arX

iv:1

405.

3152

v2 [

cond

-mat

.mtr

l-sc

i] 3

Nov

201

4

Phonon-drag effect in FeGa3

Maik Wagner-Reetz, Deepa Kasinathan, Walter Schnelle, Raul Cardoso-Gil, Helge Rosner, and Yuri GrinMax-Planck-Institut für Chemische Physik fester Stoffe

Nöthnitzer Straße 40, 01187 Dresden, Germany

Peter GilleLudwigs-Maximilians-Universität München

Theresienstraße 41/II, 80333 München, Germany

The thermoelectric properties of single- and polycrystalline FeGa3 are systematically investigatedover a wide temperature range. At low temperatures, below 20K, previously not known pronouncedpeaks in the thermal conductivity (400-800 W K−1 m−1) with corresponding maxima in the ther-mopower (in the order of -16000µV K−1) were found in single crystalline samples. Measurementsin single crystals along [100] and [001] directions indicate only a slight anisotropy in both the elec-trical and thermal transport. From susceptibility and heat capacity measurements, a magnetic orstructural phase transition was excluded. Using density functional theory-based calculations, wehave revisited the electronic structure of FeGa3 and compared the magnetic (including correlations)and non-magnetic electronic densities of states. Thermopower at fixed carrier concentrations arecalculated using semi-classical Boltzmann transport theory, and the calculated results match fairlywith our experimental data. The inclusion of strong electron correlations treated in a mean-fieldmanner (by LSDA+U) does not improve this comparison, rendering strong correlations as the soleexplanation for the low temperature enhancement unlikely. Eventually, after a careful review, we as-sign the peaks in the thermopower as a manifestation of the phonon-drag effect, which is supportedby thermopower measurements in a magnetic field.

I. INTRODUCTION

Fe-based semiconductors like FeSi, FeSb2 and FeGa3have attracted much attention in the past years due totheir interesting physical properties. The hybridizationof the transition metal d orbitals with the main groupmetal p orbitals opens up small band gaps of the or-der of 0.1 eV for FeSi,1 0.03 eV for FeSb2

2 and 0.47 eVfor FeGa3.3 Unusual transport properties and their ori-gins are strongly debated within the community for thepast two decades. For example, no clear consensus hasbeen reached on the origin of the extremely high See-beck coefficient of -45000µVK−1 around 10 K in FeSb2

single crystals.4 Until now the community is split be-tween two main schools of thought, one favoring the pres-ence of strong electron-electron correlations4–6 while theother proposes phonon-drag mechanism7,8 as the sourcefor the colossal value of Seebeck effect. Herein, we presentfor the first time huge thermopower values in the or-der of -16000µVK−1 below 20 K for single crystals ofFeGa3. The experimental results are based on especiallygood quality single crystals whose chemical compositionshave been carefully checked by X-ray powder diffractionand metallographic analysis. Among the various reasonsthat can rationalize such a large Seebeck coefficient, themain candidates are (i) the presence of strong electroniccorrelations, (ii) structural phase transitions, (iii) mag-netic phase transitions, and (iv) the interaction of thephonons with the mobile charge carriers via the phonon-drag effect. For example, most of the low-temperatureanomalies including the enhanced low temperature ther-mopower in FeSi are explained upon including the elec-tronic correlations in realistic many-body calculations.9

The onset of a magnetic phase transition has beendemonstrated as the reason for the presence of dis-tinct features in thermopower in Mn2−xCrxSb.10 Unusualjumps in Seebeck coefficient data have been measuredin the parent compound of the Fe-based superconductorLaFeAsO,11 Zn4Sb3

12 and La1.85−xNdxSr0.15CuO4,13 allof which have been explained in terms of structural phasetransitions. Recently, the observation of a large nega-tive Seebeck coefficient of -4500µVK−1 at 18 K in singlecrystalline CrSb2 has been suggested to emerge from thedominating phonon-drag effect at low temperatures.14

The intermetallic compound FeGa3 was first foundduring the systematic studies in the binary system Fe-Ga. The crystal structure was originally ascribed toa non-centrosymmetric structure type IrIn3.15–17 Onthe contrary, a centrosymmetric space group P42/mnmwas suggested later for the description of the symme-try for the crystal structure of FeGa3.18 More recentstudies confirmed the centrosymmetric crystal structureand reported the first observation of semiconductingbehavior.19 Thermoelectric properties (TE) at temper-atures from 300 to 950 K with negative thermopower val-ues were later determined on polycrystalline samples.20

The first characterization on FeGa3 single crystals de-pending on the crystallographic orientation was reportedin Ref. 3 but the authors observe the appearance ofgallium inclusions of approximately 3 % in their sam-ples. FeGa3 was found to be diamagnetic, which waslater validated.21 Presence of an energy gap was estab-lished using magnetic susceptibility measurements (0.29-0.45 eV) and as well as by valence band X-ray photoemis-sion spectroscopy (≤ 0.8 eV), while 57Fe Mössbauer spec-troscopy revealed the absence of magnetic ordering.21

2

Nevertheless, considering the narrow 3d bands, Yin andPickett22 explored the option of a magnetically orderedground state in FeGa3 using total energy calculations andobtained an antiferromagnetically ordered spin-singletstate upon inclusion of correlation effects. Though noverifiable experimental evidence for a magnetic transi-tion in FeGa3 exists, muon spin rotation spectra23 showthe existence of a spin-polaron band, which is consistentwith the presence of an antiferromagnetic spin-singletscenario. Photoemission and inverse photoemission spec-troscopic experiments24 have also been performed on sin-gle crystals of FeGa3 to probe its electronic structure andprovide an estimate for the amount of correlation effectsin this material. The measured band dispersions werecomparable to calculations based on density functionaltheory (DFT) which included a Coulomb repulsion pa-rameter U ≈ 3 eV. Nonetheless, the authors conclude thatthe correlation effects in FeGa3 is not as significant as inFeSi. Recently, another study on doped Fe(Ga,Ge)3 sys-tems using total energy calculations reports an itinerantmechanism (i.e. suggesting a minor role of the electroncorrelations implicitly) for the experimentally observedferromagnetism in the n-type samples.25,26

In our opinion, the presence/absence of magnetismand/or correlations for the stoichiometric FeGa3 systemsis still an open question. Until now, there have beenno reports of anomalous transport behavior at low tem-peratures in FeGa3. We have for the first time grownwell-defined single crystals of FeGa3 without any Gainclusions and with a total mass up to 25 g and per-formed various thermodynamic and transport measure-ments. Unusually large Seebeck coefficient (in the or-der of -16000µVK−1) and thermal conductivity (400-800 WK−1 m−1) below 20 K in single crystalline sam-ples are observed, which disappears in the polycrystallinespecimen with equivalent experimental composition. Asmentioned in the opening paragraph, various scenarioscould be behind these large Seebeck coefficient and ther-mal conductivity values. In our work, all the options areexplored in detail to rationalize the observed low temper-ature feature.

