filled skutterudites — physics and chemistry of iron antimonides...

SELECTED RESEARCH REPORTS

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Introduction

The class of compounds known as “skutterudites”exhibits a wealth of topical behaviors. These mate-rials derive from the mineral Skutterudite (CoAs3)[1]. Binary skutterudites having the general chemi-cal formula TX3 are formed by the members of the9th group of the periodic table T = (Co, Rh, Ir) withpnicogens X = (P, As, Sb). No binary compoundswith iron, ruthenium, and osmium could be synthe-sized so far under equilibrium conditions, obvious-ly for electronic reasons. In order to stabilize suchcompounds it is necessary to include electroposi-tive elements as a third component leading to theformula MyT4 X12 (filled skutterudites [2,3]).Compounds with rare-earth, actinide, and alkaline-earth metals or thallium as cation M were synthe-sized. Different degrees of filling y can be realizedup to y = 1, however, the limits for y depend strong-ly on the cation M and the “host” T4 X12 and are notyet well explored. In these filled skutterudites thestabilizing M atoms reside in large voids alreadypresent in the T4 X12 framework (Fig. 1).

A variety of properties have been observed —mainly for rare-earth filled skutterudites — rangingfrom metal-insulator transitions to magnetic andquadrupole orderings, conventional and unconven-tional superconductivity, heavy-fermion/non-Fermi-liquid behavior, and fluctuating/intermediatevalency. Furthermore, interest in these compoundsis fueled by their possible use in thermoelectricapplications [4]. Many studies suggest that thephysics of filled skutterudites is governed by a sub-tle interplay of the filler ions and their surroundingtransition-metal pnicogen host structure. However,only a few publications were devoted to the physicsof the host.

In order to gain a better understanding of theseprocesses and thus, to explore novel non rare-earthskutterudites, we have successfully synthesizednew alkali-metal iron antimonides with sodium and

potassium [5]. These light “filler” atoms with s-electrons in their conduction bands are not magnet-ic and, therefore, are a good choice for the investi-gation of the d-electron influence on the structuralchemistry and the physical properties of filled skut-terudites. Surprisingly, these compounds order fer-romagnetically at about 85 K. The basic propertieshave already been reported [6,7,5]. In contrast, thealkaline-earth (Ca, Sr, Ba) compounds [3,7,8]remain paramagnetic down to 2 K. Nonetheless,our electronic structure calculations within thelocal density approach (LDA) indicate that theground states of Ca, Ba, Yb, and LaFe4Sb12 shouldalso be ferromagnetic. Obviously, strong spin fluc-tuations not described within the LDA destroy theferromagnetism.

Recently [11], we could prove that Yb inYb1–xFe4Sb12 is divalent, and that its properties arenot caused by the formation of a heavy-electronstate, induced by the Kondo effect, at low temper-

Filled Skutterudites — Physics and Chemistry of Iron Antimonides of Alkali, Alkaline-Earth, and Rare-Earth MetalsAndreas Leithe-Jasper, Walter Schnelle, Helge Rosner, Michael Baenitz, Horst Borrmann, Ulrich Burkhardt, Andrei Gippius 1, John A. Mydosh, Annegrit Rabis, Reiner Ramlau, Pratap Raychaudhuri 2, Goutam Sheet 2, Jörg Sichelschmidt, Steffen Wirth, Romain Viennois3,Frank Steglich, and Yuri Grin

Fig. 1: Cubic unit cell of iron-antimony skutteruditesMFe4Sb12 containing two formula units (yellow spheresM = alkali, alkaline-earth, rare-earth metal; red spheresFe; blue spheres Sb).

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atures as previously claimed. Consequently, theelectronic properties of Yb1–xFe4Sb12, CaFe4Sb12,and BaFe4Sb12 are found to be almost identical.These paramagnetic compounds have a hugeSommerfeld-Wilson ratio (� 24 for Yb and Ca)[11], demonstrating that they are situated close toferromagnetic order. The aforementioned similari-ty originates from a specific band structure featureat the Fermi level of all three compounds, as foundby high-resolution band structure calculations. It ismirrored in their optical properties which were thetopic of a recent investigation [12].

A study of the low-temperature specific heat ofseveral filled skutterudite compounds [9] resultedin comprehensive information on the electronicand phononic contributions, in particular on a low-lying Einstein phonon (“rattler”) [10] of the weak-ly bonded filler in these compounds. The tempera-ture dependences observed in the low-temperatureelectrical resistivity of the Fe-Sb skutterudites arequite different and a topic of current research.

As already mentioned, the suppression of ferro-magnetic order in the paramagnetic compounds islargely due to the action of spin fluctuations. Thisphenomenon was addressed by performing meas-urements of nuclear magnetic resonance (NMR)and magnetization as well as by electronic struc-ture calculations. Results are reported in [13,14,7].Our band structure calculations indicate that theferromagnetic compounds are nearly half-metallicferromagnets for which a large spin polarizationcan be expected. We could prove this theoreticalconclusion by spectroscopic investigations onpoint contacts [15].

