Enhanced thermoelectric power and electronic correlations in RuSe₂ Open Access

Recent interest in thermoelectric energy conversion induces a wide interest in the materials with high thermoelectric performance.^1,2 A narrow distribution or a large peak in the electronic density of states (DOS) close to the Fermi level has long been considered favorable for a high Seebeck coefficient (S).^3,4 Such peak could be induced by the resonant level dopants in semiconductors^5,6 or by the magnetic interaction between the local magnetic moment and itinerant electrons in many f- and d-electron based materials.^7,8 It has been reported that some strongly correlated metals (such as heavy fermion metals) and correlated semiconductors (such as Kondo insulators) show significant enhanced Seebeck coefficient and power factor. For example, large peaks in Seebeck coefficient up to 800 μV/K were observed in heavy fermion metal CePd₃,^9,10 Kondo insulator FeSi,^11–13 Ce₃Pt₃Sb₄,¹⁴ and CeFe₄P₁₂.¹⁵ 

More recently, a very large Seebeck coefficient (∼4 × 10⁴ μV/K) and huge power factor (∼2 × 10³ μW/K²  cm)^16–19 were observed in FeSb₂.²⁰ This makes the mechanism of thermopower enhancement in FeSb₂ of high interest.^21–26 The results from density functional theory without electron correlation effect can only qualitatively reproduce the temperature dependence of the Seebeck coefficient. The predicted peak value of S is only one tenth of the experimental value, suggesting the importance of strong electronic correlations.^13,23,26

Pyrite FeS₂ is a semiconductor with a band gap of (0.8–0.95) eV and a high light absorption.^27,28 FeS₂ shows a Seebeck coefficient up to ∼ − 300 μV/K at 300 K.²⁹ The Seebeck coefficient of iron dichalcogenides FeX₂ [X = (S,Se,Te)] decreases for heavier chalcogens due to decreasing energy gap but retains relatively large values of ∼|(2 − 3)| ⋅ 10² μV/K above 200 K.³⁰ 

Here, we report the detailed electronic structure, electric and thermal transport properties of pure and Ir-doped RuSe₂ pyrite. RuSe₂ shows a semiconducting behavior with an indirect gap from resistivity ∼1.5 eV. The band structure calculation shows a pileup of states near the Fermi level suggesting correlation effects. The Seebeck coefficient of RuSe₂ exceeds −200 μV/K at 730 K, showing the electron-type carriers. Ir doping introduces lattice expansion and extra electrons, which results in the significant suppression of the resistivity and the Seebeck coefficient. The sample with 20% Ir doping shows a semiconductor-metal transition at about 20 K, while the magnetic field restores the semiconducting behavior.

(Ru_1−xIr_x)Se₂ (with x = 0, 0.1, 0.2) polycrystals were made using a high-temperature solid state reaction method. Stoichiometric Ru (99.99%), Ir (99.99%), and Se (99.9999%) were ground, pelletized, sealed in a quartz tube, heated to 1000 °C, kept for about 20 h, and then the furnace was turned off. Next, the material was ground, pelletized again, and heated with the similar temperature profile at 1100 °C. Medium resolution room temperature X-ray diffraction measurements were carried out using a (0.25⋅0.25) mm² 48 keV (λ = 0.024 87 nm) focused (on the detector) X-ray beam at 28-ID-C beam line at National Synchrotron Light Source II at Brookhaven National Laboratory. The X-ray energy was selected using a horizontally focused double crystal Laue monochromator, with vertical focusing achieved using 1 m long Si mirror. Finely pulverized samples were filled into 1 mm diameter cylindrical polyimide capillaries, and the data collection was carried out in transmission geometry using Perkin Elmer amorphous silicon area detector mounted orthogonal to the beam path 1272.6 mm away from the sample. The raw 2D data were integrated and converted to intensity versus scattering angle using the software Fit2D.³¹ The average structure was assessed through Rietveld refinements³² to the raw diffraction data using the General Structure Analysis System (GSAS)³³ operated under EXPGUI (a graphical user interface for GSAS),³⁴ utilizing Pa-3 model from the literature.³⁵ Electrical transport measurements were conducted on polished samples in Quantum Design Physical Properties Measurement System PPMS-9 with conventional four-wire method. Thermal transport properties were measured in Quantum Design PPMS-9 from 2 K to 350 K, and in Ulvac ZEM-3 system at higher temperatures, both using one-heater-two-thermometer method. The relative error of each measurement was $Δ κ κ ∼5%$ and $Δ S S ∼10%$ based on standard; however, at 350 K, the discrepancy in measured values was 25%. As opposed to ULVAC ZEM-3, PPMS S, and ρ were obtained in separate measurements using TTO (thermal transport option) and ACT (alternating current transport) option on the same sample. Hence, ULVAC ZEM-3 data were normalized to PPMS values at 300 K. First principle electronic structure calculation was performed using experimental lattice parameters within the full-potential linearized augmented plane wave (LAPW) method³⁶ implemented in WIEN2k package.³⁷ The general gradient approximation (GGA) of Perdew et al.,³⁸ was used for exchange-correlation potential. The LAPW sphere radius was set to 2.5 Bohr for all atoms. The converged basis corresponding to R_mink_max = 7 with additional local orbital was used, where R_min is the minimum LAPW sphere radius and k_max is the plane wave cutoff.

