Superconductivity in monocrystalline YNiSi3 and LuNiSi3€¦ · superconductivity occurs in a...

PHYSICAL REVIEW B 99 224505 (2019)

Superconductivity in monocrystalline YNiSi3 and LuNiSi3

Fabiana R Arantes1 Deisy Aristizaacutebal-Giraldo12 Daniel A Mayoh3 Yu Yamane4 Chongli Yang4 Martin R Lees3

Jorge M Osorio-Guilleacuten2 Toshiro Takabatake4 and Marcos A Avila1

1CCNH Universidade Federal do ABC (UFABC) Santo Andreacute Satildeo Paulo Brazil2Instituto de Fiacutesica Universidad de Antioquia UdeA Calle 70 No 52-21 Medelliacuten Colombia

3Department of Physics University of Warwick Coventry CV4 7AL United Kingdom4Graduate School of Advanced Sciences of Matter Hiroshima University Higashi-Hiroshima 739-8530 Japan

(Received 25 July 2018 revised manuscript received 28 March 2019 published 11 June 2019)

We report the discovery of bulk superconductivity in the ternary intermetallics YNiSi3 and LuNiSi3High-quality single crystals were grown via the Sn-flux method and studied using magnetization specific-heatand resistivity measurements at low temperatures The critical temperatures obtained from these differenttechniques are in very good agreement and yield Tc = 136(3) K and Tc = 161(2) K for YNiSi3 and LuNiSi3respectively Magnetization measurements indicate that both compounds are among the rare cases where type-Isuperconductivity occurs in a ternary intermetallic however the jump in the specific heat at the transition islower than the value expected from BCS theory (CelγnTc = 143) in both materials and is equal to 114(9)and 071(5) for the Y and Lu compounds respectively Resistivity measurements exhibit sharp transitionsbut with critical fields μ0Hc(0) (asymp005 T for YNiSi3 and asymp008 T for LuNiSi3) considerably higher thanthose obtained from the magnetization and specific heat (asymp001 T) First-principles density functional theorycalculated electronic structure shows that these compounds have highly anisotropic and complex Fermi surfaceswith one electronic and two holelike branches One hole branch and the electron branch have a large cylindricaltopology connecting the first Brillouin-zone boundaries the former being built up by the hybridization of Y(Lu)d Ni d and Si p states and the latter being built up by Ni d and Si p states The calculated phononic structuresindicate that the coupling of the Y(Lu) Ni d and Si p electrons in the low-lying optical phonon branchesis responsible for the formation of Cooper pairs and the observed superconducting state Therefore thesecompounds can be classified as anisotropic three-dimensional metals with multiband superconducting groundstates in the weak-coupling regime

DOI 101103PhysRevB99224505

I INTRODUCTION

The search for new superconductors (SCs) has in thepast decade often focused on heavy-fermion materials andormaterials whose unit cells lack a center of inversionmdashthenoncentrosymmetric (NCS) superconductors [1] This is be-cause these materials are thought to be good candidates forunconventional superconductors which do not conform tothe Bardeen-Cooper-Schrieffer (BCS) theory [2ndash5] and canexhibit high critical fieldsmdashon the order of a few teslasmdashaswell as high critical temperatures Despite the large numberof reported studies the relationship between a materialrsquoscrystal structure and its superconducting properties is notyet firmly established Therefore it is essential to exploreunusual features of centrosymmetric superconductors in orderto unravel the role of crystalline structure per se In the sameway the study of compounds with weak electron correlationssuch as Sc- Y- La- and Lu-based SCs can enhance ourcomprehension of heavy-fermion SCs

Superconductors are traditionally categorized into type I orII according to the transition of the superconducting phase tothe normal state under an applied magnetic field type-I SCshave a Ginzburg-Landau (GL) parameter κ lt 1

radic2 and un-

dergo a first-order transition into the superconducting state ina magnetic field whereas type-II SCs present a second-orderphase transition and κ gt 1

radic2 The ratio κ = λξ connects

the two length parameters yielded by the GL equations theGL penetration depth λ and the superconducting coherencelength ξ Within this classification type-I superconductivityis normally displayed by elemental SCs eg Pb Hg andSn although several exceptions have been found such asthe binary compounds CaBi2 [6] KBi2 [7] ScGa3 LuGa3

[8] YbSb2 [9] and PdTe2 [10] the ternary cage compoundLaTi2Al20 [11] and the NCS LaPdSi3 [12] and LaIrSi3 [13]

Whereas the vast majority of superconducting binary andternary intermetallic compounds are of type II increasingnumbers of materials have been found with intermediatebehaviors Therefore type-II SCs were further classifiedinto types-II1 (κ asymp 1

radic2) -II2 (traditional type-II κ gt

1radic

2) [14] and -15 (κ 1radic

2) [15ndash17] Some examplesof type II1 are Nb [18] ZrB12 [1920] and the noncen-trosymmetric superconductors AuBe [21] RhGe [22] andLaRhSi3 [23ndash26] Type-15 SCs may include MgB2 [15ndash17]and Sr2RuO4 [27]

In the RNiGe3 (R = Y Ce) (where R represents rare earth)series [2829] with a centrosymmetric orthorhombic structurethe compounds YNiGe3 [30] and CeNiGe3 [31ndash33] are su-perconductors The former has an unusually low specific heatjump at the transition compared to the prediction of BCStheory [30] whereas the latter is an unconventional heavy-fermion superconductor under pressure

2469-9950201999(22)224505(14) 224505-1 copy2019 American Physical Society

FABIANA R ARANTES et al PHYSICAL REVIEW B 99 224505 (2019)

