Discovery of a Superhard Iron Tetraboride Superconductor

Huiyang Gou,1,2 Natalia Dubrovinskaia,2,* Elena Bykova,1,2 Alexander A. Tsirlin,3,4 Deepa Kasinathan,3

Walter Schnelle,3 Asta Richter,5 Marco Merlini,6 Michael Hanfland,7 Artem M. Abakumov,8 Dmitry Batuk,8

Gustaaf Van Tendeloo,8 Yoichi Nakajima,1 Aleksey N. Kolmogorov,9 and Leonid Dubrovinsky1

1Bayerisches Geoinstitut, Universitat Bayreuth, D-95440 Bayreuth, Germany2Laboratory of Crystallography, Material Physics and Technology at Extreme Conditions,

University of Bayreuth, D-95440 Bayreuth, Germany3Max Planck Institute for Chemical Physics of Solids, Nothnitzer Straße 40, D-01187 Dresden, Germany

4National Institute of Chemical Physics and Biophysics, Akadeemia tee 23, 12618 Tallinn, Estonia5Technische Hochschule Wildau, Bahnhofstraße 1, D-15745 Wildau, Germany

6Dipartimento di Scienze della Terra, Universita degli Studi di Milano, Via Botticelli 23, 20133 Milano, Italy7ESRF, Boıte Postale 220, 38043 Grenoble, France

8EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium9Department of Physics, Applied Physics and Astronomy, Binghamton University, State University of New York,

Vestal, New York 13850, USA(Received 22 February 2013; published 7 October 2013)

Single crystals of novel orthorhombic (space group Pnnm) iron tetraboride FeB4 were synthesized at

pressures above 8 GPa and high temperatures. Magnetic susceptibility and heat capacity measurements

demonstrate bulk superconductivity below 2.9 K. The putative isotope effect on the superconducting

critical temperature and the analysis of specific heat data indicate that the superconductivity in FeB4 is

likely phonon mediated, which is rare for Fe-based superconductors. The discovered iron tetraboride is

highly incompressible and has the nanoindentation hardness of 62(5) GPa; thus, it opens a new class of

highly desirable materials combining advanced mechanical properties and superconductivity.

DOI: 10.1103/PhysRevLett.111.157002 PACS numbers: 74.70.Ad, 61.05.cp, 62.20.-x, 62.50.-p

Modern computational materials design is gaining broadrecognition as an effective means of reducing the numberof experiments that can ultimately lead to materials dis-covery [1–3]: successful examples now include thermo-electrics, catalysts, electrode materials for Li-ion batteries,to name a few. Superconductors remain among the mostchallenging materials to develop [2,4–6]. So far theory hasonly successfully guided experiment to a discovery in afew cases related to thoroughly studied elemental materi-als, namely, silicon [7] and lithium [8] under pressure. Theprogress can be attributed to the improvement of densityfunctional theory-based methods [9,10], advances in com-pound prediction strategies [1,3], and the steady growthof computational resources. Nevertheless, the predictionof novel superconductors remains challenging [4]. First,only conventional (phonon-mediated) superconductors areunderstood well enough [4] to be described by theorieswith predictive power [5,11]. Calculation of the supercon-ducting critical temperature, Tc, is possible but exceed-ingly demanding as a viable option in high-throughputscreening for candidate materials. Second, the inversecorrelation between the stability of a compound and itsphonon-mediated superconducting Tc has been pointed outin a number of studies: a considerable density of states(DOS) at the Fermi level, beneficial for high Tc, is often anindication of structural instability [6]. One of the remark-able exceptions is the stoichiometric MgB2 material [12]with naturally hole-doped � bands and a Tc of 39 K.