II. METHODS

A. Synthesis and chemical characterization

Single crystals of FeGa3 were grown using the two-phase region FeGa3 + melt of the Fe-Ga phase dia-gram (flux-growth). The elements Fe (powder, 99.99 %,ChemPur) and Ga (shots, 99.9999 %, ChemPur) in theratio 1:20 were weighed in alumina crucibles and encap-sulated in quartz ampoules under argon atmosphere witha pressure of 200 mbar. The mixture was heated at a rateof 5 K min−1 up to 1173 K and kept at this temperaturefor 90 hours. After slow cooling from 1173 K to 473 Kthe crystals were separated from the remaining solidifiedmelt and cleaned with hydrochloric acid to remove any

residual gallium from the surface. A rectangular piece,5.8 mm in length (longest possible rectangular bar) wascut for TE characterization.

The Czochralski method was used as a second tech-nique to grow large single crystals (≈ 8 mm). Startingfrom a homogenized melt of composition Fe16.5Ga83.5that had been prepared from Fe (bulk, 99.995 %, AlfaAesar) and Ga (pellets, 99.9999 %, ChemPur), in a firstexperiment spontaneous nucleation of FeGa3 occurred ata tapered corundum tip. The general approach has beendescribed in Ref. 27. In the next crystal growth runs,use was made of [001]-oriented FeGa3 seeds to grow well-defined single crystals of a total mass up to 25 g by slowlycrystallizing from a Ga-rich melt using pulling rates aslow as 0.1 mm h−1 while gradually cooling down the meltaccording to the changing temperature of the liquid.

For polycrystalline specimens, pieces of the flux-growncrystal were ground to powder and recompacted with thespark plasma sintering (SPS) technique. Using graphitedies, a maximum temperature of 973 K with an uniaxialpressure of 90 MPa was applied for 10 minutes.

X-ray diffraction data sets of all samples were collectedon an Image Plate Guinier Camera Huber G670 (CuKα1 radiation, λ = 1.54056 Å, 3 ≤ 2θ ≤ 100 , LaB6

as internal standard, a = 4.1569(1)Å). Metallographicinvestigations were made on plain cross sections after em-bedding samples in conductive resin (PolyFast, Struers,Denmark) with additional grinding and polishing withmicron-sized diamond powders. Wavelength dispersiveX-ray spectroscopy (WDXS) investigations of the chem-ical composition were performed with a Cameca SX 100spectrometer using FeSi and GaP as standards.

B. Physical measurements

Thermal diffusivity measurements of single and poly-crystalline samples were performed with the laser flashtechnique (LFA 427, Netzsch, Germany) in the tempera-ture range from 300 to 773 K. The thermal conductivityκ was derived from the relation κ = αDCp, where α is thethermal diffusivity, D is the density and Cp is the heatcapacity, respectively. The density of the obtained pelletdetermined by the Archimedes method reaches 92 % ofthe theoretical value. Heat capacity data at high temper-atures were determined by differential scanning calorime-try (DSC 8500, Netzsch). The electrical resistivity andthe Seebeck coefficient of rectangular bars were deter-mined simultaneously in a commercial ZEM-3 equipment(ULVAC-Riko, Japan) in the temperature range from 300to 773 K.

For TE properties at low temperatures from 4 to350 K the thermal conductivity, electrical resistivity andSeebeck coefficient were measured simultaneously usinga commercial system (thermal transport option of aPPMS, Quantum Design, USA). The dependence of ther-mopower on the magnetic field (H = 0 T, 9 T) was alsomeasured. Given the fact that the thermal conductivity

3

TABLE I. Lattice parameters and experimental compositions from WDXS analysis for single- and polycrystalline samples ofFeGa3.

Experimental composition a (Å) c (Å) V (Å3) Remarks

Fe1.023(4)Ga2.98(1) 6.2661(1) 6.5597(3) 257.56(1) Single crystal(flux-grown)

Fe1.04(1)Ga2.96(1) 6.2663(1) 6.5594(3) 257.56(1) Polycrystalline SPS specimen(flux-grown)

Fe1.018(3)Ga2.982(4) 6.2661(2) 6.5596(4) 257.57(1) Single crystal (Czochralski,oriented along [001])

Fe1.013(3)Ga2.987(4) 6.2665(1) 6.5586(2) 257.55(1) Single crystal (Czochralski,oriented along [100])

FeGa3 6.2628(3) 6.5546(5) 257.09(4) Ref. 19Powder (flux-grown)

FeGa3 6.262 6.556 257.07 Ref. 3Single crystal (flux-grown)

FIG. 1. Secondary electron microstructure pictures of FeGa3 specimens: (a) flux-grown single crystal (b) polycrystallinespecimen after SPS of flux-grown single crystal, (c) single crystal obtained from Czochralski method and oriented along [001]and (d) single crystal obtained from Czochralski method and oriented along [100].

is very high at low temperatures, we additionally reducedthe cross section (thinned) at the middle of the sampleas depicted in the inset of Fig. 12 in order to maximizethe heat flow, while reducing the temperature jumps atthe contacts of the sample to the heater and to the heatsink.

Heat capacity measurements in zero-field (ZF) andin field with H = 9 T were carried out using a relax-ation method (HC option, PPMS). Magnetic propertieswere measured on a SQUID magnetometer (MPMS-XL-7, Quantum Design). Zero-field cooling (ZFC, measuredin warming) and field cooling magnetization data weretaken in various fields up to H = 7 T.

C. Calculational details

The total energy calculations to obtain the densityof states (DOS) and band structure were performed us-ing the full potential nonorthogonal local orbital code(FPLO)28 employing the local density approximation(LDA). The Perdew and Wang29 exchange correlationpotential was chosen for the scalar relativistic calcula-tions. Additionally, we have explored the possibility ofthe presence of strong correlations in the Fe 3d shellby including an on-site Coulomb repulsion U via the

LSDA+U method, applying the “atomic limit” doublecounting term (also referred to as “fully localized limit”(FLL)). The projector on the correlated orbitals was de-fined such that the trace of the occupation number ma-trices represent the 3d gross occupation. The total ener-gies were converged on a dense k mesh with 2176 points(30×30×30) for the conventional cell in the irreduciblewedge of the Brillouin zone. The transport propertieswere calculated using the semiclassical Boltzmann trans-port theory30–32 within the constant scattering approx-imation as implemented in BoltzTraP.33 This approxi-mation is based on the assumption that the scatteringtime τ determining the electrical conductivity does notvary with energy on the scale of kBT . Additionally, nofurther assumptions are made for the dependence of τon the temperature. This method has been successfullyapplied to many narrow band gap materials includingclathrates, RuIn3 derivatives and as well as other inter-metallic compounds and oxides.32,34–37 Since the evalua-tion of transport integrals requires an accurate estimationof band velocities, the energy bands are calculated on afine mesh of 9126 k-points in the irreducible wedge of theBrillouin zone.