In this paper we present a detailed characterization of twononmagnetic compounds of the RNiSi3 series (those with R =Y Lu) expected to show many of the same features as YNiGe3

with Tc = 046 K [30] We report on the discovery via re-sistivity magnetization and specific-heat measurements ofbulk type-I superconductivity in single crystals of YNiSi3 andLuNiSi3 with critical temperatures Tc = 136(3) K for YNiSi3

and Tc = 161(2) K for LuNiSi3 We also present densityfunctional theory (DFT) calculations to obtain the electronicproperties of these compounds

II METHODS

YNiSi3 and LuNiSi3 single crystals were synthesized viathe Sn-flux method originally used to grow YbNiSi3 [34] Aproportion of 11345 (YLuNiSiSn) was used as detailedin previous work [35] wherein the crystalline structures wereverified by powder x-ray diffraction (PXRD) analysis andwavelength dispersive electron-probe microanalysis (EPMA)of the single crystals conducted in a JEOL JXA-8200 mi-croanalyzer The crystal compositions were determined byaveraging over ten different points of a polished sample

Resistivity between 004 and 4 K was measured with astandard four-probe ac method in a homemade system insidea commercial Cambridge Magnetic Refrigeration mFridgemF-ADR50 with applied magnetic fields in two orientationsparallel or perpendicular to the crystal plate main surfacesSpecific heat between 037 and 5 K was measured on crystalswith total mass of about 7 mg under applied fields parallelto the plates using the 2τ thermal relaxation method in theQuantum Design Physical Property Measurement System

Magnetic susceptibility was measured in a Quantum De-sign Magnetic Property Measurement System magnetometerwith an iQuantum 3He insertmdashin this case the field wasperpendicular to the plate surfaces Proper evaluation of themagnetization measurements in SCs must take into accountthe demagnetization factor (N) due to the sample shape sincethe volumetric susceptibility of a bulk SC must approach χ simminus1 below the critical temperature In our case the platelikeshape of the crystal made it simple to estimate N sim 05 forYNiSi3 and N sim 07 for LuNiSi3 with the magnetic fieldapplied perpendicular to the main surface of the sample(H b)

Spin-polarized first-principles DFT calculations includingspin-orbit coupling (SOC) in a second-variational schemehave been carried out using the full-potential augmented-plane wave method with local orbitals (FP-APW + lo)as implemented in the ELK code [36] For the exchange-correlation energy functional we have used the generalizedgradient approximation and its PBEsol parametrization [37]The muffin-tin (MT) radii of Y Lu Ni and Si are set toRY

MT = 27777 RLuMT = 27495 RNi

MT = 20563 and RSiMT =

20563 au respectively The parameter RMT|G + k|max gov-erning the number of plane waves in the FP-APW + lo methodis chosen to be 95 The Brillouin zone (BZ) is sampled with auniformly spaced k grid of 8 times 8 times 8 for the structural relax-ation and 16 times 16 times 16 for the calculation of the dispersionrelation E (k) the total and site projected densities of states(DOS) and the Fermi surface (FS)

III EXPERIMENTAL RESULTS

Previous work on the series RNiSi3 [35] showed by PXRDanalysis that these compounds crystallize in the orthorhombicspace group Cmmm The experimental lattice constants aregiven in Table I of the Supplemental Material [38] Elementalanalysis using EPMA revealed average sample compositionsof Y096(11)Ni100(19)Si309(18) and Lu100(1)Ni068(2)Si313(2) withan upper limit of sim500 ppm Sn impurities in both crystalsLuNiSi3 crystals thus form with significant Ni vacancies asobserved in the RNiGe3 series [28] This effect is small forYNiGe3 but is more pronounced for heavier rare earths as inthe case of LuNiGe3 There were some small NiSi2 crystallitesattached to the surface of the crystals (a diamagnetic non-superconducting metallic silicide [39ndash41]) that could be easilyremoved by polishing Besides Sn (Tc = 37 K) no othersuperconducting impurity was detected so we may claim thatthe superconducting transitions presented below are due tothese new intermetallic compounds

In the following sections we describe the characteristicsof the superconductivity in YNiSi3 and LuNiSi3 throughmagnetization specific-heat and resistivity experiments

A YNiSi3

Figure 1 shows the magnetic characterization ofYNiSi3χ (T ) [Fig 1(a)] was measured under an appliedfield of μ0H = 2 mT following a zero-field-cooled warmingprotocol At 131(2) K there is a relatively sharp transitionwith χ rising from the value of minus1 as expected bythe complete field expulsion of a bulk SC Figure 1(b)shows the M(H ) curves at several temperatures below thesuperconducting transition They are marked by a type-I SCbehavior with M = minusH at low fields and an abrupt jump atHc The transition in some type-I SC can be broadened bythe presence of impurities inhomogeneities and even a highdemagnetization effect however the type-I behavior of thissample is very clear attesting to the quality of the crystal

The critical fields extracted from the curves in Fig 1(b)were used to plot the phase diagram displayed in Fig 1(c)The points were fitted by the empirical parabolic law [42]

Hc(T ) = Hc(0)

[1 minus

(T

Tc

)2] (1)

yielding an estimated critical field μ0Hc(0) = 96(2) mTFigure 2(a) shows the dependence of the total heat-capacity

(Cp) on T for YNiSi3 at zero field and with H ranging from5 mT up to 1 T a field well above that in which the super-conductivity is suppressed At zero field there is a jump at135(5) K agreeing with the bulk superconductivity observedin the magnetization measurements The data also seem toshow a double peak which could be a sign of a doubletransition over a narrow temperature range but the resolutionis not sufficient to allow a definitive conclusion For thecurves measured under applied fields the transition tempera-ture shifts to lower T with values comparable to the criticaltemperatures observed in Fig 1(b) The jumps in Cp(T )in 5 and 6 mT are higher than in zero field suggesting afirst-order transition for H = 0 Figure 2(b) shows the de-pendence of CpT with T for the same data displayed in

