We report on de Haas-van Alphen (dHvA) and band-structure studies of the iridium-pnictide superconductor BaIr2P2 (Tc=2.1 K). The observed dHvA frequencies can be well understood by our band-structure calculations with two bands crossing the Fermi energy leading to a strongly corrugated Fermi-surface cylinder around the X point and a highly evolved, multiconnected Fermi surface extending over the whole Brillouin zone. The experimental effective masses are found to be considerably larger than the calculated band masses suggesting strong many-body interactions. Nevertheless, Tc remains only moderate in BaIr2P2 contrary to isostructural iron pnictides which probably is related to the largely different Fermi-surface topologies in these materials

Bartkowiak, M

Bergk, B

Berry, N

Bianchi, AD

Blackburn, S

Côté, M

Fisk, Z

Förster, T

Ignatchik, O

Seyfarth, G

Sheikin, I

Wosnitza, J

eScholarship - University of California

UC IrvineUC Irvine Previously Published WorksTitleFermi surface of the superconductor BaIr2P2Permalinkhttps://escholarship.org/uc/item/8jd9m0z5JournalPhysical Review B, 92(13)ISSN2469-9950AuthorsFörster, TBergk, BIgnatchik, Oet al.Publication Date2015-10-01DOI10.1103/physrevb.92.134518Copyright InformationThis work is made available under the terms of a Creative Commons Attribution License, availalbe at https://creativecommons.org/licenses/by/4.0/ Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaPHYSICAL REVIEW B 92, 134518 (2015)Fermi surface of the superconductor BaIr2P2T. Förster,1 B. Bergk,1,* O. Ignatchik,1 M. Bartkowiak,2 S. Blackburn,3 M. Côté,3 G. Seyfarth,3,4,5 N. Berry,5 Z. Fisk,5I. Sheikin,4 A. D. Bianchi,3 and J. Wosnitza1,61Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany2Laboratory for Developments and Methods, Paul Scherrer Institute, CH-5232 Villigen, Switzerland3Départment de Physique and RQMP, Université de Montréal, Montréal H3C 3J7, Canada4Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, UJF, F-38042 Grenoble, France5Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, USA6Institut für Festkörperphysik, TU Dresden, D-01062 Dresden, Germany(Received 28 August 2015; published 20 October 2015)We report on de Haas–van Alphen (dHvA) and band-structure studies of the iridium-pnictide superconductorBaIr2P2 (Tc = 2.1 K). The observed dHvA frequencies can be well understood by our band-structure calculationswith two bands crossing the Fermi energy leading to a strongly corrugated Fermi-surface cylinder around theX point and a highly evolved, multiconnected Fermi surface extending over the whole Brillouin zone. Theexperimental effective masses are found to be considerably larger than the calculated band masses suggestingstrong many-body interactions. Nevertheless, Tc remains only moderate in BaIr2P2 contrary to isostructural ironpnictides which probably is related to the largely different Fermi-surface topologies in these materials.DOI: 10.1103/PhysRevB.92.134518 PACS number(s): 71.18.+y, 74.25.Jb, 74.70.XaShortly after the discovery of superconductivity in iron-pnictide compounds [1] the question arose whether thismaterial combination is decisive for the realization of highsuperconducting transition temperatures. One route—of themany possible ones—to investigate this is the substitutionof Fe by other transition-metal elements. Predominantly, thiswas done for the ternary 122 material class, that forms in thetetragonal ThCr2Si2 structure, for which superconductivity at38 K was reported for (Ba,K)Fe2As2 first [2].Indeed, earlier research on P-containing ternary materialswith such 122 structure was reported already some timeago (see [3,4] and references therein). After 2008, thefield received new momentum when a number of other122 materials containing either As or P were reported tobecome superconducting [5–9]. However, the superconductingtransition temperature Tc remained rather low with a fewkelvins. This fact suggests a possible conventional pairingmechanism in these noniron containing superconductors. Inorder to substantiate this notion, however, detailed informationof the electronic structure is needed here. Especially, accurateknowledge on the degree of two dimensionality is necessaryto test for possible nesting between electron and hole bands,essential for the extended s-wave pairing scenario as suggestedfor the iron pnictides [10–14].A very powerful way for the determination of the Fermi-surface topologies and many-body interactions are mea-surements of magnetic quantum oscillations. Especially, incombination with state-of-the-art band-structure calculations,this allows the detailed determination of the electronic bandstructure and of the band-resolved mass enhancement [15,16].Some recent reviews of such investigations