Diffraction data for all three compositions are well explained within pyrite-type Pa-3 structure, comprised of 3D network of distorted (squashed) Se6 octahedra that coordinate Ru/Ir. Irregularity of the octahedra is reflected in principal axes deviating from 90° (see Figure 1). Refined structural parameters are summarized in Table I. Lattice parameter increases on substituting Ru with larger Ir. Average Ru-Se near neighbor distance decreases slightly with doping, whereas departure for regularity in octahedral angles increases slightly. Debye-Waller factors increase slightly with doping as well, consistent with presence of quenched disorder introduced by chemical substitution. The Ir doping limit is 20% and above that the synthesis resulted in mixed phases of Pa-3 space group of pure RuSe₂ and Pnma space group of pure IrSe₂.

Fig. 2 shows the electrical and thermal transport properties. The resistivity of RuSe₂ [Fig. 2(a)] shows typical semiconducting behavior. The fitting for thermal activation conductivity [the solid line in Fig. 2(b)] estimates that the main band gap is ∼1.5 eV. The slope of the resistivity or the energy gap changes in the low temperature range, possibly due to the native d-states or impurity states within the main band gap, similar to Fe_1−xRu_xSb₂.³⁹ The Seebeck coefficient [Fig. 2(c)] approaches 180 μV/K at 350 K and shows a peak of about 247 μV/K at about 730 K. The thermal conductivity of RuSe₂ [Fig. 2(d)] is rather high in the whole range of measured temperatures.

The semiconducting behavior of RuSe₂ is consistent with the first principle calculation results (Fig. 3). The density of states [Fig. 3(a)] shows a gap with size of 0.4 eV, whereas the band structure [Fig. 3(b)] indicates that RuSe₂ is a indirect-gap semiconductor. However, the gap size from the density functional theory (0.4 eV) is much smaller than the transport gap (about 1.5 eV), suggesting that the electron correlations may be important. There are several narrow bands just below the Fermi level with Ru 4d orbital character [the heavy lines in Fig 3(b)]. This is confirmed by the large pileup of states [Fig. 3(a)]. But there is also significant hybridization between Ru 4d and Se p orbitals indicated by the overlap between the peaks from Ru and Se below and above the Fermi level.

The high Seebeck coefficient of RuSe₂ should come from the peaks in density of states just below the Fermi level [Fig. 3(a)], with major contribution from the narrow d-bands. Although the Seebeck coefficient of RuSe₂ is high, its power factor is small because of the high resistivity.

Ir doping introduces carriers and is effective in enhancing the conductivity; however, it also significantly suppresses Seebeck coefficient [Figs. 2(a) and 2(c)]. The 10% Ir doped sample still shows semiconducting behavior but the residual resistivity decreases by two orders of magnitude at 2 K and in half at 200 K when compared to pure RuSe₂. Further increase in Ir substitution suppresses the resistivity even more. The sample with 20% Ir doping shows a semiconductor-metal crossover at ∼30 K; below that temperature, the resistivity begins decreasing with decreasing temperature [Figs. 2(a) and 4(a)]. The thermal conductivity is also suppressed by Ir doping [Fig. 2(d)], possibly due to the lattice disorder introduced by the doping. The 10% Ir doping reduces the Seebeck coefficient to only about 2 μV/K at 300 K [inset in Fig. 2(c)].

The magnetic field has significant influence on the transport of Ru_0.8Ir_0.2Se₂ in the low temperature range [Fig. 4(a)]. Above the semiconductor-metal crossover at ∼30 K, the application of magnetic field has minute effect on the resistivity. But below it, in the metallic regime, the magnetic field enhances the value of resistivity and changes its temperature dependence. In 4 T field, the ρ (T) still undergoes the semiconductor-metal transition at the same temperature but then changes to semiconducting behavior below 4 K. The 9 T magnetic field totally smears out the semiconductor-metal transition and restores the semiconducting behavior. The magnetoresistance ratio (MR) is always positive at 2 K and tends to saturate in higher fields [Fig. 4(b)].

