Correlated Evolution of Colossal Thermoelectric Effect and Kondo Insulating Behavior

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Correlated evolution of colossal thermoelectric effect and Kondo insulating behavior

Cite as: APL Mater. 1, 062102 (2013); https://doi.org/10.1063/1.4833055 Submitted: 11 October 2013 . Accepted: 11 November 2013 . Published Online: 02 December 2013

M. K. Fuccillo, Q. D. Gibson, Mazhar N. Ali, L. M. Schoop, and R. J. Cava

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APL Mater. 1, 062102 (2013); https://doi.org/10.1063/1.4833055 1, 062102

Correlated evolution of colossal thermoelectric effect and Kondo insulating behavior M. K. Fuccillo,a Q. D. Gibson, Mazhar N. Ali, L. M. Schoop, and R. J. Cava Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA (Received 11 October 2013; accepted 11 November 2013; published online 2 December 2013)

We report the magnetic and transport properties of the Ru1−xFexSb2 solid solution, showing how the colossal thermoelectric performance of FeSb2 evolves due to changes in the amount of 3d vs. 4d electron character. The physical property trends shed light on the physical picture underlying one of the best low-T thermoelectric power factors known to date. Some of the compositions warrant further study as possible n- and p-type thermoelements for Peltier cooling well below 300 K. Our ﬁndings enable us to suggest possible new Kondo insulating systems that might behave sim- ilarly to FeSb2 as advanced thermoelectrics. © 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4833055]

The thermoelectric effect is the reversible conversion between a temperature gradient and an electric potential. For a given material, the efficiency of this process is quantified by the figure of merit, ZT = S2T/ρκ, where S is the Seebeck coefficient (the ratio of the thermoelectric voltage to the temperature difference across the sample), T the temperature, ρ the electrical resistivity, and κ the thermal conductivity.1 The current state of the art in Peltier cooling materials is ZT ≈ 1, which is about 10% of the Carnot limit2 and good enough to construct coolers that are 25% as efficient as typical compression-expansion systems.3 Higher values, of course, are always desired. One strategy for raising ZT is to reduce the lattice contribution to κ by selectively scattering phonons rather than electrons – an important area of development for FeSb2-based materials because a large thermal conductivity is the main factor limiting their practical use.4–6 Another approach is to focus 2 exclusively on the other terms in ZT, i.e., the power factor PF = S /ρ. For pure FeSb2 this factor is extremely high, greatly exceeding that of its isostructural homologues FeAs2 and RuSb2,aswellas 7–11 state-of-the-art Bi2Te3-based materials. This is mainly because, at 12 K, S for FeSb2 reaches a colossal magnitude of 45 000 μV/K, which is orders of magnitude larger than common values.8 This is surprising because S is an entropic quantity that vanishes at absolute zero. A clearer understanding of the origin of the colossal S and how this parameter can be enlarged for other materials, even if only to fractions of the size as for FeSb2, could lead to a revolution in the cooling industry and the implementation of next-generation devices that require cooled electronics. Although small in comparison to S for FeSb2, exceptionally large Seebeck coefficients are found in metals containing dilute magnetic impurities12 and in semiconductors containing resonant level dopants13, 14 and highly degenerate electronic bands.15 Among all these systems, including FeSb2, there is a shared commonality that plays a role in the large S: namely, a large peak in the 16 electronic density of states (DOS) near the Fermi level, EF. However, only in the former class of materials were magnetic interactions between localized and itinerant electrons also suggested to play a role.12 Observation of this same effect – i.e., the “Kondo effect” – in semiconductors has led to the term Kondo insulators (KIs).17 Examples of the anomalous peaks in S for these materials occur 18, 19 20 21 in FeSi, Ce3Pt3Sb4, and CeFe4P12, reaching about 500, 350, and 800 μV/K, respectively.

aAuthor to whom correspondence should be addressed. Electronic mail: [email protected]

2166-532X/2013/1(6)/062102/81, 062102-1 © Author(s) 2013 062102-2 Fuccillo et al. APL Mater. 1, 062102 (2013)