The problem of thermodynamic instability can bemitigated under high pressure. When quenched to normalconditions, materials with a large DOS at the Fermi levelmay remain metastable and show superconductivityfacilitated by this large DOS. Kolmogorov et al. [9]systematically examined the Fe-B system and showedthat a previously unknown compound, FeB4, may existunder normal conditions in a previously unobservedorthorhombic crystal structure. The material was predictedto have naturally electron-doped bands and a largeelectron-phonon coupling [9], which indicate that FeB4

might be a ‘‘conventional’’ Fe-based superconductor(rare cases are known, see [13–15]), as opposed to therecently discovered family of ‘‘unconventional’’ Fe-basedsuperconductors [2,16]. Bialon et al. [17] suggested thatthe predicted FeB4 phase could be synthesized underpressure. The wide and growing interest in Fe-basedsuperconductors [2], simple chemical composition, andexpected mild pressure-temperature conditions for synthe-sis [17] make iron tetraboride a good case for testing thecomputational predictive power and, thus, the degree ofour theoretical comprehension of such a complex physicalphenomenon as superconductivity. Here, we report syn-thesis of an iron boridewith a so-far unknown composition,the verification of theoretical predictions regarding thestructure and superconductivity of this material, and thefinding of its unexpectedly low compressibility and veryhigh hardness.

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The experimental Fe-B phase diagram [18] at ambientpressure shows only two compounds, tetragonal Fe2B andorthorhombic FeB (Ref. [19]), although hexagonal FeB2

(Ref. [20]) and rhombohedral FeB�49 (Ref. [21]) have alsobeen reported in literature. Metastable cubic Fe23B6 andorthorhombic Fe3B phases have also formed in a numberof experiments [22–24].

We have undertaken a series of high-pressure experi-ments [25] aimed at the synthesis of the predicted boron-rich Fe-B phases (FeB2 and FeB4 [9]). Independent ofpressure, a major component of the reacted mixture wasstoichiometric FeB (Table S1, Ref. [25]). At low pressures(3 GPa and below) and temperatures of 1323 to 1973 Konly known phases, orthorhombic FeB and rhombohedralFeB�49, were produced. Experiments at pressures of 8 to18 GPa and temperatures of 1523 to 2023 K (Table S1 [25])led to the synthesis of previously unidentified orthorhombicFeB4, Fe2B7, and tetragonal Fe1þxB50 (x � 0:04) phases.The compounds crystallize from themelt and by optimizingthe sample geometry, heating duration, and temperaturegradients along the capsules it was possible to increasethe amount of boron-rich Fe-B phases. However, as seenin Fig. 1(a), all the products of the high-pressure synthesis,and particularly FeB4 and Fe2B7, are found in a tight mutualintergrowth, so that the procedure of phase separation ischallenging.

We have manually selected small pieces of FeB4 andcarefully characterized them with x-ray diffraction, wave-length dispersive x-ray, and energy dispersive x-ray micro-probe analysis (performed in SEM and TEM) [25] prior tofurther experiments. The largest pieces of phase-pure FeB4

produced so far have dimensions on the order of 150�150� 100 �m3. Maximal weight of phase-pure polycrys-talline samples is of about 0.14 mg. We note, however, thatstandard characterization techniques are not sensitiveenough to detect trace amounts of ferromagnetic impurities,

such as metallic iron that is almost inevitably present insamples recovered after the high-pressure synthesis. Theseimpurities are seen in magnetic susceptibility measure-ments (see [25]), but do not affect any of our conclusionsregarding the superconductivity and superhardness ofFeB4.The crystal structures of FeB4, Fe2B7, and Fe1þxB50

have been solved from single crystal x-ray diffractiondata (Table S2 [25]). A detailed description of Fe2B7 andFe1þxB50 is out of the scope of the present Letter and willbe published elsewhere.According to the single crystal x-ray and electron dif-

fraction [25], FeB4 adopts an orthorhombic Pnnm (Z ¼ 2)crystal structure. The refined structure was confirmed byhigh-angle annular dark-field scanning transmission elec-tron microscopy (HAADF-STEM) images along the [100],[010], and [001] directions [Fig. 1(b), Figs. S10, S11].Additionally, planar defects confined to the (010) planeswere occasionally observed in FeB4. These defects arenot abundant in the material, as indicated by the absenceof any related diffuse intensity on the electron diffractionpatterns (Fig. S9).A polyhedral model of the FeB4 structure is shown in