Chemical Physics of Filled Skutterudites

The preparation of poly- and single crystallinematerial and the basic crystallographic features ofthe new compounds NaFe4Sb12 and KFe4Sb12 werealready reported in the last Scientific Report [5] andin Ref. [6,7,11]. Single crystal X-ray diffraction(XRD) analysis of NaFe4Sb12 corroborates the fulloccupancy (100%) of the Na. Fe and Sb positionsdo also not show any deviation from full occupan-cy. This result is confirmed by WDXS analyses andfor KFe4Sb12 [7]. Similar results are obtained forCaFe4Sb12 and BaFe4Sb12, however, for the La andthe Yb compound deviations from full occupancyof the filler site were found (La0.79Fe4Sb12 (x = 0.21)and Yb0.95Fe4Sb12 (x = 0.05)).

At room temperature, all filler atoms in [Fe4Sb12]skutterudites display a large displacement parame-ter. Detailed investigations were performed forNaFe4Sb12. Powder neutron diffraction measure-ments show that the atomic displacement parame-ter of Na is strongly temperature dependent, whilethe values for Sb and Fe show only a weak oralmost no dependence on temperature. At 2 K, thedisplacement (Uiso) values for all three positionsare of similar magnitude close to zero. The differ-ence between the displacement parameters for Naand Fe (Sb) extrapolated to T = 0 is less than0.005 Å2, which range roughly 3 mean e.s.d. Thiscorresponds to the common thermal motion(Einstein oscillator) of sodium atoms inside theslightly oversized antimony cage. No indications ofa lock-in-type phase transition were found. Atroom temperature, off-center displacements of thesodium atom can be ruled out due to the sphericaldistribution of the difference electron density in thevicinity of the Na position [7]. The thermal expan-sion of NaFe4Sb12 was studied by powder XRDdown to 15 K. For the temperature range100–300 K, the linear coefficient of thermal expan-sion is as low as � = 11 × 10–6 K–1 and reveals arather rigid material. The pressure dependence ofthe unit-cell volume of NaFe4Sb12 in the range upto 9.5 GPa is typical for intermetallic compounds.The least-squares fit of a Murnaghan-type equationof state to the data leads to a zero-pressure unit cellvolume V0 = 772.78 Å3 and to a bulk modulus B0= 85(1) GPa using B0’ = 4 [7].

Full occupation of the M position in NaFe4Sb12and KFe4Sb12 raised the question about the originof their stability. To get more insight into this topic,the analysis of the chemical bonding with the elec-tron localization function (ELF, �) method wasperformed. NaFe4Sb12 displays only three types ofattractors in the valence region which can be takenas a fingerprint for direct (covalent) atomic interac-tions (Fig. 2). Two of them are located on the short-est Sb-Sb contacts d1 and d2 in the Fe-Sb frame-work, confirming the covalent character of theinteraction between the Sb atoms belonging toneighboring [FeSb6] octahedra. The third one islocated slightly off the Fe-Sb bond lines, showinga pronounced covalency of these bonds, too(Fig. 2b). No unique attractors were found in thevalence region between the sodium and frameworkatoms.


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The basins of ELF attractors are defined by zero-flux surfaces in the gradient field of ELF. The low-est ELF values at the interconnect points betweentwo basins indicate the degree of charge separation.The basin of the sodium inner shell interconnectswith the framework basin only at a very low valueof � (< 0.1). Both facts — the absence of bondingattractors in the vicinity of sodium atoms and theclear charge separation — strongly suggest a

charge transfer from sodium to the Fe-Sb frame-work. Another relevant topological feature of ELFin NaFe4Sb12 is the structuring of the inner shell ofthe iron atoms (see the isosurface with � = 0.72 inFig. 2b). This highlights a participation of the inner-shell electrons of iron in the interactions inthe valence region between the atoms. Integrationof the total electron density in the ELF basins forthe Sb-Sb attractors gives electron counts of 1.74and 1.79 for d1(Sb–Sb) and d2(Sb–Sb), respective-ly. For the Fe–Sb contacts, a count of 2.03 elec-trons was obtained (Fig. 2b). In case of the innershell of the iron atoms, 13.76 electrons were found(14 expected), which is in good agreement with thecalculation for free atoms and confirms the partici-pation of the inner-shell electrons in the interac-tions in the valence region. For the core region ofthe sodium atoms 9.98 electrons were found fromthe integration, in good agreement with the valueof 10 expected from the Aufbau principle for Na+.This would give a charge transfer of 1.02 electronsfrom each Na to the [Fe4Sb12] polyanion. Thepolyanion is formed by 6 Sb–Sb (d1), 6 Sb–Sb (d2),and 24 Fe–Sb bonds. This yields a total count of69.90 electrons for the polyanion and results in acharge transfer of 0.94 electrons from each Na tothe polyanion [7]. Accordingly, the total electronbalance can be written as Na0.98+[Fe4Sb12]0.98–.Considering the strong overlap of the 3s band of Nawith the Sb 5p band in the density of states (DOS)and taking into account the rectangular arrange-ment of the Sb–Sb bonds in the structure (Fig. 1),we propose a transfer of the sodium charge to theSb–Sb bonds. Following the ELF representation,the NaFe4Sb12 structure has to be considered as athree-dimensional covalently bonded polyanionicframework of Fe and Sb atoms with Na cationsembedded into the cavities. This scenario is inagreement with the large rigidity of the structure.