224505-2

SUPERCONDUCTIVITY IN MONOCRYSTALLINE hellip PHYSICAL REVIEW B 99 224505 (2019)

FIG 1 Magnetization measurements for YNiSi3 (a) Tempera-ture dependence of χ with μ0H = 2 mT using a zero-field-cooledwarming (ZFCW) protocol (b) M(H ) curves at several temperaturesbelow the superconductor transition (c) Hc vs T phase diagram witheach Hc(T ) value extracted from the curves in (b) and the fit madeusing Eq (1)

Fig 2(a) whereas the inset shows CpT vs T 2 measuredwith μ0H = 300 mT The normal-state Cp was fit with the

FIG 2 (a) Temperature dependence of Cp at several magneticfields for YNiSi3 (b) CpT vs T for the same curves displayedin Fig 2(a) The inset shows CpT vs T 2 for a larger range oftemperature (c) Electronic contribution of specific heat for H = 0with the fits obtained with the models given in Eqs (5) and (6)

expression Cp(T )T = γN + βT 2 + BT 4 where the first termis due to the electronic contribution and the βT 2 + BT 4

terms describe the phonon contribution following the De-bye model The fit yields γN = 404(9) mJ molminus1 Kminus2

β =00961(5) mJ molminus1 Kminus4 and B = 00090(5) mJ molminus1 Kminus6The Debye temperature can be evaluated using

θD =(

n12π4R

5β

)13

(2)

224505-3


where n = 5 is the number of atoms per formula unit and R isthe molar gas constant yielding θD = 466(9) K The valuesof γN and θD are comparable to those obtained in the previouswork at high temperatures γN = 41 mJ molminus1 Kminus2 and θD =393 K [35] The density of states at the Fermi-level [N (EF)]is obtained using the relation

N (EF) = 3γN

π2k2BNA

(3)

where kB is the Boltzmann constant and NA is the Avo-gadro number resulting in N (EF) = 171 stateseV fu Theelectron-phonon coupling constant λe-ph is calculated usingMcMillanrsquos formula [43]

λe-ph = 104 + μlowast ln(θD145Tc)

(1 minus 062μlowast) ln(θD145Tc) minus 104 (4)

where μlowast is usually taken between 01 and 015 Us-ing a μlowast of 0125 yields λe-ph = 043(2) placing YNiSi3

in the weak-coupling regime together with the NCSLaPdSi3 [12] (λe-ph = 051) LaRhSi3 [24] (λe-ph = 05) andTh7Fe3 (λe-ph = 059) [44] It should be noted that McMil-lanrsquos formula works better for pure metals because theDebye temperature is not properly defined in compoundscontaining elements with such large differences in theiratomic masses

Figure 2(c) shows the electronic heat-capacity (Cel) ob-tained by subtracting the βT 3 + BT 5 terms from the zero-fielddata For a BCS superconductor the jump of Cel is expectedto have an s-wave gap with CelγNTc = 143 however theestimated value for this compound is 114(9) significantlylower than expected This has also been observed for theternary type-I SC LaIrSi3 [13] and for the similar compoundYNiGe3 [30] in both cases it was hypothesized that sucha low value of the specific-heat jump is related to a largeanisotropy in the superconducting gap

We have tested four different models to fit the Cel datain the superconducting regime a single-gap α model for aBCS SC (CSG

el ) a double-gap α model (CDGel ) a single-gap α

model with a contribution from a nonsuperconducting fraction(CSGNF

el ) and finally an anisotropic gap model (CANIel ) in

order to verify the hypothesis discussed above The first threemodels are given by the equations below

CSGel = A1γNTc exp

(minusSG0 kBT

) (5a)

CDGel = A2γNTc

[f exp

(minusDG10 kBT

)+ (1 minus f ) exp

(minusDG20 kBT

)] (5b)

CSGNFel = A3γNTc exp

(minusSGNF0 kBT

) + γ2T (5c)

where Airsquos are scale factors 0 is the superconduct-ing gap and f is the superconducting fraction for eachgap (DG model) For the anisotropic model we usedthe integral form of the Cel(T ) formula given by BCStheory and we considered an angular- and temperature-dependent gap (T θ ) representing a single extended s-wave

TABLE I Fitted parameters of Cel in the superconducting regionfor YNiSi3 Ai α and a are dimensionless 0 is measured in10minus23 J and γ2 is measured in mJ molminus1 Kminus2

Cel model Ai 0 f γ2 αprime a

SG 67(7) 24(1)DG 15(1) 13(1) 45(2) 011(1)SGNF 10(1) 35(2) 24(1)ANI 055(6) 54(3) 095(9) 067(7)

gap [24546]

CANIel (T ) = A4

N (EF)

πT

int 2π

0dφ

int π

0dθ sin θ

timesint hωD

0minus part f

partE

(E2 + 1

2β

d2(T θ )

dβ

)dE

(6a)

f = [1 + exp(βE )]minus1 (6b)

(T θ ) = 0(T )(1 + αprime cos 2θ ) (6c)

0(T ) = ANI0 tanh

[(πkBTc

ANI0

)radica(TcT minus 1)

]

(6d)

Here h is the reduced Planck constant β = 1kBT ωD isthe Debye frequency αprime is the anisotropy parameter (αprime = 0corresponds to an isotropic s-wave gap) [46] and a is a con-stant that depends on the coupling strength and the geometryof the gap [4748]

Table I presents the fit parameters for all four models Thesimplest model CSG

el yielded a poor fit to the data meaningthat the simple s-wave model does not describe this compoundwell The three other more complex models fit the data betterAlthough the quality of the fits is similar these three mod-els represent distinct physical hypotheses The double-gap α

model assumes that there are two superconducting gaps andcan be thought of as a simplified modeling of a more realisticscenario with a distribution of gaps The α model with a non-superconducting fraction on the other hand assumes that afraction of the material is in the normal state due to impuritiesor other inhomogeneities And finally the anisotropic modelas the name suggests considers a superconducting gap withanisotropy Given that these are high-quality single-crystalsamples we do not expect a large nonsuperconducting frac-tion thus our results indicate that the superconducting gap isprobably not simple with a magnitude close to 5 times 10minus23 J

