycrystalline Ag_2−δTe under different magnetic fields are shown in Fig. 4c and d, respectively. Below 150 K, a peak value of Z_N is observed around 100 K, followed by an increase in Z_N with the further increasing temperature, which is consistent with the transverse power factor behavior (Fig. 3d). After introducing the temperature parameter, Z_NT increases with temperature up to 300 K. Due to the increased transverse power factor and decreased thermal conductivity in polycrystalline Ag_2−δTe, the Z_N shows a remarkable increase when a magnetic field is applied. Specifically, at temperatures below 150 K, a peak Z_N value of 2 × 10⁻⁴ K⁻¹ is achieved under 7 T at 100 K. Moreover, at 300 K, the maximum Z_N value reaches 4.7 × 10⁻⁴ K⁻¹ under 14 T, corresponding to a peak Z_NT of 0.15. The saturated magnetic field for Z_N and Z_NT exhibits similar behavior, increasing from 3 T at 75 K to 14 T at 300 K (Fig. S5a and b†). Such behaviors can be attributed to the variation in the saturated magnetic field of PF_N and κ_xx with temperature observed before (Fig. 3d and 4a). The Z_NT near room temperature of narrow-band-gap semiconductors, Re₄Si₇ (ref. 20) and Bi₇₇Sb₂₃,¹⁹ is 0.1 at 400 K and 0.06 at 300 K, respectively. The Z_NT value 0.15 of Ag_2−δTe in this work is comparable with those of state-of-the-art transverse thermoelectric materials, indicating that Ag_2−δTe is a promising material for MTE applications.

For practical applications of transverse thermoelectric materials, besides the maximum peak Z_N, a high average Z_N over a wide temperature range is even more meaningful. Table S1† presents the average Z_N values reported in previous literature, obtained by integrating the temperature-dependent Z_N values over the measured temperature range and dividing by the temperature difference (ΔT). The average Z_N values of single crystals are relatively large. However, the optimal performance temperature range is usually very narrow. For instance, the average Z_N values of WTe₂ and NbSb₂ are 193 × 10⁻⁴ K⁻¹ at 7–16 K and 26.6 × 10⁻⁴ K⁻¹ at 5–70 K, respectively. Furthermore, the large-scale synthesis of high-quality single-crystal materials remains challenging. In contrast, polycrystalline samples have a relatively wide applicable temperature range. For example, the average Z_N values of Ag₂Se,³³ Bi₇₇Sb₂₃ (ref. 19) and NbSb₂ (ref. 18) are 0.23 × 10⁻⁴ K⁻¹ at 80–300 K, 2.15 × 10⁻⁴ K⁻¹ at 50–300 K and 9.75 × 10⁻⁴ K⁻¹ at 5–100 K, respectively. From liquid nitrogen temperature to room temperature, Ag_2−δTe is comparable with the state-of-the-art transverse thermoelectric material Bi₇₇Sb₂₃ and shows a 12-fold improvement compared to Ag₂Se, which is also a polycrystalline silver chalcogenide material.

Conclusions

In this work, we investigate the transverse magneto-thermoelectric properties of polycrystalline Ag_2−δTe. We observe a significant peak value of transverse thermopower of 625 μV K⁻¹ at 75 K under a magnetic field of 14 T, which can be attributed to the enhanced bipolar effect near the N–P transition temperature. An average Z_N value of 2.9 × 10⁻⁴ K⁻¹ over a wide temperature range of 80–300 K under a magnetic field of 14 T is achieved. These results suggest that polycrystalline Ag_2−δTe holds great promise for transverse energy conversion applications due to its relatively high transverse thermoelectric performances.

Author contributions

Mingyu Chen: material synthesis, sample testing, data analysis, and writing & editing, Tao Feng: PPMS measurement and review, Nan Yin: support for PPMS measurement, Quan Shi: support for PPMS measurement, Peng Jiang: conceptualization, supervision, writing, and review & editing, and Xinhe Bao: review & editing.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Key R&D Program of China (2022YFA1203600), CAS Interdisciplinary Innovation Team (JCTD-2019-08), and DNL Cooperation Fund (DNL202018). We thank Wenqing Zhang from the Southern University of Science and Technology for helpful discussions.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta07394g

‡ These authors contributed equally to the work.

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