Thermal Properties — Electronic andStructural Dynamics

As already mentioned, the prominent structuralfeature of the filled skutterudites is the unique crys-tallographic position of the cation in an oversizedicosahedral void formed by pnicogen atoms. Thisleads to anomalously large displacement parame-ters of the “filler” cation, a thermal motion com-monly termed “rattling”. The phonon-dominated

Fig. 2: Electron localization function � for NaFe4Sb12. (a) Crystal structure of NaFe4Sb12 with shortest inter-atomic distances Fe-Sb and Sb–Sb. Isosurfaces of ELFillustrate the covalent interaction between Fe and Sb (�= 0.53) and between Sb atoms (� = 0.56). The isosur-face for � = 0.72 shows the structuring of the thirdshell for the Fe atoms; see text. (b) Electron counts forrelevant bonds in the NaFe4Sb12 structure.

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thermal conductivities of filled skutterudites areroughly an order of magnitude smaller than thoseof its unfilled equivalents [4,10]. The mechanismof the suppression of the thermal conduction by the“rattler” is not yet fully understood [10]. It is alsounclear whether this thermal motion is mostly har-monic or implies a multi-well potential and, even-tually, a structural lock-in transition at low temper-atures. The availability of filled skutterudites withcations of atomic mass spread between ca. 23 (Na)and 173 (Yb) offered the possibility to obtain moreinformation on the “rattler”, its influence on trans-port properties and its interplay with electronicdegrees of freedom.

In the following we will present an analysis ofthe contributions to the specific heat cP(T) of skut-terudites with [Fe4Sb12] host [9]. For temperaturesabove 100 K the values of cP(T) for M = Na, K,Ca, and La0.79 are almost identical. The data for thecompounds with M = Na, K display a small sec-ond-order anomaly at TC = 81 K (transition mid-point, M = Na) and 80 K (M = K), respectively,with widths below 1% of TC, in good agreementwith the Curie temperatures determined from mag-netization measurements [7].

Figure 3 displays the low-temperature specificheat below 14 K. It is obvious that the electronicterms �T for the compounds with Na, K, Ca, and Baare of the same size (� = 100–120 mJ mol–1 K–2).Only for very low temperatures, cP(T) can be fittedby a simple model cP(T) = �T + �T 3 including thelinear electronic Sommerfeld term and the DebyeT 3 lattice term. In order to account for the thermalexitation of the loosely bonded cation, an Einstein

term (characteristic temperature �E) for the atom onthis site needs to be combined with the Debyemodel (Debye temperature �D) for the remainingatoms of the polyanion. The specific heat at lowtemperatures is fitted by cP(T) = �T + �T 3+ �T 5 +� (T / �E) where � contains the initial Debye tem-perature �D(0), and is the Einstein function. TheDebye contribution �T 5 is already of importance fortemperatures at which the Einstein term becomessignificant. This model is not expected to work athigher temperatures where optical phonon modes ofthe [Fe4Sb12] host need to be taken into account.Also, the contributions to cP(T) of La1–xFe4Sb12 can-not be analyzed on the basis of zero-field data dueto the presence of a strongly field-dependent spinfluctuation contribution [9].

Fits where both � and � were allowed to varywere found to be of limited use since there exists astrong numerical anti-correlation of � with � [9].We therefore neglected the Debye T 5 term (� = 0)which is a useful approximation for T/�D(0) <0.05. The obtained parameters agree with alterna-tive fits for which � was fixed to 3R (R = molar gasconstant) multiplied by the cation filling factor [9].For the light cations M = Na, K, the agreement isexcellent while for M = Ca, Ba, and La slightlylarger values � are found. Only for M = Yb a minorimpurity (Yb2O3 phase) hampers the exact determi-nation of �, �D, �, and �E. As an example, a fit andits individual contribution are shown for theCaFe4Sb12 data in Figure 4.

The Sommerfeld coefficient � of the electronicspecific heat of the Na, K, Ca, and Ba compoundsrange from 98 to 116 mJ mol–1 K–2. Also,

Fig. 3: Specific heat capacity of filled skutteruditesMFe4Sb12 (M = Na, K, Ca, Ba, La0.79, Yb0.95) below 14K in a cP/T vs. T 2 representation. The lines show the fitsof the model described in the text.