Resistivity is not considered a robust technique to char-acterize a new bulk superconductor because it can be easilyaffected by impurities that can form a percolation path throughwhich the superconducting current can flow For this systemthe sample used to measure the resistivity had to be carefullychosen and polished due to the presence of small amountsof Sn flux that could mask the compoundrsquos transition InFig 3 we show ρ(T ) measurements at several applied fieldsalong the directions H b [Fig 3(a)] and H perp b [Fig 3(b)]Unfortunately due to both the geometry of the equipment andthe sample it was not possible to change the direction of theapplied field without changing its direction with respect to the

224505-4


FIG 3 Temperature dependence of the resistivity for YNiSi3

with H ranging from zero up to 015 T (a) shows the configurationwith H perp I and H b and (b) with H I and H perp b

current so a discussion on the presence of any anisotropicmagnetoresistance effects is left for future work

At zero field there is a sharp transition at 142(2) K withρ(T ) quickly reaching zero even with a highest available datapoint density The residual resistivity before the superconduct-ing transition is ρ0 = 033(3) μ cm obtained by averagingthe values estimated in both directions and the residual re-sistivity ratio (RRR) already published [35] is 54(5) Withincreasing magnetic field there is very little broadening of thetransition however for H higher than 20 mT the transitionis no longer complete Comparison of Figs 3(a) and 3(b)indicates that there is an important anisotropy with the con-figuration displayed in Fig 3(b) showing higher Tc for thesame H and a complete superconducting transition even underthe presence of an applied field of 40 mT Measuring downto 40 mK allows the observation of a partial transition underfields as high as 015 T in the configuration shown in Fig 3(b)The critical fields obtained with these measurements are con-siderably higher than those observed in the magnetization andspecific-heat measurements We will return to this point in theDiscussion section

The thermodynamic quantities related to the first-ordersuperconducting transition can be evaluated using the zero-field electronic specific-heat data displayed in Fig 2(c) Theequations below give the relationship between the internal

FIG 4 (a) Temperature dependence of the internal energy dif-ference (U ) latent heat (T S) and free-energy (F ) for YNiSi3These curves were calculated using the specific-heat measurementsat zero field and Eq (7) (b) Temperature dependence of the criticalfield Hc(T ) obtained from different techniques using the free energyshown in (a) and the specific-heat magnetization and resistivitymeasurements as a function of the applied field

energy (U ) latent heat (T S) free energy (F ) andcritical field [Hc(T )] and how we can evaluate them from thespecific-heat data

F (T ) = minusμ0V H2c (T )

2= U minus T S

U (T ) =int Tc

T[Cs(T

prime) minus Cn(T prime)]dT prime (7)

S(T ) =int Tc

T

Cs(T prime) minus Cn(T prime)T prime dT prime

where V is the volume of a formula unit Figure 4(a) showsthe dependence of U T S and F with temperature forYNiSi3 The dependence of Hc(T ) obtained with this methodis displayed in Fig 4(b) and yields a critical field μ0Hc(0) of70(7) mT lower than the one obtained from magnetization[Fig 1(c)] Along with this curve we display in Fig 4(b) thebehavior of Hc(T ) for YNiSi3 obtained with the experimental

224505-5


results presented above including the data shown in Fig 1(c)The values of Hc and Tc resulting from the ρ(T ) curves wereobtained taking the temperature corresponding to a decreasein 50 of ρ0 and we disregarded the curves that did not reachzero resistivity although the transitions can be observed withfields as high as 150 mT Despite all the results pointing totype-I superconductivity it is notable that the critical fieldsobtained from resistivity with configuration H perp b are abouteight times higher at low temperatures compared to the othertechniques This could be an effect of surface superconductiv-ity that only ρ(T ) can probe but as it is highly anisotropic itseems a robust effect

The techniques discussed above allow us to obtain thebasic superconducting parameters for YNiSi3 The electron-density n can be calculated considering the contribution ofthe three electrons from Y3+ and the presence of four for-mula units per unit cell of the compound (Z = 4) yielding

n = 12Vcell = 370 times 1028 mminus3 where Vcell = 32449 Aring3

forYNiSi3 [35] Assuming a spherical Fermi surface kF isgiven by kF = (3nπ2)13 which leads to an effective massmlowast = h2k2

FγNπ2nk2B = 154m0 where m0 is the free-electron

mass and γN is in volume units [the density of YNiSi3

is 47459(2) gcm3] The mean free path is given by l =hkFne2ρ0 = 347 nm The London penetration depth λL canbe estimated from the relation λL = (mlowastμ0ne2)12 and isequal to 34(3) nm Finally the BCS coherence length inthe clean limit is ξ0 = 018h2kFkBTcmlowast = 780(80) nm Us-ing the relations λGL = λL(1 + 075ξ0l )12

radic2 and ξGL =

074ξ0(1 + 075ξ0l )minus12 for T = 0 [49] we obtain κ =λGLξGL = 0113(11) This value puts YNiSi3 in the type-I limit since κ lt 1

radic2 in line with the results from the

previous measurements

B LuNiSi3

The superconducting properties of LuNiSi3 are very sim-ilar to YNiSi3 but the superconductivity occurs at a highercritical temperature [Tc = 161(2) K] As the ionic radius ofLu3+ is smaller than Y3+ LuNiSi3 has a smaller unit-cellvolume than YNiSi3 confirmed by previous x-ray analysis[35] This increase in Tc may be a consequence of a chem-ical pressure effect from the reduced volume making thesecompounds good candidates for subsequent low-temperaturepressure studies