4

FIG. 2. (Color online) Tetragonal crystal structure of FeGa3

according to Ref. 19. The large (grey) atoms are Fe, whilethe smaller (Ga1 - red, Ga2 - light-blue) atoms are Ga[Fe at 4f (0.3437,0.3437,0); Ga1 at 4c (0,0.5,0); Ga2 at 8j(0.1556,0.1556,0.2620)]. The polyhedra surrounding the Featom is composed of 8 Ga atoms: two nearest neighbor Ga ata distance of 2.37 Å(Ga1), two next nearest neighbor Ga at adistance of 2.39 Å(Ga2), and four third nearest neighbor Ga ata distance of 2.50 Å(Ga2). Each Fe atom also has one anotherFe atom at a distance of 2.77 Å, forming so-called "dimers" inthe (001) plane. The polyhedrons of the iron atoms belong-ing to the same "dimer" are sharing a common face; whilepolyhedrons of different "dimers" are corner-sharing.

III. RESULTS AND DISCUSSIONS

A. Chemical characterizations

According to metallographic investigations, the ob-tained single crystals of FeGa3 via flux-growth andCzochralski method were free of non-reacted elemen-tal iron or remaining gallium melt (Fig. 1). All X-raydiffraction patterns (See Supplemental material38) of thesingle- and polycrystalline samples were indexed with thetetragonal FeGa3 structure type (space group P42/mnm,Fig. 2) without any additional phases. The refined lat-tice parameters and chemical compositions from WDXSanalysis are collected in Table I. The experimental com-position for all samples are identical within the typicalerror limits of the methods. One characteristic feature isthe small excess of iron atoms in comparison to the idealcomposition. In the paper, thermoelectric and thermo-dynamic characterizations are performed mainly on sin-gle crystals obtained from Czochralski method. The re-

0 200 400 600 800 100010-5

10-4

10-3

10-2

10-1

100

101

T (K)

(m)

single crystal [001] (Ref. [3]) single crystal [100] (Ref. [3])

single crystal (flux-grown) polycrystalline (flux-grown, SPS) single crystal [001] (Czochralski) single crystal [100] (Czochralski)

(m)

T (K)

0 100 200 300

10-2

10-1

100

101

FIG. 3. (Color online) Electrical resistivity in dependence onthe temperature for single- and polycrystalline FeGa3 speci-mens. For comparison single crystal data Ref. 3 are includedin the inset. Band gap calculation with the Arrhenius lawρ(T ) = exp(Eg/2kBT ) gives energy gaps of 0.38-0.51 eV.

0 50 100 150 200 250 3002.0x1019

4.0x1019

6.0x1019

8.0x1019

1.0x1020

1.2x1020

FeGa3 [100] (Czochralski) FeGa3 [001] (Czochralski)n

(ele

ctro

ns c

m-3)

T (K)

FIG. 4. (Color online) Charge carrier concentration n as afunction of temperature for the oriented FeGa3 single crystals(Czochralski method).

sults can be qualitatively inferred for all single crystallinesamples, since the chemical composition of all the sam-ples are identical. Any difference in the thermoelectricproperties in polycrystalline material in comparison tothe single crystals can be attributed to the changes ofthe microstructure.

B. Thermoelectric properties

The logarithmic plot of the electrical resistivity as afunction of temperature is shown in Fig. 3. For all sam-ples, semiconducting behavior is observed. The extrinsicregion at low temperatures is characterized by high resis-

5

tivity values implying high-purity and high-crystallinityof our materials. The flux-grown crystal shows higherresistivity with a terminated saturation range already at280 K, signifying the lower level of defects and impuritiesas compared to the other samples. This arises from thefact that the flux grown single crystals were additionallycleaned with hydrochloric acid which tend to remove ex-trinsic impurities. From the intrinsic region above 350 K,band gaps were calculated with the Arrhenius law ρ(T )= exp(Eg/2kBT ), giving a value of 0.50 eV.39 The exper-imental data are very well comparable to previously pub-lished results (0.47 eV).3 A slight anisotropy in FeGa3 isobserved below 200 K, with a reduced electrical resistivityin the [100] direction as compared to the [001] direction.A crossover becomes apparent around 250 K leading toslightly reduced resistivity values in the [001] directionabove room temperature.

To determine the carrier concentration, we measuredHall resistivity as a function of magnetic field for selectedtemperatures along [100] and [001] directions for the cur-

1

10

100

1000

0 100 200 300 400 500 600 700 800

-1000

-800

-600

-400

-200

0

T (K)

single crystal (flux-grown) polycrystalline (flux-grown, SPS) single crystal [001] (Czochralski) single crystal [100] (Czochralski)

el /

tota

l

(W K

-1 m

-1)

200 400 6000.0

0.1

0.2

0.3

0.4

T (K)

S (

V K

-1)

S (

V K

-1)

T (K)

-20,000

-15,000

-10,000

-5,000

5 10 15 20 25 30

FIG. 5. Top: Temperature dependence of the thermal conduc-tivity for FeGa3 specimens. The inset represents the contri-bution of the electronic part to the total thermal conductivityestimated with the Wiedemann-Franz law κel = ρL0 T. Bot-tom: Seebeck coefficient of FeGa3 specimens depending on thetemperature. The inset shows high values for the flux-grownsingle crystal. The black solid curve in the inset representsthe error for the Seebeck coefficient measurement, with ∆T

= 10−3 K.

rent flow. The Hall resistivity data were fit with a lin-ear function for both directions between 10 and 300 K.The determined RH are negative in the entire tempera-ture range, indicating electrons being the main carriers.The carrier concentration calculated using n = -1/eRH,is plotted in Fig. 4 as a function of temperature (withe = 1.602×10−19C). The carrier concentration does notvary significantly between 100 and 300 K, with room tem-perature values: n[001] = 9.52×1019 cm−3 and n[100] =1.03×1020 cm−3. Below 50 K, we observe an abrupt de-crease of n with the lowest value of 4×1019 cm−3 at 20 K.Such a feature in n is quite unusual and could arise from alow-mobility impurity band close to the conduction bandedge, as was shown to be the case for Ge.40 Recently,another compound where such a feature was observedis the antiferromagnetic semiconductor CrSb2

14 and theauthors determined an occupied low-mobility donor bandat 2 K to be causing the minimum in the carrier concen-tration.