The clear suppression of the value and the slope of the resistivity indicate that the Ir-doping induces the decrease of the band gap. The 10% Ir doping only introduces 0.1 electrons per unit cell. This will result in a slight shift of the Fermi level toward higher energy direction [Fig. 3(a)], within the framework of the density functional theory. Since 10% Ir-doped RuSe₂ is still a semiconductor, it is reasonable to believe that the Fermi level is still in the gap. If so, this slight shift of the Fermi level could not induce the huge suppression of the Seebeck coefficient [Fig. 2(c)]. Since the Seebeck coefficient is related to the energy slope of the density of states near the Fermi level, this implies the effect of electronic correlations. The 5d electrons of Iridium feature less localized (i.e., more extended) wave functions when compared to 4d electrons of Ruthenium. Hence, Iridium substitution not only introduces extra carriers but also reduces the electronic correlations. Furthermore, since the magnetic field restores the semiconducting behavior in sample with 20% Ir level, the original semiconducting behavior in pure RuSe₂ could be related to some extent to the magnetic mechanism. Taken together with enhanced thermopower, our results suggest that physical properties of RuSe₂ may share some similarity with the correlated electron semiconductor FeSb₂.^19,20 The comparison of the electronic structure, electronic and magnetic correlations of pyrite RuSe₂ to marcasite FeSb₂ could be important for studies of structural effects on correlated electron thermoelectricity and deserves further studies.

Electronic structure of pyrites, such as NiS_2−xSe_x, is related to the occupation of d orbitals which have significant influence on the band filling and correlation effect.⁴⁰ Pyrites and marcasites both feature distorted octahedral coordination of transition metals (e.g., Fe or Ru) in the local structure.⁴¹ Whereas the octahedra share common corners in the cubic pyrite unit cell and the resulting crystal field at Ru in RuSe₂ has trigonal symmetry, the orthorhombic marcasite unit cell features linear chains of edge-sharing octahedra parallel to orthorhombic c-axis. In both cases, d-electrons dominate the electronic states near the Fermi level. In RuSe₂, the t_2g orbitals are completely filled as opposed to t_2g orbitals in marcasite FeSb₂.^41,42 This inhibits a possibility for thermally induced anisotropic metallic states and thermally induced enhanced Pauli susceptibility.^19,20,43 On the other hand, when comparing RuSe₂ to RuSb₂, Se(4p4) has an extra electron when compared to Sb (5p3). So it is expected that the occupation of d orbitals in RuSe₂ is different from RuSb₂ which would change correlation strength. This is reflected in the density of states: Ru d-states in RuSe₂ (Fig. 3) are more enhanced near the Fermi level when compared to RuSb₂.³⁹ Triangular arrangement of metal (i.e., Ru) atoms in pyrite lattice of RuSe₂ (Fig. 1) could enhance the correlation effects in RuSe₂ even further via geometric frustration. This has been theoretically considered⁴⁴ and experimentally verified in pyrite NiS₂.⁴⁵ Since geometrical frustration coupled with strong Coulomb interaction may enhance thermoelectric power,^46,47 putative antiferromagnetic states in RuSe₂ materials are of interest. The figure of merit ZT = S²/ρκ value at 300 K (730 K) is only about 0.003 (0.005 assuming about 100 W/Km). Thermal conductivity is rather high and very far away from the amorphous limit. Nanoengineering of RuSe₂ objects may reduce thermal conductivity and could lead to much larger values of ZT.^48–51 

In conclusion, we report enhanced thermoelectric power and electronic correlations in RuSe₂ RuSe₂ show a semiconducting behavior with a thermally activated gap. The band structure calculation confirmed the semiconducting characteristic, albeit with significantly underestimated gap implying the importance of the electron correlation effect. The Seebeck coefficient of RuSe₂ approaches −250 μV/K near 730 K, showing the electron-type carriers. Small Ir doping results in the significant suppression of the resistivity and the Seebeck coefficient. The sample with 20% Ir doping shows a semiconductor-metal transition at about 20 K, while the magnetic field restores the semiconducting behavior at low temperature. Our results shows the large Seebeck coefficient of RuSe₂ and implies the important role of electron and magnetic correlations.

Work at Brookhaven is supported by the U.S. DOE under Contract No. DE-AC02-98CH10886. X-ray scattering data were collected at 28-ID-C x-ray powder diffraction beam line at National Synchrotron Light Source II at Brookhaven National Laboratory. Use of the National Synchrotron Light Source II, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-SC0012704.