Fig. 1(c) and Fig. S1 (Ref. [25]). The structure is remark-ably close to that theoretically predicted [9] (Table S2[25]), and found very recently also for CrB4 [26,27].Despite the very small size of the available phase-pure

samples, we were able to confirm the prediction of super-conductivity in FeB4. While resistivity measurements arepresently unfeasible, magnetic susceptibility data collectedon polycrystalline samples indicate superconductivity inFeB4. Magnetic susceptibility measurements under zero-field-cooling (ZFC) conditions reveal a strong diamagneticresponse of FeB4 samples below 3 K (Fig. 2). Above 3 K,FeB4 is weakly paramagnetic with a nearly temperatureindependent susceptibility above 70 K. Additionally, oursamples showed a weak ferromagnetic signal of unknown

FIG. 1 (color online). (a) The backscattered electron SEM image of the polished surface of a high-pressure sample. The central partof the image (dark gray field) represents FeB4 produced by the reaction of Fe with B after melting. The adjacent area on the rightappears brighter as it is composed of the phases with lower boron content, namely, Fe2B7 and FeB. The surrounding black field isnonreacted boron which, however, underwent a pressure-induced phase transformation from �-B to �-B. Boron intrusions also fill thecracks in the FeB4 phase. (b) The high resolution [001] HAADF-STEM image of FeB4 (bright dots correspond to the Fe columns).Occasional planar defects (marked with arrowheads) are confined to the (010) plane and are visible as lines running parallel to the aaxis and consisting of pairs of the Fe columns with a shorter projected intercolumn distance in comparison with the FeB4 matrix [25].(c) Crystal structure of FeB4 presented as a packing of columns of FeB12 polyhedra along the c direction; the columns are connected bycommon edges of the adjacent polyhedra, whose centers (Fe atoms) are displaced with respect to each other by 1=2 along the bodydiagonal of the unit cell.

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origin below30K. This signal is certainly extrinsic, becauseits magnitude varies from sample to sample (see [25]).

The strong diamagnetic response of FeB4 is a clearfootprint of superconductivity. The drop in the volumesusceptibility (�V) is 4�ð��VÞ ¼ �1:3 that correspondsto the demagnetization factor of N ¼ 0:23 according to4�ð��VÞ ¼ �1=ð1� NÞ. This value of N is close toN ¼ 1=3 expected for a spherical sample.

The bulk nature of superconductivity is confirmed byheat capacity measurements showing a jump at the super-conducting transition around 3 K (Fig. 3). This jump issystematically shifted to lower temperatures in appliedmagnetic fields. Using the onset of superconductivityas a measure of Tc, wemapped the temperature dependenceof the upper critical field Hc2. It increases upon cooling,with an initial slope of �0dHc2=dT ¼ �0:5 T=K atTcð0Þ � 2:9 K. At lower temperatures, Hc2ðTÞ bendsdownwards. The critical field at zero temperature isextrapolated as �0Hc2ð0Þ ¼ �0:693Tc�0ðdHc2=dTÞ �1:0 T according to the Werthamer-Helfand-Hohenbergformula [28]. Alternatively, Hc2ð0Þ can be determinedfrom a fit with the empirical formula Hc2ðTÞ ¼ Hc2ð0Þ�ð1� ðT=TcÞ�Þ yielding �0Hc2ð0Þ ¼ 1:05 T and � ¼ 1:25.Both estimates of Hc2ð0Þ are far below the Pauli-paramagnetic limit for weak electron-phonon coupling�0Hc2½Tesla�¼1:86Tc½Kelvin��5:4T [29] and corrobo-rate phonon-mediated superconductivity in FeB4. In con-trast, unconventional superconductors may have criticalfields above the Pauli-paramagnetic limit.