Yet, even these other KIs pale in comparison to FeSb2 as thermoelectrics. While the challenging task of formulating an accurate theoretical description of the Kondo insulating behavior in FeSb2, and how it contributes to the colossal thermoelectricity, is still being intently studied,7–10, 22–26 as are other models,27–29 our work starts from a different viewpoint. We present the evolution of the FeSb2–RuSb2 system as an example that illustrates how an elementary understanding of the basic principles of the Kondo effect is enough to augment the chemically directed exploration for enhanced thermoelectric materials based on conventional semiconductors. While FeSb2 is a paramagnetic semiconductor at room temperature with unconventional transport properties, isostructural and nominally isoelectronic RuSb2 is a conventional diamagnetic 10 semiconductor with a relatively low Seebeck coefficient. The diamagnetism of RuSb2 derives from its non-localized Ru 4d orbitals hybridizing strongly with the surrounding Sb orbitals, leading to the normal behavior expected for a small band gap semiconductor. For FeSb2 on the other hand, the Fe 3d orbitals are intrinsically more localized and the hybridization with the Sb states is poorer, though not completely absent, leading to a system tending toward partially localized behavior. This makes possible the critical prerequisite for the Kondo effect: an interaction between itinerant (s or p) and localized (d or f) electrons with magnetic character. The more electron states of both types that lie near the Fermi level, EF, the greater their interaction affects the transport properties. Hence, FeSb2, which has a higher density of magnetic d-states near EF, exhibits more correlation effects than RuSb2. Furthermore, doping FeSb2 with other 3d transition metals, such as Cr, Co, and Ni, whose d-electrons lie at different energies, tends to diminish the correlation effects – smearing out 5, 30 20 the peak in S and closing the Kondo gap. Similar behavior was seen in Nd-doped Ce3Pt3Sb4. In contrast to previous studies, here we report the thermoelectric and magnetic properties of the Ru1−xFexSb2 solid solution. In this system, the formal electron count and crystal structure are un- changed, enabling semi-localized states from Fe to be titrated into an inert host and thus the strength of electron correlation effects to be controllably tuned; the resulting evolution of the electronic and magnetic properties that is achieved in this way is remarkable and can likely be applied to other systems. Polycrystalline pellets of Ru1−xFexSb2 were synthesized via solid state reaction. Stoichiometric amounts of Ru (99.95%), Fe (99.9%), and Sb (99.999%) powders (∼200 mesh) were blended and compacted into 400 mg or 600 mg pellets (d = 6.35 mm) in a hydraulic press. The pellets were placed inside alumina crucibles and heated in evacuated quartz ampoules for at least 30 h, then reground, re-pelletized, and re-heated for at least two more nights. Ru-rich samples (x ≤ 0.30) were heated at 800 ◦C, and Fe-rich samples (x ≥ 0.50) were heated at 600 ◦C to avoid FeSb formation. This procedure resulted in solid pellets for x ≤ 0.25 and x = 0.50 (compacted to ∼80%–90% the theoretical density), but for x = 0.30, 0.75, and 1 the powders did not sinter to form solid pellets, likely caused by an increase in hardness resulting from the greater Fe content. Thus, these three samples are excluded from the transport property analysis. Nevertheless, as stoichiometric FeSb2 is included in the present analysis, single crystals were grown via self-flux from an initial composition of constituents Fe0.05Sb0.95 for Seebeck coefficient measurement. X-ray powder diffraction data were collected using a Bruker D8 Focus diffractometer using Cu Kα radiation to ensure phase purity and to track the changes in lattice parameter with composition. Lattice parameter refinements were performed with Bruker-AXS TOPAS 2.1 software. Seebeck coefficient measurements were performed with a modified MMR Technologies Seebeck measurements system (SB-100). Resistivity and Hall data were collected with a Quantum Design (QD) Physical Property Measurement System (PPMS). The Hall coefficient (RH) was measured at 300 K while the magnetic field was varied from +1Tto−1Tor+5Tto−5T(RH depends linearly on the field in all cases), and the relation n =−1/RHe was used to determine the carrier concentration. Magnetic susceptibility data were gathered in a 3 T field using a QD Magnetic Property Measurement System (MPMS) SQUID dc magnetometer. Electronic structure calculations were performed in the framework of density functional the- ory using the Wien2k code42 with a full potential linearized augmented plane-wave and local orbitals basis together with the Perdew-Burke-Erzenhof parameterization of the generalized gradient 43 approximation. For RuSb2 and FeSb2, the experimental lattice parameters and atomic positions were used. For the 1/16, 1/8, and 1/4 substituted RuSb2 a2× 2 × 2 supercell was used, in 062102-3 Fuccillo et al. APL Mater. 1, 062102 (2013)

(a) (b)

(c)