for metallic andsuperconducting iron pnictides are given in Refs. [17,18].Here, we report on a detailed de Haas–van Alphen (dHvA)study in combination with band-structure calculations of the*Current address: Institut für Werkstoffwissenschaft, TU Dresden,D-01062 Dresden, Germany.122 iridium phosphide BaIr2P2. This is a superconductorwith a moderate transition temperature of Tc = 2.1 K asfound for polycrystalline samples [6] and single crystals [7].Using some of the latter high-quality crystals, we observeddHvA oscillations that agree well with predictions of ourband-structure calculations. Besides a strongly corrugatedcylindrical, quasi-two-dimensional Fermi-surface sheet, athree-dimensional highly branched Fermi surface is found.Considerable mass-enhancement factors between 1 and 3 areobtained.The BaIr2P2 single crystals were grown using a metal-fluxtechnique [19]. In this case, a Pb flux with additional Cu toincrease solubility was used. Details of the crystal-growthprocedure are given in [7]. Typical sample dimensions usedfor our experiments are 0.2 × 0.2 × 0.02 mm3. The dHvAeffect was measured by use of torque magnetometers. For thatCuBe capacitive cantilevers with 25- to 50-μm thicknesseswere fabricated and fixed on platforms that could be rotated insitu around one axis. Placing the sample on these cantilevers,the dHvA effect is measured as field-dependent oscillationsof the capacitance. The measurements were performed at theDresden High Magnetic Field Laboratory (HLD) in a super-conducting 20-T magnet and at the Grenoble High MagneticField Laboratory (LNCMI-Grenoble) using a resistive magnetin fields up to 34 T. In both cases, the cantilevers were mounteddirectly in the 3He/ 4He mixtures of top-loading dilutionrefrigerators.The band structure was calculated using the full-potentiallocal-orbital FPLO code [20]. Exchange and correlation po-tentials were estimated using the local density approxima-tion [21]. The room-temperature structural data of Ref. [7]were used. We further allowed the P atoms to relax their zposition, since we realized that for other 122 compounds thismodifies the calculated Fermi surface significantly [16]. Inthe case of BaIr2P2 there was a small (0.4%) change in z,but the band structure remained unaltered within error bars.Since spin-orbit coupling is relevant for Ir, we also performedfull-relativistic calculations. Although this modifies the band1098-0121/2015/92(13)/134518(4) 134518-1 ©2015 American Physical SocietyT. FÖRSTER et al. PHYSICAL REVIEW B 92, 134518 (2015)15 16 17 18B (T)-20020Δtorque (arb. units)BaIr2P2Θ010 = 63o16 17 18B (T)1.1191.1211.120torque (arb. units)(b)0 2 4 6 8F (103 T)0246AFT (arb. units)(c)Fα2Fα3(a)FIG. 1. (Color online) (a) Torque signal of BaIr2P2 obtained atabout 30 mK between 15 and 18 T. The field was rotated by 63◦ fromthe c towards the a axis. (b) Oscillating part of the torque signal afterbackground subtraction. (c) Spectrum of the oscillating signal afterFourier transformation with two clearly resolved dHvA frequencies.dispersion far away from the Fermi energy, the Fermi surface,and the effective masses change only marginally [22].A typical torque signal for our BaIr2P2 sample is shownin Fig. 1(a). On a smoothly varying background weaklyvisible oscillations appear. After subtracting the background,using fourth-order polynomials, the oscillating dHvA signalis clearly resolved [Fig. 1(b)], reflecting the excellent signal-to-noise ratio of our torque data. The oscillating data show afast dHvA oscillation modulated by a slower one. The Fouriertransformation confirms the existence of only two fundamentaldHvA frequencies at this magnetic-field orientation which arelabeled Fα2 = 530 T and Fα3 = 2975 T [Fig. 1(c)]. For theshown example, with the magnetic field applied at an angle010 = 63◦ rotated from the c towards the a axis, the dHvAoscillations have rather large amplitudes with negligible noise.This is not the case for all field orientations. Although weobserve dHvA oscillations for all orientations, some dHvAsignals appear barely above the noise level.In order to better resolve such small signals and possiblydetect further dHvA branches we performed additional exper-iments in static fields up to 34 T at the LNCMI in Grenoble.One example of the measured background-subtracted dHvAsignal is shown in the inset of Fig. 2. For this field orientation(010 = 8◦), one strong low dHvA frequency with Fα1 =429 T and one weak high frequency (Fβ1 = 8130 T) canbe resolved. The latter dHvA oscillations are visible at thehighest fields in the background-subtracted torque signal and,with a good signal-to-noise ratio, in the Fourier-transformedspectrum (Fig. 2).We studied the angular dependence of the dHvA oscillationsfor many different