The temperature dependence of the thermal conduc-tivity is plotted in Fig. 5(a). Remarkably huge peaks areobserved for all single crystals in the temperature rangefrom 13–16 K. Maximum values of ≈350 WK−1 m−1 forthe single crystal (Czochralski method) with heat flowalong [001] direction, ≈500 WK−1 m−1 for the singlecrystal (Czochralski method) along [100] direction and≈800 WK−1 m−1 for the unoriented single crystal (flux-grown) are observed, which are in contrast to previouslypublished data (≈ 17.5 WK−1 m−1) on oriented singlecrystals.3 Due to the presence of grain boundaries inpolycrystalline FeGa3, which act as additional scatter-ers for phonons, the peak collapses yielding values of only≈30 WK−1 m−1 at 21 K. At high temperatures, the ther-mal conductivity for the single crystalline samples differonly slightly. No significant anisotropy in thermal con-duction for FeGa3 is observed over the whole temper-ature range. As expected, the polycrystalline materialshows the lowest thermal conductivity among all investi-gated samples at high temperatures, being consistent toalready published data.20 The inset of Fig. 5(a) shows theelectronic contribution to the total thermal conductivityestimated via the Wiedemann-Franz law κel = ρL0 T,where L0 = 2.45×10−8 WΩK−2 is the Lorenz number.Below 400 K the total thermal conductivity is mainlydetermined by the lattice thermal conductivity, havingnearly no contribution from the electronic part.

The results of the thermopower measurements are de-picted in Fig. 5(b). In general, n-type behavior with elec-trons as majority carriers is observed over the whole tem-perature range, which is in contrast to the isostructuralcompounds RuIn3

41 and RuGa3,42 where a crossover be-havior from n to p type is observed above room temper-ature. This is in line with the observed small Fe excessin our synthesized samples (see Table I.).43 At high tem-peratures, above 400 K similar behavior is observed forall samples independent from the crystallographic ori-entation. Below 400 K, distinct differences in absolutevalues are observed. The polycrystalline specimen with

6

the highest defect concentration (e.g. grain boundaries)exhibits the lowest minimum Seebeck coefficient, compa-rable to published data.20,44 The slight anisotropy is pre-sumably electronically driven with an intersection pointof the [100] and [001] curves around 200-250 K, as al-ready observed in the electrical resistivity. Analogous tothe sequence of the phonon peaks in the thermal con-ductivity, maximum thermopower values of -750µVK−1

(single crystal via Czochralski method in [001] direc-tion) and -1000µVK−1 (single crystal via Czochralskimethod in [100] direction) appear. The inset of Fig. 5(b)shows the maximum thermopower value in the order of-16000µVK−1 measured for the unoriented single crystal(flux-grown). Though the low temperature maximum inthe thermopower occurs at the same temperature (≈ 12K) for all single crystalline samples, the magnitude of Sfor the flux-grown crystal is 16-20 times larger than ofthe Czochralski single crystals. One main reason for thisfeature is the non standardized nature of the thermal gra-dient arising from the length difference between the sam-ples: ≤ 6 mm (flux-grown) vs. 8 mm (Czochralski). Theobtained values of thermopower are comparable to pub-lished data on single crystals of intermetallic CrSb2

14 orFeSb2,5 but differ significantly to orientation-dependentmeasurements on FeGa3.3 The authors of Ref. 3 reportgallium inclusions of up to 3% in their single crystallinesamples, which could explain the difference between theirdata and our experimental thermopower.

The enhancement of thermopower at low temperaturesin certain narrow band gap semiconductors has beenshown to arise from increased electron-electron correla-tions, i.e. correlated semiconductors like Kondo insula-tors. Specifically, for iron-based semiconductors like FeSiand FeSb2 large Seebeck coefficients at low temperatures(+500µVK−1 at 50 K in FeSi,1 -45000µVK−1 at 10 Kin FeSb2

4) have been reported. This feature has beenargued to arise due to the presence of strong electroniccorrelations in these two systems.6,45 Though no staticmagnetic ordering has been observed in pure FeGa3 un-til now, weak ferromagnetic order has been observed25

for the Ge-doped FeGa3−xGex with x = 0.13 and weaklycoupled local moments have been observed for Co-dopedFe1−xCoxGa3 with x = 0.05.46 These attributes in FeGa3are also similar to FeSi and FeSb2 where no static mag-netic order is observed in the pure compounds, but ferro-magnetic metallic states are discerned in FeSi0.75Ge0.25,FeSb2−xTex and Fe1−xCoxSb2.47–49

C. DFT calculations

Previously, two works have addressed the eventualityof strong electronic correlations in FeGa3 using DFT-based calculations, but resulted in contradictory scenar-ios with one paper suggesting the presence of strong elec-tronic correlations in the Fe 3d orbital,50 while the otherrefutes this scenario.51 In both these papers, the authorsonly consider the band structure of non-magnetic or mag-

0

3

6

9

total

0

1

2

3dxy

3dxz , 3dyz

3d3z2-r

2

3dx2-y

2

0

0.2

0.44s4py

4pz

4px

-4 -3 -2 -1 0 1 2Energy (eV)

0

0.2

0.4

Den

sity

of s

tate

s (s

tate

s eV

-1 f.

u.-1

)

4s4py , 4px

4pz

FeGa3

Fe

Ga1

Ga2

=EF

FIG. 6. (Color online) Non-magnetic total and site projectedelectronic density of states of FeGa3.

netic FeGa3, but not the band structure-derived thermo-electric coefficients. Calculation of Seebeck coefficientsinvolve the calculation of the band velocities, which arequite sensitive to the underlying band dispersions. Sincethere are no other additional parameters involved in thecalculation of the Seebeck coefficients, the results aredirectly comparable to the experimental measurements,thus this could be used to identify the presence of strong

Γ X M Γ Z R A

-0.3

0

0.3

0.6

0.9

1.2

1.5

Energ

y (

eV

)

Γ X M Γ Z R A

-0.3

0

0.3

0.6

0.9

1.2

1.5

LDA

LSDA+U

EF

FIG. 7. (Color online) Comparison of the non-magnetic LDAand the AFM LSDA+U band structures of FeGa3. The near-est neighbor Fe atoms are ordered antiferromagnetically inthe LSDA+U calculation. A U value of 2 eV and a J valueof 0.625 eV was used.