FIG. 1. Evolution of the thermoelectric properties of Fe-doped RuSb2. (a) Seebeck coefficient (S) as a function of temperature and composition. The data for FeSb2 (x = 1) are towards the front, while RuSb2 (x = 0) has been projected onto the back wall. With more Fe, the peak shifts to lower T and becomes larger and narrower. (b) Value of the Seebeck coefficient peak as a function of composition. x = 0.10 and 0.20 samples are included here but not in the previous panel to preserve the latter’s clarity. (c) Thermoelectric power factor (PF = S2/ρ) as a function of T. The v-shaped features mark crossovers between n-type and p-type transports (closed and open circles, respectively) at temperatures corresponding to sign changes in S.The composition can be tuned to make n-orp-type thermoelements for different temperature ranges. space group P2/m, to accommodate the substitution; an ordered substitution was assumed. For all calculations the plane wave cutoff parameter RMTKmax was set to 7 and the Brillouin zone was sampled by 2000 k-points. Spin-orbit coupling was included. Figure 1(a) shows the evolution of S as a function of temperature as the composition of 31 Ru1−xFexSb2 is varied from x = 0–1. As the Fe doping percentage is increased from 1% to 100%, the broad peak in S gradually shifts toward lower temperature, while becoming progressively sharper and increasing in magnitude. The dependence of the magnitude of the peak on Fe doping is shown in Figure 1(b); an increase in S with x often accompanies an increase in the DOS at the Fermi level,16 an implication common to our other transport data, as well. The temperature at which the peak is centered, TS_peak, and that at which the Seebeck coefficient crosses over from n-top-type, TS_np, both follow a similar exponentially decreasing dependence on Fe concentration, as discussed below. Figure 1(c) shows the temperature dependence of PF for the compositions shown in the main panel (calculated with resistivity data shown in Figure 2). The x = 0 curve is broad and n-type, but increasing x leads to interesting behavior. With greater Fe content, v-shaped features representing n-p crossovers appear below room temperature and generally shift towards lower temperatures; the lower-T regime has an n-type S, whereas in the higher-T regime it is p-type. The implication is that both n- and p-type legs could be made from Fe-doped RuSb2 in a practical thermoelectric device, where different compositions could be used at different temperatures. For example, if the thermal conductivity of Ru1−xFexSb2 alloys can be selectively suppressed to a greater extent than in the end members, then an n-type leg of a Peltier cooler designed to cool from 200 K to 10 K could have a segmented design consisting of Ru0.95Fe0.05Sb2 on the hotter side (operating at 125 K < T < 200 K) in series with Ru0.50Fe0.50Sb2 next, and finally FeSb2 below 50 K. Segmented p-type legs operating at higher temperatures can also be imagined. The optimum segment compositions, lengths, and cross-sectional areas would of course need to be optimized. Hence, the system Ru1−xFexSb2 offers a host of compositions that are ideal candidates for future thermal transport studies to determine whether the system is suited for utility in practical devices. The main panel in Figure 2 shows how the temperature dependence of the resistivity (ρ)evolves as a function of composition. The most evident feature is that each of the curves has two distinct activation energy gaps (except for x = 0) with a shoulder that gradually moves towards lower T with increasing x. The high-T activation barrier represents the main band gap in the electronic 062102-4 Fuccillo et al. APL Mater. 1, 062102 (2013)