angles by rotating the crystal around therelevant axes of the tetragonal unit cell, namely around the a(010) and c axis (001). The experimentally observed dHvAfrequencies are shown in Fig. 3. The data sets measured inDresden (open symbols) and in Grenoble (closed symbols)agree perfectly. Some of the dHvA branches lead to rather0 5 10F (103 T)0246AFT (arb. units)BaIr2P2Θ010 = 8o24 28 32B (T)-10010Δtorque (arb. units)Fβ1Fα1FIG. 2. (Color online) Background-subtracted torque signal (in-set) and corresponding Fourier transformation (main panel) measuredat about 30 mK at the LNCMI in Grenoble. The field was rotated by8◦ from the c towards the a axis.weak amplitudes only and can just be resolved at the highestfields used. As a measure of the relative dHvA amplitudes weconverted the logarithm of these amplitudes to symbol sizesin Fig. 3 [23]. In other words, the small symbols of, e.g., thebranches α4 and β1 depict the fact that the corresponding dHvAamplitudes are 10–20 times smaller than, e.g., some of the α1amplitudes.The solid lines in Fig. 3 show the angular dependence of theextremal orbits as obtained from band-structure calculations.For that, the FPLO code was used resulting in the dispersionrelations as shown in Fig. 4. There are two bands crossing theFermi energy, colored in green (band 49) and red (band 50).The main contributions to band 49 (50) arise from 31% (34%)Ir 5d, 21% (10%) Ba 5d, and 28% (39%) P 3p orbitals.FIG. 3. (Color online) Angular dependence of the measured(symbols) and calculated (lines) dHvA frequencies. The opensymbols were obtained at the HLD in Dresden in magnetic fields upto 18 T and the closed symbols at the LNCMI in Grenoble in fields upto 34 T. The symbol size is a measure of the Fourier-transformationamplitude [23].134518-2FERMI SURFACE OF THE SUPERCONDUCTOR BaIr2P2 PHYSICAL REVIEW B 92, 134518 (2015)0.50−2−1012Energy (eV)X ZFIG. 4. (Color online) Band structure of BaIr2P2 calculated usingthe FPLO code. Two bands, colored in red and green, are crossing theFermi energy, set to zero. The inset shows the Brillouin zone withsymmetry points.Having such dispersion relations calculated for a dense24 × 24 × 24 k mesh, we obtain the Fermi surfaces of thetwo bands as shown in Fig. 5. Thereby, the red-coloredband in Fig. 4 leads to a strongly corrugated quasi-two-dimensional cylindrical Fermi surface [Fig. 5(a)], whereasthe multiconnected complicated Fermi surface in Fig. 5(b)originates from the green-colored band in Fig. 4. Some of theextremal cross sections, i.e., of the orbits leading to dHvAoscillations, for fields aligned along c and roughly along a areshown by solid lines in Fig. 5 [24].(a)(b)FIG. 5. (Color online) Calculated Fermi surface of BaIr2P2 orig-inating from (a) the red and (b) green band crossing the Fermi energy(Fig. 4). Some of the dHvA orbits are depicted by solid lines andlabeled.TABLE I. Comparison between calculated and measured dHvAfrequencies and effective masses for different bands and fieldorientations in BaIr2P2.Measured Calculated010 orbit F (T) m/me F (T) mb/me8◦ α1 429 1.0(3) 545 0.278◦ β1 8130 – 8135 0.7455◦ α2 540 1.0(4) 436 0.3855◦ α3 3030 1.3(1) 2930 0.64A comparison between the calculated and measured dHvAfrequencies for some orbits is given in Table I. The agreementbetween theory and experiment is excellent, especially whentaking into account that no adjustable parameter was used.This very good agreement can as well be seen in Fig. 3where the calculated dHvA frequencies (lines) coincide nicelywith measured data. Only for some angles theory predicts afew additional dHvA orbits that are not seen in experiment,maybe due to their small dHvA amplitudes. Indeed, thecalculated band masses of these latter orbits lie between about1 and 2.1 me, i.e., are considerably larger than calculatedfor the experimentally observed orbits (see below). Togetherwith a Dingle temperature of about 4.7 K, as obtained forthe α3 orbit, much weaker dHvA signals than the onesobserved are expected for these heavier-mass orbits; i.e., thesepredicted dHvA orbits might have signal amplitudes that mostprobably are below our resolution limit. On the other hand,the experimentally observed dHvA signals, such as the β1frequencies, fit perfectly to the predicted data, even in absolutenumbers, and the angular dependences of all observed αfrequencies are well reproduced. In absolute numbers, thedifference for the latter frequencies seems large at first sight.However, taking into account that the cross section of the totalBrillouin zone perpendicular to c is about 33 kT, the differencebetween the calculated and measured values is only about 0.4%of that area.For selected angles, we determined the effective masses mof some dHvA orbits from the temperature