7

0 100 200 300 400 500 600 700 800T (K)

-600

-500

-400

-300

-200

-100

0S

(µV

K-1

)

LDA n ~1.0x1020

electrons cm-3

LDA n ~4.0x1019

electrons cm-3

LDA+U n ~1.0x1020

electrons cm-3

FIG. 8. (Color online) Calculated thermopower as a func-tion of temperature for FeGa3 for the two scenarios: LDA(non magnetic) and LSDA+U (antiferromagnetic, U = 2eV). There is a significant difference in the calculated ther-mopower between LDA and LSDA+U , with the LDA curvebeing more in accordance with the experimentally measuredthermopower.

correlations in FeGa3. To that end, we have first calcu-lated the non-magnetic LDA density of states for FeGa3and the results are collected in Fig. 6. Consistent withprevious calculations and as well as our experiments, weobtain a semiconductor with a band gap of ≈ 0.52 eV.The valence and conduction band edges of FeGa3 are de-rived primarily from Fe d states with only a small mix-ing of Ga. This feature is more clearly visible in thesite projected DOS in Fig. 6. Note the large differencein the y-axis values between Fe and Ga site projectedDOS. The valence band maximum is comprised mainly ofFe-3dx2

−y2 orbital character, while the conduction bandminimum consists mainly of Fe-3d3z2

−r2 orbital charac-ter. There are sharp peak-like features in the DOS on ei-ther side of the Fermi level arising from flat bands. Thesesharp features are conducive for enhanced thermoelectricproperties.52,53

As mentioned previously, though no magnetism hasbeen observed for FeGa3 in experiments, recently therehas been some discussion about the presence of strongCoulomb correlations emerging from the narrow 3d bandsof this semiconducting system using DFT based cal-culations. Using LSDA+U with FLL double countingscheme, a structure wherein the nearest neighbor Fe sitesare coupled antiferromagnetically with local moments onFe of the order of 0.6µB was found to be stable.50 Addi-tionally a semiconducting gap of the order of 0.5 eV wasobtained, similar to the experiments. To the contrary,using an optimized double counting scheme (screened bythe Yukawa screening length λ) no magnetic momenton the iron ions was obtained.51 Recently, another DFTwork discusses the possibility of itinerant magnetism forboth Ge (on the Ga- site) and Co (on the Fe site) dopedsystems.26 Itinerant Stoner ferromagnetism for the doped

systems was readily obtained without invoking the needfor preexisting moments in the parent semiconductingstate, as well as without the need for correlation terms.Furthermore, the Seebeck coefficients was calculated asa function of doping, though only for the non-magneticground state. In our work, we calculate the Seebeck co-efficients of FeGa3 for both the un-correlated (LDA) andcorrelated (LSDA+U) scenarios to shed more light onthe proceeding discussions. Collected in Fig. 7 are theresults of the LSDA+U calculation (with FLL doublecounting scheme) for U = 2 eV, with a Hund’s exchangeJ = 0.625 eV. The magnetic pattern used for this cal-culation is similar to that proposed in Ref. 50 with thetwo nearest Fe neighbors ordering antiferromagnetically(AFM). Surprisingly, the resulting AFM LSDA+U bandstructure close to the Fermi edge, including the size ofthe semiconducting gap is quite similar to that of thenon-magnetic LDA calculations. Moving away from theFermi edge we observe some differences between the LDAand LSDA+U bands in both the valence and conductionchannels. These small differences could in turn alter thetransport coefficients since they depend on the band ve-locities. Significant changes in the calculated Seebeck co-efficients between LDA and LSDA+U calculations couldprovide an alternative view for identifying the presenceor absence of magnetism and correlations (described in amean-field manner) in FeGa3.

To that end, we have calculated the transport coef-ficients using the semiclassical Boltzmann theory. Thesimilarity of the band gaps between LDA and AFMLSDA+U calculations permits a direct comparison be-tween the two scenarios.54 Collected in Fig. 8 are cal-culated data of the Seebeck coefficient as a function oftemperature within LDA and LSDA+U for a carrier con-centration n ≈ 1.0×1020 electrons cm−3, obtained fromHall effect measurements for a temperature range 100-300 K. The low temperature enhancement in the Seebeckcoefficient observed in the experiments around 20 K isnot observed in either of the calculated curves. Decreas-ing the carrier concentration to n ≈ 4.0×1019 electronscm−3 also does not produce the low temperature fea-ture. The Seebeck coefficient increases monotonically upto 500 K for LDA and up to 700 K for LSDA+U , afterwhich it starts to decrease. Above 150 K, the absolutevalues and the shape of S within LDA are more in accor-dance with the experimental observations and is largerthan within LSDA+U by a factor of two. Though thelow temperature feature is absent in our calculations, wecan nevertheless infer that strong correlations, treatedin a mean-field manner do not improve the descriptionof the Seebeck coefficient in FeGa3. More sophisticatedcalculations that treat Coulomb correlation U beyonda mean-field approximation are necessary to obtain amore in-depth understanding of the role of correlationsin FeGa3.55,56

8

10-3

10-2

10-1

100

101

102

0 100 200 300

0 20 40 60 80 1000.000

0.005

0.010

0.015

log T

log

Cp

T (K)

Cp (

J m

ol-1 K

-1)

single crystal [001] (Czochralski, ZF) single crystal [001] (Czochralski, 9T)

-3

-2

-1

0

1

2

0.5 1.0 1.5 2.0 2.5

Fit of dataCp(T ) = T + T 3 + T 5

= 0.03 mJ mol-1 K-2

Cp /

T (J

mol

-1 K

-2)

T 2 (K2)

FIG. 9. (Color online) Top: Magnetic field dependence of thespecific heat for a FeGa3 single crystal (Czochralski method)oriented along [001] in zero-field (ZF) and high field (H =9T). The inset shows a log-log plot. Bottom: Specific heatdata below 10 K in a C p/T vs. T 2 representation resultingin a Sommerfeld coefficient of γ = 0.03 mJmol−1 K−1.

D. Heat capacity and susceptibility measurements

We proceed to investigate the likelihood of a phasetransition as a source for the low temperature featuresin S and κ. To this end, we have measured the heatcapacity and magnetic susceptibility for FeGa3. The re-sults of the heat capacity measurement is collected inFig. 9(a). The zero field measurement does not showany jumps or kinks over the entire temperature range.Moreover the data for 9 T and low temperatures are alsocoinciding with the zero-field data. This implies thatthere are no structural phase transitions in FeGa3. Thevalue of the electronic specific heat coefficient γ is ob-tained by plotting Cp/T versus T 2 (Fig. 9(b)) and fittingthe data to Cp = γT + βT 3 + δT 5. We obtained a bet-ter fit when including the T 5 term, which is associatedto both the higher order terms of the Fourier series of aharmonic oscillator and as well as to anharmonic terms.57

This results in γ = 0.03 mJ mol−1 K−2, close to zero asexpected for a semiconductor and consistent with previ-

0

2x10-4

4x10-4

6x10-4

8x10-4

1 10 100

1 10 100-2.0x10-4

-1.5x10-4

-1.0x10-4

-5.0x10-5

(emu/mol)

T (K)

(emu/mol)

single crystal [001] (Czochralski)polycrystalline(flux-grown, SPS, factor 1/2)

T (K)

H (T) = 0.1/ 3.5 / 7.0/ // /

(emu/mol)

T (K)

0 5 10 15 20

2.2x10-4

2.4x10-4

2.6x10-4

T = 6.4K

FIG. 10. Top: Temperature dependence of magnetic sus-ceptibility for FeGa3 single crystal (Czochralski method) ori-ented along [001] and powder made of the single crystal (flux-grown), which was additionally washed with hydrochloric acidin (Top) low external field of H = 0.1 T and (Bottom) highexternal fields of 3.5 and 7.0 T. The inset in the upper panelshows the magnification of temperatures below 20 K.

ously published values.3,25 The Sommerfeld constant γin the electronic specific heat can be compared to thebare value γb determined from the bare reference densityof states at the Fermi level, N(0) (γb = π2k2BN(0)/3 =2.359N(0)), where N(0) is in states/(eV f.u.) and γb is inmJ mol−1 K−2. From Hall effect measurements, for a car-rier concentration of n ≈ 1.0×1020 electrons cm−3 (100-300 K) and n ≈ 4.0×1019 electrons cm−3 (< 100 K), weuse the N(0) from our band structure calculations andobtain γb = 0.06 mJ mol−1 K−2 and 0.01 mJ mol−1 K−2

respectively, consistent with the experimental observa-tion.