To elucidate the nature of the observed superconductingtransition, we compared the transition temperatures in thesamples containing different boron isotopes (Fig. 2). Thesample enriched with the heavier B isotope shows a lower

Tc (2.95 and 2.89 K for Tonset or 2.82 and 2.70 K for Tmid inthe 10B and 11B samples, respectively), as expected for aphonon-mediated superconductor. Indeed, our tentativeestimate of the isotope effect [25] yields �Tc � 0:05 K ingood agreement with�Tc � 0:06–0:12 K, as found experi-mentally. Specific heat data provide further evidence forphonon-mediated superconductivity. The specific heat ofthe normal state, as measured in the applied field of 1 T,follows Cp¼�nTþ�T3 with �n ¼ 10:2ð2Þ mJmol�1 K�2

and� ¼ 0:025ð1Þ mJmol�1 K�4 determined from the fit ofCp=T vsT2 up toT ¼ 12 K (see [25], Fig. S8). This� value

yields the quite high Debye temperature �D � 730 K indi-cating predominantly hard phonons, which are indeedexpected for superhard FeB4 (see below). The value of �n

corresponds to NðEFÞ ¼ 4:3 states eV�1 ðf:u:Þ�1 at theFermi level and suggests a strong renormalization of theelectronic DOS compared to the LDA result of NðEFÞ �1 state eV�1 ðf:u:Þ�1 [9]. At zero field, the jump inCp at the

superconducting transition is �Cp � 35 mJ=molK yield-

ing �Cp=�nTc � 1:18 in reasonable agreement with 1.43

expected for the BCS limit with weak electron-phononcoupling. The proximity of�Cp to the BCS value is indica-

tive of the conventional, phonon-mediated superconduc-tivity in FeB4. This finding is further corroborated by afit of the zero-field CpðTÞ with the BCS expression by

Muhlschlegel [30] yielding �n ¼ 8:8ð1Þ mJmol�1 K�2 inreasonable agreement with �n derived from the 1 T data.Metal borides are known for their high hardness [31], so

that characterization of the elastic behavior of the newlysynthesized boride and its stability under pressure is an

FIG. 2 (color online). Magnetic susceptibility of FeB4 mea-sured in an applied field of 1 mT ZFC. The susceptibility isnormalized to the unit of volume (�V) and multiplied by 4� tofacilitate the comparison with the expected value of 4��V ¼ �1for the ideal superconductor with the demagnetization factor ofN ¼ 0. Two sets of data were collected on the samples enrichedwith 10B and 11B isotopes. Dashed lines denote the procedurefor determining the onset temperature Tonset (see Ref. [25]). Themidpoints of the susceptibility drop (Tmid) are shown as well.

FIG. 3 (color online). Specific heat (Cp) of FeB4 measured onthe 10B-enriched sample. The jump in Cp indicates the bulk

superconductivity with Tonset � 2:9 K in zero field. External mag-netic field shifts the transition to lower temperatures. The criticalfield Hc2 estimated from Tonset in different fields is plotted as aninset and approximated by the empirical formula Hc2ðTÞ ¼Hc2ð0Þð1� ðT=TcÞ�Þ shown by the dashed line. The WHHestimate of�0Hc2ð0Þ ¼ 1:0 T is shown aswell. In themain figure,the solid line is the BCS fit including a Gaussian broadening [30](see text for details).