Figure 4: Specific heat capacity of CaFe4Sb12 below14.1 K. The lines give the contributions of the indivi-dual terms of the fit to the model (see text).


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Yb1–xFe4Sb12 shows a value in this range, fully con-sistent with the large similarities in the electronicdensity of states (DOS) at EF [7,11]. Interestingly,only the intrinsic � of the skutterudite with thetrivalent La-ion (effective charge 3(1–x)) is signif-icantly different, even after considering the strongspin fluctuation contribution [9,16,18].

The initial Debye temperature �D(0) increaseswith the charge of the cation from 243 K (Na) to267 K (Ca) and 274 K (La) indicating an increas-ingly covalent bonding within the [Fe4Sb12]–z

polyanion structure with increased charge ze trans-ferred to it from the cation. A slight decrease of�D(0) with increasing atomic mass of the cation isobserved for the divalent cations Ca, Ba, and Yb.This might indicate a weak coupling of the fillervibrations to the host lattice acoustic phononmodes, i.e., the two phonon systems cannot be treat-ed as totally independent, even at low temperatures.

The Einstein temperatures �E are between 62 Kand 104 K. The values can be compared with thosederived from diffraction investigations, inelasticneutron scattering, EXAFS, or nuclear inelasticscattering Mössbauer investigations. For example,for M = La the value of �E is available from sever-al methods: a calculation by Feldman et al. [19]gives 7.1 meV (82 K), inelastic neutron scatteringby Viennois et al. [20] yields 7 meV (81 K) forLa1–x and a fit to the higher-temperature heat capac-ity by Sales et al. [4] results in 79 K, in good agree-ment with our value (77 K) for a sample with La1–x.

Electrical Resistivity and Magnetoresistance

The normalized electrical resistivity ((T) – 0) /(300 K) of differently prepared compact samplesof the six skutterudites is given in Figure 5 [9].Here, the bulk density of the samples has a verystrong influence on the absolute resistivity and theresidual resistivity. However, the common featureof the normalized (T) curves is a shoulder around70–100 K. Such a change of slope at elevated tem-perature is often due to s-d scattering, where lightcharge carriers are scattered off more heavy elec-trons forming a narrow band near EF. The shoulderis most pronounced for MFe4Sb12 with divalentcations M. In addition, for M = Ba it is found at ahigher temperature compared to M = Ca, Yb. Theshoulder has vanished for La1–xFe4Sb12. In the fer-romagnetic Na and K compounds the shoulder is

overlaid by the small phase transition anomaly at —most remarkably — the same temperature (Curietemperature TC � 80 K). It is likely that the ferro-magnetic ordering and the shoulder originate fromthe same band structure feature near EF [9].

The inset of Figure 5 shows the low-temperaturebehavior of the normalized resistivity in zero mag-netic field [9]. Again, a clear distinction betweenthe skutterudites with monovalent, divalent, andtrivalent cations can be made. (T, H) was fitted byT-power laws with exponent � (plus 0(H)) for tem-peratures up to 7 K. A surprisingly stable power-law behavior is the T � T 1.9 dependence found forthe ferromagnetically ordered Na and K com-pounds, � is even stable up to 20 K and increasesfrom 1.9 in zero field to 2.0 with H = 9 T. Thisexponent is reminiscent of the common Fermi liq-uid T 2 dependence while the compounds are ferro-magnetic. In contrast, the nearly ferromagneticcompounds (Ca, Yb) display much larger values of�. Most interestingly, for CaFe4Sb12 a high expo-nent � � 3 is essentially stable for fit intervals withhigh limits from 7 K up to 20 K. The Ba com-pound shows almost the same � as the Yb com-pound. The values of �, obtained from (T, H) of allthree compounds, however, strongly decrease withincreasing magnetic field and recover the usual T 2

dependence in a wide temperature interval. TheLa1–xFe4Sb12 sample displays strongly differentexponents � of 1.61–1.68 (in zero field) — close toT 5/3, the typical value for ferromagnetic spin fluc-tuations — and no shoulder at higher temperatures.With increasing field � tends to higher values but

Fig. 5: Normalized electrical resistivity of filled skut-terudites MFe4Sb12 (M = Na, K, Ca, Ba, La1–x, Yb1–x). Xassigns single crystal samples (La, Yb), all other sam-ples are spark plasma sintered (SPS) material. The insetshows data below 7K.

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to 1.7 �B/Fe-atom. While for the ferromagnets — asexpected — the Weiss temperature � is positive andclose to the Curie temperature, the paramagneticisomorphic compounds show lower, but still posi-tive values for �. The dimensionless Sommerfeld-Wilson-ratio (� 0/�, where 0 is the low-T plateauvalue of (T) and � the Sommerfeld coefficient ofthe electronic specific heat) is very high (around24), indicating that these compounds (especially theCa and Yb-filled ones) are close to a ferromagneticinstability. Only La1–xFe4Sb12 with x = 0.21 (filledwith 0.79 La3+ cations, i.e. max. 2.37 transferredelectrons) displays a significantly lower paramag-netic effective moment (1.2 �B/Fe-atom) and a neg-ative Weiss temperature � = –50 K.