The temperature dependence of the magnetic suscep-tibility measured at various fields is displayed in Fig. 10.For fields of 3.5 T and 7 T, the measured χ(T ) for the[001] oriented single crystal (Czochralski method) is neg-ative for the entire temperature range up to 300 K anddiamagnetic. The slight upturn at low temperatures orig-inates from the tiny amounts of Fe impurities in the sys-tem. This fact is clearly visible in the low field 0.1 T data

9

where the susceptibility values at low temperatures arepositive. For the [001] oriented single crystal (Czochral-ski method), in 0.1 T field, we observe a sharp downwardturn around 6.4 K. We were able to correlate this fea-ture to the onset of superconductivity from tiny amountsof Ga inclusions in thin film form (Tc = 7.6 K).58 Thegallium inclusions were removed by grinding the sampleand washing it with diluted hydrochloric acid (H2O:HCl= 1:1). The susceptibility measurements on the so ob-tained polycrystalline sample did not show any downturnat low temperatures. Consistent with the heat capacitymeasurements, we do not observe any other anomalousfeatures in χ(T ) that could point towards the possibilityof a magnetic phase transition.

E. Phonon-drag mechanism

Having excluded both structural and magnetic phasetransition at low temperatures, and as well as the pres-ence of strong electronic correlations in FeGa3, anotherpossible explanation for the unusually strong signal be-low 20 K in the thermopower and the thermal conduc-tivity is a phonon-drag mechanism. The peaks in thethermal conductivity and Seebeck coefficient for all thesingle-crystalline samples always occur at the same tem-perature, ≈ 20 K. Moreover, the trend in the peak in-tensity between κ and S are similar: κpolycrystalline <κ[001] < κ[100] < κunoriented and Spolycrystalline < S[001] <S[100] < Sunoriented. The peak in the low temperaturethermal conductivity for the flux-grown single crystal ismore than 25 times larger than for the polycrystallinesample. Similarly, the peak in the Seebeck coefficients forthe flux-grown single crystal is also larger than the pow-der sample (prepared from the flux-grown sample) by afactor of ≈ 30. Such features have been observed in othersemiconductors including single crystals of Ge,59 Si60

and CrSb2,14 nano-composite FeSb2,8 reduced TiO2,61,62

ultra-thin films of FeSi2 and MnSi1.7/FeSi2,63 which havesubsequently been demonstrated to arise from phonon-drag effects. Phonon drag can be defined as the effectarising from a preferential scattering of the charge car-riers by the phonons in the direction of the flow (i.e.,the drag on the charge carriers exerted by the phononsstreaming from hot to cold end in thermal conduction)and mostly evidenced at low temperatures. With increas-ing temperatures, the magnitude of the phonon-drag in-fluenced Seebeck coefficient decreases rapidly. This isdue to the reduced relaxation time for the long wave-length phonons, which interact with the electrons/holes,as a result of the increase in the carrier concentration.Due to this electron-phonon coupling at reduced temper-atures, the Seebeck coefficient can now be written as asum of the conventional electron-diffusion part Sd andanother term arising from the phonon-electron interac-tion Sp, the so-called phonon-drag contribution.

S = Sd + Sp

0 20 40 60 80 100T (K)

-1200

-800

-400

0

S (

µV K

-1)

Sexp ([100], Czochralski)

Sd calculatedSp calculated

Single crystal (Czochralski method) [100]

FIG. 11. Comparison of the measured Seebeck coefficient withthe calculated values of the diffusive (Sd) and phonon-drag(Sp) parts as a function of temperature for a single crystal ofFeGa3 (Czochralski method) along [100]. The Sp term dom-inates the low temperature regime, indicative of a significantphonon-drag effect in this system.

0 10 20 30 40-1000

-800

-600

-400

-200

0

H = 0T H = 9T

S (

V K

-1)

T (K)

FIG. 12. Temperature dependence of the Seebeck coefficientfor a single crystal of FeGa3 (Czochralski method) orientedalong the [100] direction, measured both at 0T and 9T mag-netic fields. The magnetic field was applied along [100], paral-lel to the crystallographic orientation. The lack of significantchanges in S at 0T and 9T supports the non-electronic ori-gin of the colossal low temperature values and thus can beattributed to phonon-drag mechanism. The slight differencein the thermopower data compared to Fig. 5 is due to thechange in the shape of the sample to improve the heat flow(see inset).

Though an accurate quantitative calculation for aphonon-drag contribution is difficult to obtain, one canrealize an estimate by calculating the electron-diffusionpart and subtracting it from the measured total See-beck coefficient. For a semiconductor with a complexband structure and whose spin-orbit splitting is negligi-

10

ble (<< kBT ), the electron-diffusion part as suggestedby Herring,64 can be written as

Sd = ∓86.2

[

ln4.70× 1015

n+

3

2ln

m∗

m+

|∆ǫT |

kBT+

3

2lnT

]

where, the minus and plus signs are for the n and p-type carriers respectively, n is the charge carrier densitydenoted in cm−3, m and m∗ are the bare and inertialeffective masses of the electron, respectively, |∆ǫT | refersto the average energy of the transported electrons rel-ative to the band edge, kB is the Boltzmann constant.Usually, |∆ǫT | is of the order of kBT , and in the diffusivelimit (i.e., lattice scattering by phonons of long wave-length), Herring64 proposes an additional approximationof |∆ǫT | = 5/2 + r with r = -1/2. Fig. 11 displays theSd values obtained from the above equation using m∗

= m and n from Hall resistivity measurements (Fig. 4).Subsequently, Sp was calculated by subtracting Sd fromthe total S. We note that the Sp contribution to thetotal S is dominant over the electron-diffusive Sd termin the low temperature regime and thus indicative of asignificant phonon-drag effect in FeGa3.

Another method to eliminate the possibility of an elec-tronic origin to the colossal low-temperature Seebeck co-efficient is to measure in high magnetic fields.14 If the sys-tem is dominated by the phonon-drag mechanism, only asmall response in the magnetic field is expected. To con-firm this scenario, we measured the Seebeck coefficientfor a [100] oriented FeGa3 single crystal (Czochralskimethod) at 9 T and the results are displayed in Fig. 12.The lack of difference between the 0 and 9 T data up to40 K is apparent and upholds the non-electronic origin ofthe pronounced peak in Seebeck coefficient.