Figure 5 shows the magnetic measurements for LuNiSi3

after taking into account the demagnetization factorcorrectionχ (T ) displayed in Fig 5(a) was collected usinga ZFC-FCW protocol with an applied field of μ0H = 1 mTperpendicular to the plate (H b) The transition occurs at158(2) K with χ (T ) approaching minus1 at low temperaturesThe M(H ) curves displayed in Fig 5(b) at severaltemperatures below Tc present the same features of atype-I SC observed for YNiSi3 A fit of the experimentalcritical field points in the phase diagram [Fig 5(c)] usingEq (1) yields μ0Hc(0) = 104(2) mT

The dependence of the specific heat on T at severalapplied fields for LuNiSi3 is presented in Fig 6 Fig-ure 6(a) shows a sharp transition at 163(2) K in zero fielddue to the superconducting transition The transition shiftsto lower temperatures with an increasing applied field as

FIG 5 Magnetization measurements for LuNiSi3 (a) Temper-ature dependence of χ with μ0H = 1 mT using a ZFCW-FCWprotocol (b) M(H ) curves at several temperatures below the super-conductor transition (c) Phase diagram with Hc extracted from thecurves in panel (b) and the fit of Eq (1)

expected The main panel in Fig 6(b) shows the curveCpT vs T whereas the inset shows CpT vs T 2 measured

224505-6


FIG 6 (a) Temperature dependence of Cp in several magneticfields for LuNiSi3 (b) CpT vs T for the same curves displayed in(a) The inset shows CpT vs T 2 for a larger range of temperature(c) Electronic contribution of specific heat for H = 0 with the fitsobtained with the models given in Eqs (5) and (6)

with μ0H = 9 mT and the fit above the superconductingtransition The value of γN = 397(9) mJ molminus1 Kminus2 wasfound (slightly below that for YNiSi3) yielding a jump ofCelγNTc = 071(5) also below the value expected fromBCS theory The experimentally estimated Debye tempera-ture was 474(8) K [β = 00910(5) mJ molminus1 Kminus4 and B =0000 44(9) mJ molminus1 Kminus6] similar to the previous work athigh temperatures (484 K) [35] The value of the electron-phonon coupling constant following Eq (4) is λe-ph = 044(2)also placing LuNiSi3 in the weak-coupling regime The

TABLE II Fitted parameters of Cel in the superconducting regionfor LuNiSi3 Ai α and a are dimensionless 0 is measured in10minus23 J and γ2 is measured in mJ molminus1 Kminus2


SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)

density of states at the Fermi level is following Eq (3)N (EF) = 169 stateseV fu

Figure 6(c) shows Cel vs T in the superconducting regimeand fits using the models described in Eqs (5) and (6) The fitparameters are given in Table II The results are very similar toYNiSi3 and it is not possible to determine which compoundhas a larger superconducting gap

Resistivity measurements for LuNiSi3 (Fig 7) were con-ducted in the same configurations used for YNiSi3 A sharptransition at 163(2) K takes place in zero field and significantanisotropy is observed comparing Figs 7(a) and 7(b) withthe higher critical fields occurring for the geometry withH perp b in the same way as YNiSi3 In Fig 7(b) a completetransition occurs up to 80 mT The residual resistivity before

FIG 7 Temperature dependence of the resistivity for LuNiSi3

with H ranging from zero up to 015 T (a) shows the configurationwith H perp I and H b and (b) shows the configuration with H Iand H perp b

224505-7


FIG 8 (a) Temperature dependence of the internal energy dif-ference (U ) latent heat (T S) and free energy (F ) for LuNiSi3These curves were calculated using the specific-heat measurementsat zero field and Eq (7) (b) Temperature dependence of the criticalfield Hc(T ) obtained from different techniques using the free energyshown in (a) and using the specific-heat magnetization and resistiv-ity measurements as a function of the applied field

the superconducting transition for this compound is ρ0 =18(3) μ cm and RRR = 38(4) [35]

We performed the same thermodynamic analysis usingEq (7) for LuNiSi3 and results are displayed in Fig 8(a)Overall the energies and latent heat curves for both com-pounds are very similar but reach higher absolute values forLuNiSi3 Figure 8(b) shows the Hc(T ) curve obtained usingEq (7) and the data from Fig 8(a) with a critical field of about83 mT and the Hc(T ) curves obtained with the experimentalresults presented above As for YNiSi3 the Hc(T ) curvesfor LuNiSi3 obtained from magnetization specific heat andresistivity with H b are very similar whereas the curve withH perp b in the resistivity gives much higher critical fields

Following the same analysis used for YNiSi3 the electrondensity of LuNiSi3 yields n = 383 times 1028 mminus3 with Vcell =31362 Aring

3[35] Assuming a spherical Fermi surface the

effective mass is mlowast = 151m0 [the density of LuNiSi3 is65696(3) gcm3] the estimated mean free path is equal to

l = 63 nm lower than for YNiSi3 and the London penetra-tion depth is 33(3) nm Finally the BCS coherence length inthe clean limit is ξ0 = 690(70) nm and using the equationsabove for λGL and ξGL we obtain κ = 042(4) This valuealso puts LuNiSi3 in the type-I limit but much closer to theborderline value of 0707

IV THEORETICAL RESULTS

Since Ni is commonly a magnetic ion we first checkedfor the possibility of magnetic order by starting from differentspin configurations [including Y(Lu) and Ni atoms with paral-lel spins Y(Lu) and Ni atoms with antiparallel spins for eachsublattice etc] but all starting configurations converged to anonmagnetic ground state with zero local magnetic momentsie diamagnetic compounds are obtained These results arecompatible with the magnetic measurements reported previ-ously [35] and with the results presented in the ExperimentalResults section of this paper