The occurrence and stability of ferromagnetism inthe filled skutterudites with the [Fe4Sb12] host hasbeen investigated by FPLO band structure calcula-tions using the fixed spin moment (FSM) approach.The FSM method calculates the total energy and theelectronic structure for a given, fixed magneticmoment. For M = Na, K (Fig. 7, lower curves), thecalculations result in a ferromagnetic ordering withan energy gain of about 0.05 eV (2 mHartree) perunit cell. This energy gain is large enough to over-come the strong spin fluctuations present inMFe4Sb12. For M = Yb, Ca, Ba this energy gain isconsiderably smaller (Fig. 7, middle curves). There-fore, strong ferromagnetic spin fluctuations impedethe magnetic order for these compounds. In anexternal magnetic field, these fluctuations are sup-pressed. From our calculations, we predict a meta-magnetic transition for the skutterudites with a

Fig. 6: Inverse magnetic susceptibility H/M(T) of filledskutterudites MFe4Sb12 with various cations M = Na, K,Ca, Ba, La, Yb.

Fig. 7: Relative energy vs. magnetic moment per Fe-atom resulting from fixed spin moment (FSM) calcula-tions for various filled skutterudites MFe4Sb12 (M = Na,K, Ca, Ba, La, Yb; 1 Hartree � 27.2 eV).

the T 2 law is clearly not achieved for H = 90 kOe. The ratio A/� 2 (where A is the coefficient of the

T 2 in (T)) in zero field can only be calculated forNaFe4Sb12 and KFe4Sb12. The resulting values forT < 7 K (3.68×10–8 and 1.75×10–8 �m (mol K/J)2,respectively) [9] are significantly smaller than thecommon value of � 1×10–7 �m (mol K/J)2, indi-cating that electron-electron scattering is not dom-inating in the ferromagnetically ordered phase.Turning now to the data taken at H = 90 kOe, wefind A/� 2 values of 3.67 for Na, 1.30 for K, 2.38for Ca, 0.88 for Yb1–x, and 1.63×10–8 �m(mol K/J)2 for La1–xFe4Sb12, respectively. Sincejust the lower bound of the resistivity and A valuesseem to be intrinsic, it can be concluded that theratio A/� 2 of all MFe4Sb12 is about 10–8 �m(mol K/J)2, i.e., one order of magnitude below theso-called Kadowaki-Woods ratio for most(enhanced and heavy) Landau-Fermi liquids.Further investigations are currently underway.

Occurrence of Ferromagnetism in Fe-SbSkutterudites

The magnetic properties of the filled skutteru-dites MFe4Sb12 are summarized in Figure 6. Allparamagnetic susceptibilities can be approximatedby a Curie-Weiss law. The appearance of this tem-perature dependence of (T) is not due to localizedmagnetic moments but to spin fluctuations of itin-erant (3d) electrons [21]. Interestingly, the com-pounds with alkali and alkaline-earth metals dis-play almost the same paramagnetic moment of 1.5


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divalent filler. According to the FSM calculations,with increasing magnetic field a transition to a fer-romagnetically ordered state is predicted in thesequence Yb, Ca, Ba. Recently, this metamagnetictransition has been observed experimentally for M= Ca, Sr, Ba [22], for M = Ca already at Hext �140 kOe and at higher fields for M = Sr and Ba.For M = La, the energy gain from ferromagneticordering is rather small. Thus, a metamagnetictransition is unlikely or could be expected only atextremely high fields.

Magnetic Resonance Studies on Fe-SbSkutterudites

In the last Scientific Report [5] it was shown thatthe magnetic resonance (NMR/NQR) on the 23Na (I= 3/2) and 121,123Sb (I = 5/2, I = 7/2) nuclei is apowerful local probe to study the magnetism aswell as to obtain information about the local sym-metry at the nuclei sites of NaFe4Sb12 [23]. Further23Na-NMR investigations on the solid solution(Na1–xCax)Fe4Sb12 confirm the intrinsic nature of the ferromagnetic transition at 85 K [24].Comparative NMR and NQR studies on Fe-Sbskutterudites with monovalent (Na), divalent (Ca,Ba) and trivalent (La) filler ions were performed.The 121,123Sb-NQR study combined with ab-initiolinearized augmented plane-wave calculations pro-vides microscopic evidence for disorder on thefiller site [13]. This is also confirmed by 23Na- and139La-NMR investigations. One scenario to explainthe NMR results is based on the presence of intrin-sic vacancies existing in the structure [13].