FIG. 2. Evolution of the electrical resistivity (ρ) with composition. With more Fe, the resistivity decreases at all temperatures and thus enhances the thermoelectric performance. In each curve containing Fe, the shoulder between the two distinct exponential behaviors is a signature of the Kondo effect. Left inset: In the high-T regime, the decrease in slope with Fe content indicates a decrease in the band gap. x = 0.10 and 0.20 samples are included here but not in the main panel to preserve the latter’s clarity. Right inset: Due to the decreased band gap, greater Fe content also causes the room temperature ρ to decrease exponentially (left axis), while the p-type carrier concentration increases exponentially (right axis). structure,8–10 and can be estimated from the slope of the straight parts of the curves in the left inset. The low-T transport arguably arises from native8–10, 23 d-states or impurity30 states within the gap, and it has been suggested30 that variable-range hopping dominates there. Our data show that the main band gap clearly decreases monotonically with increasing x. Further, it can be seen that the resistivity generally decreases at high and low T with x; the room temperature behavior is shown in the right inset (left axis) to decrease exponentially with increased Fe content. This is directly related to the fact that the carrier concentration increases exponentially with increased Fe content, as shown in the same inset (right axis). (The Hall coefficient RH =−1.6, 7.1, 4.0, 0.58, 0.14, 0.036, 0.015, and 0.0038 cm3/C for x = 0, 0.01, 0.05, 0.10, 0.15, 0.20, 0.25, and 1.0.) Both of these behaviors bear the mark of a smaller band gap, here caused by an increased localization of states near EF (see below). The main panel in Figure 3 shows the temperature dependence of the magnetic susceptibility (χ)forx = 0, 0.05, 0.10, 0.15, 0.20, and 0.25. The host material RuSb2 was already shown to be diamagnetic over the whole temperature range, while FeSb2 was previously shown to transition from diamagnetic to thermally enhanced Pauli-like paramagnetic behavior upon increasing temperature.9, 10 However, here we show for the first time how the transition between the two regimes evolves. For Fe-doped RuSb2, all samples are diamagnetic at low T (upper inset), but at low and high T, χ increases with temperature and x. The low temperature susceptibility data revealed a very small Curie tail in every sample up to x = 0.025, suggesting their high purity. (The magnetic data for Fe-rich samples with x ≥ 0.30, as well as x = 0.01, showed the presence of small magnetic impurities and are therefore excluded from the analysis.) The increase in the paramagnetic susceptibility (at low 32 and high T, see lower insets) with x further supports an increasing density of states near EF with increasing Fe content. The temperature at which the paramagnetic signal begins to dominate over the diamagnetic one, Tpara_onset, is noted by arrows in the main panel that point out where the slope of each curve becomes positive. This transition temperature occurs at lower T with more Fe. This suggests that progressively less thermal energy is required to excite the same amount of electrons, and hence implies that more Fe causes a smaller band gap. The decrease in band gap and increase in the density of states near EF suggested by the Seebeck, resistivity, and magnetic data are supported by electronic structure calculations, as shown in Figure 4. The right inset based on our experimental data justifies the lattice parameters selected for the calculations and indicates how the electronic structure changes with the crystal structure. The 062102-5 Fuccillo et al. APL Mater. 1, 062102 (2013)

FIG. 3. In Fe-containing samples, the magnetic susceptibility (χ) transitions from diamagnetism to a thermally enhanced Pauli-like paramagnetism with heating. The x = 0(RuSb2) sample is purely diamagnetic and χ decreases slightly with T.In the others, the approximate transition temperature (Tpara_onset) is indicated by the arrows to occur at the minimum of each curve, which moves to lower T as Fe is added. At very low T (upper inset) the small Curie tails indicate the sample purity, and the ﬂatter, diamagnetic portions of the curves systematically increase, linearly depending on the Fe content (lower left inset). At 300 K, the paramagnetic signal also linearly increases with more Fe.

FIG. 4. Electronic structure calculations. Fe doping enhances the density of d-states near EF, causing both the conduction and valence bands to become more localized. Left inset: Band structure of the theoretical compound with x = 0.0625, where heavy plotting represents d-states that are solely due to Fe. The ﬂat portions of the curves illustrate the partially localized character of these states. Right inset: The experimental lattice parameters for comparison to the corresponding electronic structures and to indicate the unit cell dimensions for the calculations. noteworthy features shown in the main panel are a progression from less to more localization in states near the Fermi energy as the Fe content increases: i.e., two prominent peaks just above and below EF become sharper and move closer together. The fact that these Fe d-bands move towards each other is a consequence of their hybridizing less with the Sb states. However, whereas the difference between the DOS in the two end members, FeSb2 and RuSb2, is the sharpness and location of the peaks, the transition is not a smooth smearing out of the sharp peak to a broader one. Rather, as 062102-6 Fuccillo et al. APL Mater. 1, 062102 (2013)