IV. SUMMARY

We have synthesized single crystalline and polycrys-talline samples of the narrow band gap semiconductorFeGa3. A band gap of ≈ 0.5 eV is obtained from elec-trical resistivity measurements. Systematic investigationof the thermoelectric properties of the single- and poly-crystalline samples reveal pronounced peaks around 20K in the thermal conductivity (400-800 WK−1m−1) andthe Seebeck coefficient (in the order of -16000µVK−1).Such large values have previously not been reported forFeGa3. To identify the origin of the low temperature en-hancement, we investigated various possibilities. DFT-based band structure calculations and subsequent mod-eling of the Seebeck coefficient using semiclassical Boltz-mann transport theory yielded a Seebeck coefficient ofthe same order as the experiment above 300 K with LDA.

Inclusion of strong electronic correlations arising fromthe narrow Fe-d bands treated in a mean-field manner(LSDA+U) does not improve this comparison, renderingstrong correlations as an explanation for the low tempera-ture enhancement in Seebeck unlikely. Heat capacity andmagnetic susceptibility measurements under different ap-plied magnetic fields do not show any kinks or jumpsaround 20 K and thus excludes a magnetic or structuralphase transition as a reason for the low-temperature peakin Seebeck coefficient. Comparing the trend in Seebeckcoefficient and thermal conductivity among the varioussamples, and based on estimates of the phonon-drag con-tribution to the Seebeck coefficient and the negligible re-sponse in a high magnetic field, we conclude that thelow-temperature enhancements in FeGa3 are due to aphonon-drag effect.Note added in revision : During the submission of this

draft, we became aware of another recent work on the bi-nary FeGa3 and the hole doped variants Fe1−xMnxGa3and FeGa3−yZny.65 In contrast to our work which fo-cusses on the anomalous thermoelectric properties ofFeGa3 at very low temperatures (below 50 K), Gamża et.

al. focus on the magnetic properties of both the binaryand the hole doped variants up to very high tempera-tures (≈ 800 K).65 Comparison of the lattice parameters,electrical resistivity and thermodynamic measurementsof our flux-grown single crystals with that of Gamża et.

al.65 demonstrates the similarity between our samples. A

fit to the Arrhenius law for the intrinsic region (> 350 K)of the resistivity gave a band gap of 0.5 eV in our work forthe single crystals grown using the Czochralski method,while Gamża et. al. obtain a value of 0.4 eV for their flux-grown samples.65 Signatures of a complex magnetic or-dering is presented based on neutron diffraction measure-ments. In contrast, LDA+DMFT (dynamical mean fieldtheory) calculations do not show any hint of long-rangeantiferromagnetic ordering.65 However, in our work, ap-plying LSDA+U as a simple mean-field treatement ofelectronic correlations, we could stabilize a simple AFMorder. Nevertheless, this approximation did not improvethe description of the thermopower.66

ACKNOWLEDGMENTS

The authors acknowledge X-ray powder diffractionmeasurements and WDXS analysis by the competencegroups Structure and Metallography at the MPI CPfS.We also thank Ralf Koban for help with physical proper-ties measurements. D.K., H.R. and Yu.G. acknowledgefunding by the DFG within SPP 1386.

1 B. Sales, E. C. Jones, B. C. Chakoumakos, J. A. Fernandez-Baca, H. E. Harmon, J. W. Sharp, and E. H. Volckmann,

Phys. Rev. B 50, 8207 (1994).2 C. Petrovic, J. W. Kim, S. L. Bud’ko, A. I. Goldman,

11

P. Canfield, W. Choe, and G. J. Miller, Phys. Rev. B 67,155205 (2003).

3 Y. Hadano, S. Narazu, M. A. Avila, T. Onimaru, andT. Takabatake, J. Phys. Soc. Jpn. 78, 013702 (2009).

4 A. Bentien, S. Johnsen, G. K. H. Madsen, B. B. Iversen,and F. Steglich, Euro. Phys. Lett. 80, 17008 (2007).

5 P. Sun, N. Oeschler, S. Johnsen, B. B. Iversen, andF. Steglich, Dalton Trans. 39, 1012 (2009).

6 P. Sun, M. Søndergaard, B. B. Iversen, and F. Steglich,Ann. Phys. (Berlin) 523, 612 (2011).

7 H. Takahashi, R. Okazaki, Y. Yasui, and I. Terasaki, Phys.Rev. B 84, 205215 (2011).

8 M. Pokharel, H. Zhao, K. Lukas, Z. Ren, C. Opeil, andB. Mihaila, Mat. Res. Soc. Comm. 3, 31 (2013).

9 J. M. Tomczak, K. Haule, and G. Kotliar,PNAS 109, 3243 (2012).

10 J. H. Wijngaard, C. Haas, and R. A. de Groot, Phys. Rev.B 45, 5395 (1992).

11 M. A. McGuire, A. D. Christianson, A. S. Sefat, B. C.Sales, M. D. Lumsden, R. Jin, E. A. Payzant, M. D.,Y. Luan, V. Keppens, V. Varadarajan, J. W. Brill, R. P.Hermann, M. T. Sougrati, F. Grandjean, and G. J. Long,Phys. Rev. B 78, 094517 (2008).

12 T. Souma, G. Nakamoto, and M. Kurisu, J. Alloys Compd.340, 275 (2002).

13 B. Büchner, M. Cramm, M. Braden, W. Braunisch, O. Hof-fels, W. Schnelle, R. Müller, A. Freimuth, W. Schlabitz,G. Heger, D. Khomskii, and D. Wohlleben, Europhys.Lett. 21, 953 (1993).

14 B. Sales, A. F. May, M. A. McGuire, M. B. Stone, D. J.Singh, and D. Mandrus, Phys. Rev. B 86, 235136 (2012).

15 K. Schubert, H. L. Lukas, H.-G. Meissner, and S. Bhan,Z. Metallkd. 50, 534 (1959).

16 K. Schubert, H. Breimer, R. Göhle, H. L. Lukas, H.-G. Meissner, and E. Stolz, Naturwissenschaften 45, 360(1958).

17 C. Dasarathy and W. Hume-Rothery, Proc. Royal Soc. A286, 141 (1965).

18 S. S. Lu and C.-K. Liang, Acta Phys. Sin. 21, 849 (1965).19 U. Häussermann, M. Boström, P. Viklund, Ö. Rapp, and

T. Björnängen, J. Sol. Stat. Chem. 165, 94 (2002).20 Y. Amagai, A. Yamamoto, T. Iida, and Y. Takanashi,

J. Appl. Phys. 96, 5644 (2004).21 N. Tsujii, H. Yamaoka, M. Matsunami, R. Eguchi,

Y. Ishida, Y. Senba, H. Ohashi, S. Shin,T. Furubayashi, H. Abe, and H. Kitazawa,J. Phys. Soc. Jpn. 77, 024705 (2008).

22 Z. P. Yin and W. E. Pickett,Phys. Rev. B 82, 155202 (2010).

23 V. G. Storchak, J. H. Brewer, R. L.Lichti, R. Hu, and C. Petrovic,J. Phys.: Condens. Matter 24 (2012), 10.1088/0953-8984/24/18/185601.