The comparison of the NMR results of the fillerions Na1+, Ba2+ and La3+ demonstrates the differentcharacter of the magnetic correlations in terms ofMoriya’s self-consistent renormalization theory[21] for itinerant magnets [14]. The spin latticerelaxation rate (1/T1) of 139La in La1-xFe4Sb12exhibits a T 1/2 temperature dependence, which is aunique feature of weakly and nearly antiferromag-netic metals, whereas in NaFe4Sb12

23Na-(1/T1) iswell described by the spin-fluctuation theory foritinerant ferromagnets in the ferro- and paramag-netic state (1/T1 proportional to T 1 below TC, Fig.8). NMR distinguishes two types of itinerant mag-netism: ferromagnetic order in NaFe4Sb12 and weakantiferromagnetic fluctuations in La1–xFe4Sb12.BaFe4Sb12 seems to be just at the border between

dominating ferromagnetic and antiferromagneticcorrelations. In this compound, 1/T1 was obtainedfrom 137Ba-NQR, where two lines of 137Ba havebeen found (�1 = 45.9 MHz and �2 = 49.0 MHz atT = 77 K).

A Pseudogap from Iron States

For the compounds MFe4Sb12 (M = Ca, Ba, Yb) weperformed investigations of their optical electronicexcitations. These are characterized by a low-ener-gy pseudogap structure, very similar for each com-pound, which could nicely be explained by highlyaccurate LDA electronic band-structure calcula-tions. The Fe-3d states generate the observedpseudogap whose characteristics appears to be verysimilar to the so-called Kondo-insulator gap foundin some 4f strongly correlated electron systems.

We have measured the near normal incidence opti-cal reflection on MFe4Sb12 (M = Ca, Ba, Yb) in awide spectral region (7 meV – 30 eV) at tempera-tures 2 K – 300 K [12]. As high accuracy for thereflection data was required, the polycrystallinesamples were coated in-situ with gold and then usedfor measuring the reference spectra. After Kramers-Kronig transformation of the reflectivity, the dissi-pative part of the optical conductivity �1(�,T) wasobtained.

Figure 8: 1/T1 normalized to the nuclear gyromagneticratio �N

2 as a function of temperature as obtained from 139La-NMR (139�N = 6.014 MHz/T), 137Ba-NQR(137�N = 4.731 MHz/T, from the �1– line) and 23Na-NMR(23�N = 11.262 MHz/T). The solid line is a calculation of1/T1 vs. T based on Moriya’s theory [21], making use ofthe field- and temperature-dependent magnetizationM(H,T) for weak itinerant ferromagnets. The dashedline is a fit to a T 1/2 power law.

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The compounds show conventional metallicbehavior in the optical conductivity �1(�,T) aboveT � 90 K whereas for T < 90 K it is continuous-ly suppressed until it reaches a minimum value atthe lowest temperature. This behavior of �1(�,T)

and its enhancement for energies between 17 and60 meV indicates the formation of a pseudogap inthe electronic charge excitations below � 17 meV(Figure 9).

Remarkably, all investigated compounds MFe4Sb12(M = Yb, Ba, Ca) show a very similar pseudogapbehavior of their optical conductivities, pointingtowards a very similar electronic band-structure.

To obtain accurate electronic structure informa-tion (Fig. 10), a full potential, non-orthogonallocal-orbital calculation scheme within L(S)DAwas used. For M = Ca, Ba, calculations includingspin-orbit coupling were performed whereas for M= Yb the LDA+U scheme was applied. To ensureaccurate band structure and density of states weused for the fully relativistic calculations a veryfine mesh of 5551 points in the irreducible part ofthe Brillouin zone. The optical pseudogap and itsdifferent appearances in BaFe4Sb12 and CaFe4Sb12as well as the sharp features are very well repro-duced by our high-resolution LDA band-structurecalculations (cf. Figs. 9 and 10; [12]). Therefore, atleast for MFe4Sb12 with M = Yb, Ca, Ba only weakelectronic correlations within the Fe3d-Sb5p bandsseem to be present. This is a completely differentmechanism than the Kondo-insulator gap scenariofor 4f heavy-fermion compounds leading, surpris-ingly however, to similar optical spectra.

Half Metallicity of Ferromagnetic FilledSkutterudites

For the ferromagnetically ordered filled skutteru-dite NaFe4Sb12, band-structure calculations withinthe local spin density approximation (LSDA) pre-dict a spin-split density of states with almost per-fect half-metallic behavior [7]. A material withsuch electronic properties is considered to be use-ful for electronic devices based upon spin control(spintronics). Consequently, new materials with ahigh degree of spin polarization have evolved astopics of particular attention in recent years [25]. Inorder to verify this prediction experimentally,point-contact Andreev reflection (PCAR) measure-ments were conducted on KFe4Sb12 and NaFe4Sb12samples [15]. Obviously, the two compounds intro-duce a new class of materials that exhibit a largedegree of spin polarization and itinerant electronmagnetism with a rather high Curie temperature TCof 80 K – 85 K.