Having established the magnetic configuration of thesecompounds we have studied their crystallographic proper-ties The crystal structure of RNiSi3 has a base-centeredorthorhombic centrosymmetric space-group Cmmm where theR = (Y Lu) and the Ni atoms are located at the Wyckoff po-sitions 4 j (m2m) and 4i (m2m) respectively There are threeinequivalent Si atoms two of them situated at positions 4iand one at 4 j The crystal structure is shown in Fig 9(a) andthe calculated and experimental lattice constants are shown inTable I of the Supplemental Material [38] The optimizationof the Wyckoff positions and lattice vectors shows the samecrystal symmetry for all calculated volumes Comparing ourresults for the equilibrium volumes with the available exper-imental data the absolute error for the lattice constants isless than 1 for both compounds whereas absolute errors inthe volume are 171 and 156 for YNiSi3 and LuNiSi3respectively Another important finding is deduced from thecalculated vibrational dispersion relation at the equilibriumvolumes where there are no imaginary frequencies and there-fore the dynamical stability of the crystal structure of thesecompounds is maintained

In order to understand the bonding properties of thesecrystalline materials we have also calculated the ELF whichgives a sound basis for a well-defined classification of bonds[5051] According to the ELF construction this function cantake values between 0 and 1 where 1 corresponds to perfectlocalization and 05 corresponds to the case of a homogeneouselectron gas Then pure ionic bonding should manifest as highvalues of the ELF close to the nuclei and very low values (sim0)uniformly distributed in the interstitial region Pure covalentbonding between two atoms should display a local maximumof the ELF on the line connecting those atoms with a typicalmaximum value of the ELF in the range between 06 and 10depending on how strong the bond is Metallic bonding whichrepresents an intermediate case between the covalent bondingand ionic bonding usually shows an almost uniform ELFdistribution in the interstitial region with typical values on theorder of 03ndash06 Figure 9(b) presents our calculated ELF forYNiSi3 We have chosen three sections to display the ELFnamely the NiSi2 and YSi layers ie the (001) and (002)planes and a section through all three atoms the (101) plane

224505-8


FIG 9 (a) RNiSi3 crystal structure dark golden black and bluespheres denote the R Ni and Si atoms respectively The mainbuilding blocks are a set of corner-sharing square pyramids formedby Si that enclose the Ni atoms and another set of edge-sharingrectangular pyramids where the base and the apex are made up ofSi and R atoms respectively Other remarkable features observedin this crystal structure are the pseudohexagons built up by Ni andSi atoms on (001) and the isosceles triangles made up by R atomson (002) (b) Calculated electron localization function (ELF) forYNiSi3 upper middle and bottom panels show the (001) (002) and(101) planes respectively

The ELF values on (001) indicate that the bond between theSi atoms forming dimers along [010] is covalent (maximumvalue of 095) and stronger than the also covalent bond(maximum value of 082) between the Si atoms that buildup the zigzag chain along [100] On the other hand the ELFvalues found in the regions connecting Ni-Si atoms reveal themetallic character of these bonds (maximum value of 048)On the (002) plane the ELF functions (maximum value of095) corroborate the covalent nature of the bonds of the Sidimers along [010] whereas the bonding between the Y andthe Si atoms is metallic (maximum value of 051) Observingthe ELF between the Y atoms that build the isosceles triangleon (002) we can deduce the bonding is ionic (maximumvalue of 021) Finally the calculated ELF on (101) shows theweakly metallic behavior of the Y-Ni bond (maximum valueof 032) To summarize all types of chemical bonds can bedistinguished in the YNiSi3 system ionic (between Y atoms)metallic (among Ni-Si Y-Si and Ni-Y) and covalent (withinthe Si dimers and zigzag chains) We do not show the calcu-lated ELF for LuNiSi3 because it is very similar to YNiSi3

and consequently the bonding properties are the sameWe have also calculated the elastic constants (see Table

II of the Supplemental Material [38]) and then the Debyetemperature using the following equation

D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13

is the average sound velocity sl =radicB+ 4

3 Gρ

is the longitudinal sound velocity st =radic

Gρ

is the

transverse sound velocity G is the isotropic shear moduluswhich is calculated in terms of the crystalline lattice constants

qD = 3radic

6π2ηα and ηα is the atomic concentration The calcu-lated values are 497 and 464 K for YNiSi3 and LuNiSi3 withabsolute relative errors of 67 and 21 in good agreementwith the experimental values

For a better understanding of the basic electronic propertiesthat may lead to the experimentally observed behavior ofYNiSi3 and LuNiSi3 we now present the calculated DFTelectronic structure for both compounds Figure 10 displaysthe calculated dispersion relations along the high-symmetrydirections of the first Brillouin zone (FBZ) and the total andprojected DOS for both compounds for one spin directionThe YNiSi3 valence bands are composed of Ni d states forthe most part a small contribution of Si p states and an evensmaller contribution of Y d states [Fig 10(a)] The valencebands of LuNiSi3 are similar to those of YNiSi3 although thepresence of Lu f states introduce almost dispersionless bandsaround 41 and 56 eV below the Fermi level [Fig 10(b)]The splitting of the f bands (15 eV) is due to the spin-orbitcoupling that in the case of LuNiSi3 is much stronger thanthe crystal-field splitting which lifts all the degeneracies ofthe Lu f states (point-group m2m) by less than 5 meV TheLuNiSi3 upper valence bands are composed mainly of Ni dstates and some contribution of Si p and Lu d states Theconduction bands are also the result of the hybridization ofd states coming from the metallic atoms with the Si p statesand for energies larger than 1 eV the contribution of Si s statesbecomes relevant as well At the Fermi level the contributionsof the projected DOS for YNiSi3 are (in statesfu spin andeV) 02131 02544 and 01719 for Y d Ni d and Si p statesrespectively In the case of LuNiSi3 the contributions at theFermi level of the Lu d Ni d and Si p states are 0223 02676and 01858 Thus we would expect an important contributionof 3d 3p and 4d orbitals in the superconductivity of YNiSi3