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important issue. No phase transitions were observed undercompression of FeB4 at ambient temperature in a diamondanvil cell up to about 40 GPa [25]. Compressibility mea-surements on both compression and decompressionrevealed the remarkably high bulk modulus, K¼252ð5ÞGPa [K0 ¼ 3:5ð3Þ, V0 ¼ 72:79ð4Þ �A] [Fig. 4(a)],and a significant degree of anisotropy in the elastic behaviorof FeB4. The structure of FeB4 is most compressible alongthe a direction, while stiffest along the b axis [Fig. 4(b)]. Itmay be related to the fact that the shortest (and thus leastcompressible) B-B contact [1.714(6) A at ambient condi-tions] in this structure is almost parallel to the b axis. Thestiffness of the FeB4 structure along the b direction is thesame as that of diamond [32] [Fig. 4(b)] suggesting thatthe iron tetraboride may have remarkably advancedmechanical properties. Figures 4(c) and 4(d) present theresults, which are obtained by an average over severalnanoindentation load-displacement charts on FeB4 withoutthe feature of a pop-in [25]. The depth dependent indenta-tion or reducedmodulusEr shows a clear plateauwithEr ¼633� 30 GPa [Fig. 4(c)] that is far ahead compared tocommon ceramic materials like alumina [33] (�350 GPa)at room temperature. However, Young’s moduli of diamond

[34] (�1000 GPa) and cubic boron nitride [35] (�900 GPa)are still considerably larger. Nevertheless the nanoindenta-tion hardness approaches an average value of 62� 5 GPa[Fig. 4(d)]. Microhardness measurements were difficult toconduct because of the small size of the phase-pure samplesof FeB4. However, several successful tests (Fig. S2) with aload of 20 N gave values of the Vickers hardness rangingfrom 43 to 70 GPa, thus confirming that FeB4 belongs to thegroup of superhard materials [36].In summary, we have prepared and characterized the

novel superhard superconductor FeB4. Our data not onlysupport the predicted orthorhombic crystal structure [9],but also confirm the superconductivity of FeB4 that waslikewise predicted theoretically. We argue that the super-conductivity of FeB4 is mediated by phonons, which ishighly unusual for Fe-based materials [2,4]. In addition,the FeB4 compound was found to be superhard, wellexceeding the expectations about its potential mechanicalproperties [26]. This finding, bridging the gap betweenthe superhardness and superconductivity community,may lead, for example, to a possibility for designing newsuperconducting nanoelectromechanical systems and/orobservation of new fundamental effects.

FIG. 4 (color online). Compressibility of FeB4 and the results of nanoindentation measurements. (a) The pressure dependence ofthe unit cell volume based on single crystal x-ray diffraction data. The fit of the pressure-volume data with the third-orderBirch-Murnaghan equation of state (solid line) gave the bulk modulus K ¼ 252ð5Þ GPa, K0 ¼ 3:5ð3Þ, and V0 ¼ 72:79ð4Þ �A3=unitcell. (b) The relative changes of the unit cell parameters as a function of pressure. The stiffness of the FeB4 structure along the bdirection is the same as that of diamond (continuous line according to Ref. [32]). Closed symbols represent the data points obtained oncompression, and open ones—on decompression. The uncertainties are not shown since they are smaller than the size of symbols.(c) Depth dependent average values of indentation modulus. (d) Hardness of FeB4. Load-displacement curves without pop-ins havebeen used for evaluation with tip compression correction.

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The work was supported by the German ResearchFoundation (DFG). N.D. thanks DFG for financial supportthrough the Heisenberg Program and the DFG Project DU954-8/1. H.G. gratefully acknowledges financial supportof the Alexander von Humboldt Foundation. A.M.A.,D. B., and G.V. T. acknowledge support from the ERCGrant No. 246791 ‘‘COUNTATOMS’’. A.A. T. was partlysupported by the MTT77 Mobilitas Grant of the ESF.

L. D., N. D., and A.N.K. conceptualized the work. L. D.and N.D. planned and coordinated the study. H. G. con-ducted all synthesis experiments and analyzed all samples;E. B. analyzed all single crystal x-ray diffraction data;A. A. T., D. K., and W. S. performed magnetic susceptibil-ity and heat-capacity measurements and analyzed the data;experiments in DAC were carried out by E. B., M.M.,M.H., L. D., and N.D.; A.M.A., D. B., and G.V. T. per-formed the TEM analysis; A. R. conducted nanoindenta-tion measurements. Y. N. performed the microprobeanalysis. The paper was prepared by N.D. with contribu-tions of all authors.

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