FIG. 5. Selected transition temperatures from all the properties. At low T, all samples exhibit behavior type I, where they are all diamagnetic, have a negative S that increases in magnitude with T, and follow the small activation gap in their electronic conduction. Heating all samples leads eventually to behavior type II via the following progression: a change from diamagnetism to paramagnetism (Tpara_onset, ), then a decline in the Seebeck coefficient (TS_peak, ●), followed by the transitional shoulder in the resistivity (Tρ _onset, ×), and finally a crossover in the Seebeck coefficient from n-top-type (TS_n-p, ). The errors are about as large as the data points. The thermoelectric properties gradually improve in the direction shown by the arrow, culminating with the colossal Seebeck coefficient peak of FeSb2 occurring at 12 K (◦,Ref.8). one progresses towards higher x, there is an emergence of a second, localized peak created by iron d-states, while the ruthenium-derived peak shrinks. This is clearly illustrated by the calculated band structure for the theoretical composition x = 0.0625 displayed in the inset, where heavier plotting indicates energy states originating from Fe 3d-orbitals. The flatness of the Fe d-bands between several k-points indicates essentially no hybridization in various directions in real space, and thus that these bands are partially localized and retain some magnetic character. (The fact that EF is not exactly at the top of the valance band is a minor error in the calculation due to the bandgap problem common to DFT calculations (inset Fig. 4). However, the trends indicated in the main panel of Figure 4 do not rely on the details of the electronic structure near the Fermi level, but rather involve only the shape and placement of the large peaks in the DOS, which are unambiguous.) The combination of both itinerant and localized behavior of this system poses a serious challenge to obtaining a correct theoretical model of the transport phenomena, but from a practical point of view it is clearly seen as a key feature that should be considered in future attempts to design electronically enhanced thermoelectrics. Figure 5 is a phase diagram constructed from selected parameters characterizing transitions seen in the presented data. In particular, the temperatures TS_peak, TS_np, Tρ_shoulder, and Tpara_onset (defined above) are all compared as a function of Fe content. Interestingly, all the samples pass through each transition in the same sequence with increasing temperature (i.e., as they pass from behavior type I to II, as displayed in Figure 5). Furthermore, all these transitions shift to lower T with increasing x, following a common exponentially decaying dependence. The significance of the transition sequence, in terms of a physical picture, is not clear at present. Another open question is why all the parameters given in Figure 5 scale linearly with each other – in other words, why the peak in the Seebeck coefficient always occurs at a temperature about 20–30 K below that of the resistivity shoulder, and so on. Further investigation into these questions may provide the key to understanding the enhanced Seebeck coefficient behavior in FeSb2. Additionally, it may be of 8, 23 33, 34 interest to study anisotropic effects, which have been observed in pure and doped FeSb2 single crystals, on the trends we report for Ru1−xFexSb2. 062102-7 Fuccillo et al. APL Mater. 1, 062102 (2013)

While RuSb2 does not seem to fit the trends displayed in Figure 5 (or, it would lie to the extreme left of the plot), the fact that the sample with just 1% Fe does fit is remarkable, as it suggests that the electronic correlation is still significant even at this low concentration. This was not expected based on the end members RuSb2 and FeSb2 alone. Furthermore, this is in stark contrast to what was seen in previous FeSb2 doping studies, where merely a few percent of Cr or Co impurities smeared out the peak in S by reducing it to 10 μV/K, despite the great concentration of Fe.5 Such observations would seem to suggest that the material needs to be a fully coherent correlated system in order to display an enhanced S, but here, starting from the opposite end of the spectrum, we have shown that interesting Seebeck coefficients caused by correlated behavior can be generated in conventional systems from much smaller concentrations of a “Kondo impurity.” This finding hints at many opportunities for testing conventional semiconductors with potential thermoelectric-enhancing dopants. The problem then is finding the right host-dopant combinations that lead to enhanced thermoelectric performance. By analogy to the present system, we envision that a thermoelectric materials design initiative could be based on doping conventional semiconductors with small amounts of potential Kondo impurities to screen candidate materials for the possibility of very large Seebeck coefficients. Likely candidates are conventional small-gap semiconductors whose crystal structures consist of 4d or 5d elements coordinated by heavy main group elements. The purpose of the 4d or 5d elements is to allow for isovalent 3d transition metal doping, whereas the heavy surrounding elements are needed because their extended orbitals are likely to hybridize with the localized 3d states and possibly because they screen localized magnetic moments that would otherwise lead to excessive scattering of 35 36 37 38 mobile charge carriers. For example, Ru1−xFexIn3, Rh1−xCoxSb2, Ir1−xCoxSe2, Pt1−xNixSb2, 39, 40 Ru1−xFexAl2, and the like might be interesting. A related example of obvious interest is the Kondo system Ru1−xFexSi, which has been synthesized but whose thermoelectric data are still needed.19, 41 Multiple dopants used simultaneously may give rise to unanticipated phenomena, and there are many possibilities in f-electron systems, as well. Since the design principles outlined here describe the system Ru1−xFexSb2, which at its extreme gives rise to the largest useful Seebeck coefficient currently known, they are well worth consideration in the continual search to drive Seebeck coefficients as high as nature will allow.

This research was supported by the Air Force MURI on thermoelectric materials, Grant No. FA9550-10-1-0553. Y. S. Hor designed the modiﬁed Seebeck measurement device and J. B. Webb helped us develop the methods used to grow crystals for this study.

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