(3d 3p and 5d orbitals for LuNiSi3)We have also estimated under the crude assumption of

the Sommerfeld model the bare specific-heat coefficientγbare = 2

3π2ηFk2B where ηF is the total DOS at the Fermi

level (in statesfu spin and eV) We have obtained forYNiSi3 and LuNiSi3 respectively ηF = 06875 and 07433(the relative errors are 196 and 12) given γbare = 324and 350 mJ molminus1 Kminus2 Furthermore we have estimatedthe specific-heat enhancement γexp

γbare= (1 + λe-ph ) obtaining

λe-ph = 0247 and 0134 for YNiSi3 and LuNiSi3 respec-tively Such values for the electron-phonon coupling confirmthat these compounds are in the weak-coupling regime

The topology of the three conduction bands crossing theFermi level is almost identical for both compounds as shownin Fig 10 [FBZ high-symmetry points and directions areshown in Fig 11(a)] The first partially occupied band (ma-genta line) crosses the Fermi level in the vicinity of the high-symmetry point T and it has a holelike character its atomiccharacter [see the inset in Fig 10(a)] is built up by Ni d andSi p states The second conduction band (violet line) crossesthe Fermi level in all the high-symmetry directions except the direction (ky) This band has an appreciable dispersion inall the directions that it crosses where its holelike characteris manifested in the H T - -S and D directions Thisband is made up by the hybridization of Y (Lu) d Ni d andSi p states except in the D direction where only the Ni and

224505-9


FIG 10 Calculated electronic structure dispersion relation total and projected DOS for (a) YNiSi3 and (b) LuNiSi3 Highlighted in colorare the three conduction bands crossing the Fermi level band 1 (magenta) band 2 (violet) and band 3 (green) The eigenvalues are shiftedto the Fermi level which is indicated by a dashed line The inset in panel (a) shows the atomic character of the dispersion relation wherethick blue red and green lines correspond to Y d Ni d and Si p states respectively The inset in panel (b) zooms in on the projected DOScontributions at the Fermi level

224505-10


FIG 11 (a) FBZ of the space-group Cmmm The main symmetry points and lines are labeled in black and red respectively (b) ExtendedFermi surface of YNiSi3 The FBZ is shown by black lines and it is oriented along the direction (ky) (c) Extended Fermi surfaceof LuNiSi3

Si orbitals are present On the other hand the third partiallyoccupied band (green line) crosses only the D directionhaving large dispersion and electron character The orbitalcharacter of this band is only due to Ni d and Si p statesAs was previously suggested [52] and later measured [34]for YbNiSi3 the three bands collectively indicate that thesecompounds are good conductors along the [100] and [001]crystallographic directions but not along [010] Our electronicstructure results for both compounds also demonstrate theirsimilarity to the isostructural compound YNiGe3 [29]

Figure 11 provides a visual representation of the calculatedFS of these compounds The first hole branch is formedby four pipes (blueyellow surfaces) centered around andparallel to the direction The second branch has twomain features a holelike rectangular cylinder (greenvioletcolors) also centered around and with its axis orientedalong the direction and a set of large holelike cylindersrunning along the FBZ boundary parallel to the directionand intricately connected around the FBZ boundaries Thethird branch is built by four large electronlike disconnectedcylinders (cyanred colors) centered around the edge of theFBZ and running parallel to the direction The first holeand the electron branches result from the hybridization ofNi d with Si p states whereas the second hole branch alsohas the contribution of Y (Lu) d orbitals Thus the twolarge cylindrical branches are most likely responsible for theobserved superconductivity in these systems

Finally we have also calculated the phononic propertiesof these compounds such as the phonon dispersion relationthe partial density of states F (ω) and the spectrum functionωminus2F (ω) We did not include the SOC in the calculation of thevibrational properties because the crystal structure and the FSare not affected by this interaction The primitive cell of thesesystems contains ten atoms therefore the phonon spectrumcontains 3 acoustic and 27 optical branches as shown inFig 12 Although the dispersion relation and partial F (ω)show an almost continuous distribution of modes across thewhole frequency range we can divide the phonon spectruminto three frequency regions acoustic (0ndash40 and 0ndash32 THzfor YNiSi3 and LuNiSi3 respectively) intermediate (40ndash122and 26ndash128 THz) and high (122ndash145 and 128ndash146 THz)The acoustic branches are made up from states of all the atomsalmost evenly for YNiSi3 whereas there is an appreciable

increment of the Lu contribution in the case of LuNiSi3 dueto its heavy mass The intermediate-frequency range has 23branches where 12 of these (up to approximately 67 THz)form the low-lying optical branches These 12 branches arebuilt up by states coming from all the atoms with Y (Lu) andSi contributions being larger than the Ni one The remaining11 intermediate branches are mainly made up of Si contribu-tions and a small contribution of Ni states The four branchesforming the high-frequency region are almost solely formedby Si contributions

From F (ω) we can also obtain the spectrum functionωminus2F (ω) that can be used as a crude alternative to the Eliash-berg function α2F (ω) these two spectral functions exhibita similar peak structure [53] We can observe that ωminus2F (ω)has its larger spectral weight in the acoustical and low-lyingoptical branches for both compounds with its more prominentpeaks located around the latter as is shown in Fig 12 These 12branches have contributions from the vibrations of all atoms[Y(Lu) Ni Si] indicating that the coupling between the delectrons from Y(Lu) and Ni to Si p electrons will formCooper pairs therefore they are responsible for the observedsuperconductivity of these compounds