dependence of thedHvA amplitudes [25,26]. The extracted values, summarizedin Table I, are close to the free-electron mass me [27]. ThedHvA amplitude of the β1 orbit could not be determinedreliably over a large-enough temperature range preventinga reasonable extraction of m here. Although the measuredeffective masses are rather small, they are still 2–4 timeslarger then the band masses mb, obtained from our band-structure calculations (Table I). Additionally, the Sommerfeldcoefficient γ = 9.3 mJ/molK2 as estimated in Ref. [7] isenhanced by a factor of 18 compared to the calculated0.53 mJ/molK2. Obviously, strong many-body interactions ex-ist in BaIr2P2 leading to equivalent mass-enhancement factors,λ = m/mb − 1, between 1 and 3 for the α orbits. Indeed, thecorresponding (green) band [Fig. 5(b)] contributes about 76%to the total density of states at the Fermi level. Consequently,if λ is mainly caused by electron-phonon interactions, BaIr2P2would be a strong-coupling superconductor with, however,only a moderate Tc of 2.1 K.134518-3T. FÖRSTER et al. PHYSICAL REVIEW B 92, 134518 (2015)Somewhat smaller, but still considerable mass enhance-ments have been found for another non-iron-containing 122superconductor, namely BaNi2P2 with Tc = 2.51 K [28].Although not explicitly, the authors of that work suggest aphonon-mediated mechanism for superconductivity, based ona theory work proposing such Cooper-pair coupling for theisostructural material BaNi2As2 [29]. It seems plausible toexpect such coupling as well in the present superconduc-tor. Indeed, for all above-mentioned materials the Fermi-surface topology is largely different from the pronouncedtwo-dimensional electronic structure of the superconduct-ing 122 iron pnictides. Therefore, extended s-wave pair-ing, as suggested for the latter materials [10–14], can beruled out as the mechanism responsible for superconduc-tivity in BaIr2P2 since the essential nesting condition ismissing.In conclusion, our angular-dependent dHvA data are inexcellent agreement with predictions from band-structurecalculations giving us a detailed picture of the Fermi-surfacetopology of BaIr2P2. Only two bands are crossing the Fermienergy and the resulting Fermi surface is highly three-dimensional, contrary to iron-containing 122 superconductors.We observe rather strong enhancements in the measuredeffective masses. Although this points to strongly coupledCooper pairs, the superconducting transition temperature israther low. More detailed calculations taking into account thephonon dynamics and density of states would be necessaryto verify the suggestion of such an electron-phonon couplingscenario.The research at UdeM received support from the Natu-ral Sciences and Engineering Research Council of Canada(Canada), Fonds Québécois de la Recherche sur la Natureet les Technologies (Québec), and the Canada Research ChairFoundation. We acknowledge support from HLD at HZDR andLNCMI, members of the European Magnetic Field Laboratory(EMFL), and the Deutsche Forschungsgemeinschaft (SPP1458).[1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am.Chem. Soc. 130, 3296 (2008).[2] M. Rotter, M. Tegel, and D. Johrendt, Phys. Rev. Lett. 101,107006 (2008).[3] W. Jeitschko and M. Reehuis, J. Phys. Chem. Solids 48, 667(1987).[4] W. Jeitschko, R. Glaum, and L. Boonk, J. Solid State Chem. 69,93 (1987).[5] T. Mine, H. Yanagi, T. Kamiya, Y. Kamihara, M. Hirano, andH. Hosono, Solid State Commun. 147, 111 (2008).[6] D. 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B 45, 13244 (1992).[22] We performed spin-polarized calculations with an initial polar-ization, but they quickly converge towards a zero magnetization.Additionally, fixed-spin-moment calculations show no local orglobal minima, besides zero magnetization.[23] Scaling between the low-field (HLD) and high-field (LNCMI)data was done by just one factor.[24] The orbits α4 and α5 lie in the interior of the shown Fermi-surfacesheet [Fig. 5(b)] and cannot be visualized in this plot.[25] I. M. Lifshitz and A. M. Kosevich, Zh. Eksp. Teor. Fiz. 29, 730(1955) [Sov. Phys. JETP 2, 636 (1956)].[26] D. Shoenberg, Magnetic Oscillations in Metals (CambridgeUniversity Press, Cambridge, 1984).[27] The relatively large error bars of the effective masses are causedby the restricted temperature range accessible in the dilutionrefrigerators. At the highest temperatures of about 1 K, thedHvA amplitudes are reduced only slightly leading to largeuncertainties in m.[28] T. Terashima, M. Kimata, H. Satsukawa, A. 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Fermi surface of the superconductor BaIr2P2

Fermi surface of the superconductor BaIr2 P2

Fermi surface of the superconductor BaIr2 P2

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