Fig. 9: Spectra of the optical conductivity �1(�,T) atselected temperatures below and above T � 90 K,where a pseudogap forms below � 17 meV. ForBaFe4Sb12 the inset shows �1(�,T) at h� = 10 meV,demonstrating the evolution of the pseudogap.

Fig. 10: Total density of states of MFe4Sb12 near theFermi level EF. For M = Yb, the scalar relativistic resultis shown without spin-orbit coupling. For M = Ca, Bathe spin orbit coupling was included leading to anupward shift as well as to a broadening of the peak�50 meV above EF.

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CaFe4Sb12BaFe4Sb12YbFe4Sb12


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The PCAR measurements were performed at2.8 K on finely polished polycrystalline samplesurfaces. Mechanically cut sharp Nb or Pb tipswere engaged onto the samples to establish con-tacts of minimum area. Differential conductanceG(V) versus voltage V characteristics of the con-tacts were recorded. The typical resistance of thecontacts in the normal state varied between10–20 �. This, combined with the sharp doublemaxima structure in the G–V spectra, symmetricabout V = 0, may point towards a ballistic nature ofthe point-contacts. In Figure 11 we show four rep-resentative spectra. The transport spin polarizationPt was extracted by fitting the spectra with aBlonder-Tinkham-Klapwijk (BTK) formula modi-fied to incorporate the effect of spin polarization.The vast majority of spectra could be analyzedusing only three fitting parameters, namely Pt, thesuperconducting energy gap � of the tip, and thebarrier parameter Z which characterizes the strengthof the potential barrier at the interface. Here, thecomparatively low Z values of these spectra ensurea good quality of the fits. Note, that those spectrawith lowest Z values have the highest impact on theextrapolated intrinsic Pt values.

Figure 12 shows the variation of the extractedvalues of Pt as a function of the barrier parameterZ. Pt decreases with increasing Z, a behavior thathas been observed earlier in a variety of ferromag-nets and is believed to arise from spin depolariza-tion at a magnetically disordered scattering barrierformed at the interface. The intrinsic value of Pt is

therefore extracted by linearly extrapolating the Ptvs. Z curve to Z = 0. The consistency of this pro-cedure is easily seen in the case of NaFe4Sb12:measurements carried out with both Pb and Nb tipsresult in the same value of the intrinsic spin polar-ization (within experimental errors), though thedecay of Pt with Z is different for the two cases dueto differences in the nature of the interfaces. Theintrinsic value of Pt extracted in this way is 67% forKFe4Sb12, and 60% for NaFe4Sb12. PCAR meas-urements were also conducted on CaFe4Sb12 and Pt = 0 was found for all fitting attempts as to beexpected for a non-ferromagnetic material.

To gain further insight into the electronic struc-ture of these materials on a microscopic level, afull-potential, non-orthogonal local-orbital calcula-tion scheme (FPLO) within the LSDA was utilized.Our band structure calculations result in a ferro-magnetic ground state for KFe4Sb12 with a nearlyinteger magnetic moment of 2.98 �B per formulaunit. The states in the spin-split region originatepredominantly from Fe-3d hybridized with the Sb-5p states. We find an almost fully polarized DOS atthe Fermi level EF for KFe4Sb12 (Figure 13). TheDOS contribution in the spin-up channel can beassigned mainly to two bands (Fermi surfaces) ofalmost pure Fe-3d character (Figure 13a). There isonly one band of strongly mixed Sb 5p–Fe 3d char-acter crossing EF in the spin-down channel (Figure13a). Due to its high value of the Fermi velocity vF� 0.3 × 106 m s–1, this band makes only a tiny con-tribution to the number of states at EF. The corre-

Fig. 12: Transport spin polarization Pt in dependenceon the Z-value for the different sample/tip combinationsmeasured. The extrapolation to zero Z yields the intrin-sic spin polarization of the two skutterudites. The indi-cated error bar is representative for all measurements.

-8 -6 -4 -2 0 2 4 6 8

0.98

0.99

1.00

1.01

1.02

1.03

-8 -6 -4 -2 0 2 4 6 8

0.88

0.92

0.96

1.00

1.04

-8 -6 -4 -2 0 2 4 6 80.94

0.96

0.98

1.00

1.02

-6 -4 -2 0 2 4 60.96

0.98

1.00

1.02

1.04

1.06

(a)

Z = 0.1P

t = 61 %

KFe4Sb

12

Nb tip

G (

V )/

Gn

∆ = 1.3 meV

(b)

Z = 0.15P

t = 53.5 %

NaFe4Sb

12

Nb tip∆ = 1.4 meV

(c)

Z = 0.08P

t = 67.3 %

KFe4Sb

12

Nb tip

G (

V )/

Gn

V (mV)

∆ = 1.3 meV

(d)

Z = 0.13P

t = 48.2 %

NaFe4Sb

12

Pb tip

V (mV)

∆ = 1.4 meV

Fig. 11: Selected conductance spectra G(V) for the skut-terudites KFe4Sb12 (a,c) and NaFe4Sb12 (b,d) taken at2.8 K. The spectra were measured (dots) using (a-c) Nbor (d) Pb tips and were normalized to the normal stateconductance Gn at high voltage. The lines present theresults of the best fits with the fit parameters given ineach panel (see text).