24 M. Arita, K. Shimada, Y. Utsumi, O. Morimoto, H. Sato,H. Namatame, M. Taniguchi, Y. Hadano, and T. Taka-batake, Phys. Rev. B 83, 245116 (2011).

25 K. Umeo, Y. Hadano, S. Narazu, T. Onimaru, M. A. Avila,and T. Takabatake, Phys. Rev. B 86, 144421 (2012).

26 D. J. Singh, Phys. Rev. B 88, 064422 (2013).27 P. Gille and B. Bauer, Cryst. Res. Tech. 43, 1161 (2008).28 K. Koepernik and H. Eschrig, Phys. Rev. B 59, 1743

(1999).29 J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).30 J. M. Ziman, Electrons and Phonons (Oxford University

Press, New York, 2001).

31 W. Jones and N. H. March, Theoretical Solid State Physics(Courier Dover, New York, 1985).

32 G. K. H. Madsen, K. Schwarz, P. Blaha, and D. J. Singh,Phys. Rev. B 68, 125212 (2003).

33 G. K. H. Madsen and D. J. Singh, Comput. Phys. Com-mun. 175, 67 (2006).

34 S. Johnsen, A. Bentien, G. K. H. Madsen, B. B. Iversen,and M. Nygren, Chem. Mater. 18, 4633 (2006).

35 D. J. Singh and D. Kasinathan, J. Electron. Mater. 36,736 (2007).

36 H. J. Xiang and D. Singh, Phys. Rev. B 76, 195111 (2007).37 D. Kasinathan, M. Wagner, K. Koepernik, R. Cardoso-Gil,

Y. Grin, and H. Rosner, Phys. Rev. B 85, 035207 (2012).38 See Supplemental Material at

http://link.aps.org/Supplemental/... for the XRD pattern.39 The unoriented bar-shaped piece, which was cut from the

flux-grown crystal could not be measured at high tempera-tures, owing to its short length For the unoriented crystal,a band gap of 0.38 eV can be estimated (calculated for theintrinsic region between 280-360 K).

40 H. Fritzche, Phys. Rev. B 99, 406 (1955).41 M. Wagner, R. Cardoso-Gil, N. Oeschler, H. Rosner, and

Y. Grin, J. Mater. Res. 26, 1886 (2011).42 M. Wagner-Reetz, R. Cardoso-Gil, W. Schnelle, and

Y. Grin, Submitted to Sol. Stat. Sci. (2014).43 According to our DFT calculations, Fe carries a small neg-

ative charge.44 N. Haldolaarachchige, A. B. Karki, W. A. Phelan, Y. M.

Xiong, R. Jin, J. Y. Chan, S. Stadler, and D. P. Young,J. Appl. Phys. 109, 103712 (2011).

45 G. Aeppli and Z. Fisk, Comments Condens. Matter Phys.16, 155 (1992).

46 E. M. Bittar, C. Capan, G. Seyfarth, P. G. Pagliuso, andZ. Fisk, J. Phys.: Conf. Series 200, 012014 (2010).

47 S. Yeo, N. Nakatsuji, A. D. Bianchi, P. Schlottmann,Z. Fisk, L. Balicas, P. A. Stampe, and R. J. Kennedy,Phys. Rev. Lett. 91, 046401 (2003).

48 R. Hu, V. F. Mitrović, and C. Petrovic,Phys. Rev. B 79, 064510 (2009).

49 R. Hu, V. F. Mitrović, and C. Petrovic,Phys. Rev. B 74, 195130 (2006).

50 Z. Yin and W. E. Pickett, Phys. Rev. B 82, 155202 (2010).51 J. M. Osorio-Guillén, Y. D. Larrauri-Pizarro, and G. M.

Dalpian, Phys. Rev. B 86, 235202 (2012).52 G. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. USA

93, 7436 (1996).53 J. K. Freericks, D. O. Demchenko, A. V. Joura, and

V. Zlatić, Phys. Rev. B 68, 195120 (2003).54 We make a note about plotting the experimental and cal-

culated Seebeck coefficients in separate plots: In DFT, itis instructive to calculate the Seebeck coefficient for a fixedcarrier concentration, while in reality the carrier concen-tration may vary as a function of temperature during ex-perimental measurements (see Fig. 4). Hence, a combinedplot of the experimental and calculated Seebeck coefficientswould be misleading. For cases where the carrier concen-tration is temperature dependent, comparison between ex-periment and calculation is more qualitative than quanti-tative.

55 C. Grenzeback, F. B. Anders, G. Czycholl, and T. Pr-uschke, Phys. Rev. B 74, 195119 (2006).

56 J. K. Freericks and V. Zlatić, Phys. Rev. B 64, 245118(2001).

57 R. Pässler, AIP Advances 3, 082108 (2013).

12

58 G. Kieselmann, Ga elements, Ga films, Ga/X junctions.In R. Flükiger and W. Klose (eds.) Ac - Na, vol. 21a ofLandolt-Börnstein - Group III Condensed Matter, 249 -258 (Springer, Berlin-Heidelberg-New York, 1985).

59 T. H. Geballe and G. W. Hull, Phys. Rev. 94, 1134 (1954).60 T. H. Geballe and G. W. Hull, Phys. Rev. 98, 940 (1955).61 W. R. Thurber and J. H. Mante, Phys. Rev. 139, A1655

(1965).62 J. Tang, W. Wang, G.-L. Zhao, and Q. Li, J. Phys.: Con-

dens. Matter 21, 205703 (2009).63 Q. R. Hou, B. F. Gu, Y. B. Chen, and Y. J. He, Modern

Phys. Lett. B 25, 1829 (2011).64 C. Herring, Phys. Rev. 96, 1163 (1954).

65 M. Gamża, J. M. Tomczak, C. Brown, G. Puri, A. Kotliar,and M. C. Aronson, Phys. Rev. B 89, 195102 (2014).

66 The neutron diffraction pattern of Gamża et. al. (Ref. 65)shows a complex magnetic ordering in FeGa3. UsingLSDA+U , we have stabilized only a simple AFM orderwherein nearest neighbor Fe sites are ordered antiferro-magnetically. The discrepancy between the measured andcalculated Seebeck coefficient could then arise for two pos-sible reasons: the treatement of correlations in a mean-fieldmanner is insufficient or the simple AFM order we consideris not a good approximation for the complex magnetic or-der observed in the experiments.