0.0 0.1 0.2 0.30

20

40

60

80

100NaFe4Sb

12 / Pb tip

NaFe4Sb

12 / Nb tip

KFe4Sb

12 / Nb tip

Pt (

%)

Z

104


sponding Fermi surfaces, colored according to vFvalues, are given in Figure 13b,c and 13d for the rel-evant spin-up and spin-down bands, respectively.The band structure calculations result in spin polar-izations Pt of 99.6 % for KFe4Sb12, and 99 % forNaFe4Sb12. These calculated values are significant-ly larger than the measured ones: 67 % and 60 %,respectively.

In case of spin polarization measurements it isimperative to bear in mind that in addition to theDOS at EF, N(EF), also the Fermi velocity vF mayinfluence the obtained value. From the band struc-ture calculations we find very different vF for thetwo spin channels (Fig. 13). As a result, the calcu-lated spin polarization is reduced in the skutteru-dite materials in which the high value of Pt stemsfrom the almost completely spin-polarized DOS atEF. The opposite behavior is found in so-calledtransport half metals (e.g., the manganites) inwhich the high values of the transport spin polar-ization Pt are mainly due to extremely different val-ues of vF.

We note that the spin polarization as obtained fromband-structure calculations does not include severalfactors which are detrimental to a large transport spinpolarization. First, the weak itinerant ferromagneticnature of the filled skutterudites is associated withlarge spin fluctuations [6,7] which may reduce thespin polarization from its theoretical value. The pres-ence of strong ferromagnetic fluctuations in thesecompounds was already indicated above. Note thatthe high field magnetization value (when spin fluctu-ations are quenched) is the one that corresponds toband structure calculations. Hence, a crude correla-tion between magnetization and spin polarizationwould suggest a 50 % decrease in the spin polariza-tion arising from this effect alone. Second, it has beenseen in several compounds that Pt of the surface canbe reduced with respect to its bulk value. In addition,spin-orbit coupling in the ferromagnet would alsoreduce the spin polarization at the Fermi level. Third,our contacts might not be in the pure ballistic regime.From the band-structure calculations, the expectedspin polarization is P1 = 0.968 for a contact in the bal-listic regime and P2 = 0.765 in case of a purely diffu-sive contact putting emphasis on the actual nature ofthe contact in our PCAR measurements. Consideringthese factors, the observation of 67 % spin polariza-tion in KFe4Sb12 is indeed surprising. The key torobustness of the transport spin polarization againstthese detrimental effects may indeed lie in the factthat Pt in this material is primarily governed by thedensity of states (rather than the Fermi velocity) ofthe majority (spin-down) channel, which is verysmall over a relatively large energy range close to EF.This renders Pt less sensitive not only to fluctuationeffects but also with respect to impurity scattering, anaspect which is of importance to realize its applica-tion potential.

Fig. 13: Calculated density of states (DOS) and Fermisurfaces for KFe4Sb12. (a) DOS resolved for the indivi-dual bands relevant at EF. Spin-down band 176 has anon-vanishing DOS at EF (cf. dashed line that representsa factor of 10 magnification). (b,c) Fermi surfaces forthe most contributing spin-up bands 173 (b) and 174 (c).The color coding indicates the Fermi velocities vF. (d)Fermi surface and velocity for the relevant spin-downband 176.


105

Summary

In our detailed study of the Fe-Sb-based skutteru-dites, stabilized by non-magnetic cations, interest-ing aspects and consequences of the electronicproperties of the host structure could be unraveled.One particular point is the occurrence of weak bandferromagnetism when transferring one electron tothe [Fe4Sb12] host by incorporation of Na+ and K+

ions. Strong spin fluctuations destroy this groundstate in compounds with Ca2+, Sr2+ and Ba2+ ions,whereas in case of trivalent filler ions (e.g. La3+)antiferromagnetic spin fluctuations become domi-nant. Exceptional agreement between band struc-ture calculations and experiments could beachieved. This is demonstrated by the confirmationof the temperature-dependent optical band pseudo-gap found in CaFe4Sb12 (and in the isoelectronic Baand Yb compounds) by high-resolution LDA cal-culations. Moreover, the ferromagnetic Na andKFe4Sb12 compounds were predicted by LDA cal-culations to be nearly half-metallic ferromagnets.This interesting property could be experimentallyproofed by measuring a large transport spin polar-ization by point contact spectroscopy.

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________1 Moscow State University, Moscow, Russian Federa-

tion.2 Tata Institute of Fundamental Research, Mumbai,

India.3 Université de Montpellier II, Montpellier, France.

filled skutterudites — physics and chemistry of iron antimonides...

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