V DISCUSSION

To summarize both YNiSi3 and LuNiSi3 present bulksuperconductivity showing the features of type-I supercon-ductors with κ = 0113(11) for YNiSi3 and κ = 042(4) forLuNiSi3 The main superconducting parameters for both com-pounds are given in Table III

The discovery of type-I superconductivity in ternary com-pounds is not unprecedented with recent publications report-ing the appearance of type-I superconductivity in the cagecompound LaTi2Al20 [11] and in the NCS LaPdSi3 [12] andLaIrSi3 [13] compounds The case of the NCS LaRhSi3 iseven more intriguing since it has been recently reported asa type-II1 superconductor with κ = 025 [2426] This com-pound has a phase diagram with resistivity and susceptibilitymeasurements giving an exceptionally high upper criticalfield (asymp120 mT) compared to Hc(0) obtained from standardspecific-heat and magnetization measurements (asymp20 mT) in-terpreted as arising from surface superconductivity

224505-11


FIG 12 Calculated phonon dispersion relation and F (ω)ω2 and partial density of states F (ω) for (a) YNiSi3 and (b) LuNiSi3

DFT results show that both YNiSi3 and LuNiSi3 have anonmagnetic ground state and that although SOC does notaffect the FS of these compounds SOC does act significantlyon the Lu f states below the Fermi level resulting in a largesplitting of these orbitals that overcomes the insignificantcrystal-field splitting ELF shows that for both compoundsthere are three types of atomic bonding metallic covalentand ionic The metallic bond is observed between Lu(Y) andSi on the (002) plane and the Ni and Si atoms on the (001)plane The electronic structure indicates that these compoundsare good conductors along the [100] and [001] directions butnot along [010] From the FS we find that the second holebranch is built up by hybridization of Y(Lu) d Ni d and Si

TABLE III Experimental superconducting parameters forYNiSi3 and LuNiSi3 The value of Hc(0) was estimated from themagnetization measurements

YNiSi3 LuNiSi3

Tc (K) 136(3) 161(2)γN (mJ molminus1 Kminus2) 404(9) 397(9)θD (K) 466(9) 474(8)λe-ph 043(2) 044(2)CelγNTc 114(9) 071(5)μ0Hc(0) (mT) 96(2) 104(2)λL (nm) 34(3) 33(3)ξ0 (nm) 780(80) 690(70)κ 0113(11) 042(4)

p states whereas Ni d and Si p states hybridize to form theelectron branch These branches connect the FBZ boundariesand are responsible for the observed superconductivity Thepartial F (ω) and spectrum function ωminus2F (ω) indicate thatthe coupling of Y(Lu) Ni d and Si p electrons in the low-lying optical phonon branches will form the Cooper pairsresponsible of the superconducting state These findings showthat these compounds are anisotropic three-dimensional (3D)metals with a multiband superconducting state

The larger spectral weight ωminus2F (ω) present in LuNiSi3

for the low-lying optical branches together with the large ηF

might explain the higher critical temperature seen in LuNiSi3

VI CONCLUSION

We have reported the discovery of superconductivity inYNiSi3 [Tc = 136(3) K] and LuNiSi3 [Tc = 161(2) K] bycharacterizing the superconducting behaviors of single crys-tals through magnetization heat-capacity and resistivity ex-periments with support from DFT band-structure calculationsBoth compounds show bulk superconductivity with featuresthat are typical of type-I SC but with a low jump in thespecific heat [CelγnTc is equal to 114(9) and 071(5) forthe Y and Lu compounds respectively] Resistivity mea-surements show a highly anisotropic behavior between themeasurements under an applied field with the configurationH perp b displaying the highest critical fields DFT calculationsshow that these compounds are anisotropic 3D metals with amultiband superconducting ground state

224505-12


ACKNOWLEDGMENTS

The authors acknowledge financial support from Brazilianfunding agencies CAPES CNPq and FAPESP (ContractsNo 201119924-2 No 201217562-9 No 201420365-6and No 201701827-7) Colombian agency COLCIENCIAS

(Convocatoria Doctorados Nacionales No 757 de 2016)and Vicerrectoriacutea de Investigacioacuten Universidad de AntioquiaEstrategia de Sostenibilidad No 2018-2019 (Colombia) Wealso acknowledge fruitful discussions with G Eguchi andJ Sereni

[1] F Kneidinger E Bauer I Zeiringer P Rogl C Blaas-Schenner D Reith and R Podloucky Physica C (Amsterdam)514 388 (2015)

[2] J Bardeen L N Cooper and J R Schrieffer Phys Rev 106162 (1957)

[3] M R Norman Science 332 196 (2011)[4] T Das and C Panagopoulos New J Phys 18 103033 (2016)[5] M Smidman M B Salamon H Q Yuan and D F Agterberg

Rep Prog Phys 80 036501 (2017)[6] M J Winiarski B Wiendlocha S Gołab S K Kushwaha P

Wisniewski D Kaczorowski J D Thompson R J Cava andT Klimczuk Phys Chem Chem Phys 18 21737 (2016)

[7] S Sun K Liu and H Lei J Phys Condens Matter 28 085701(2016)

[8] E Svanidze and E Morosan Phys Rev B 85 174514(2012)

[9] L L Zhao S Lausberg H Kim M A Tanatar M Brando RProzorov and E Morosan Phys Rev B 85 214526 (2012)

[10] H Leng C Paulsen Y K Huang and A de Visser Phys RevB 96 220506(R) (2017)

[11] A Yamada R Higashinaka T D Matsuda and Y AokiJ Phys Soc Jpn 87 033707 (2018)

[12] M Smidman A D Hillier D T Adroja M R LeesV K Anand R P Singh R I Smith D M Paul and GBalakrishnan Phys Rev B 89 094509 (2014)

[13] V K Anand D Britz A Bhattacharyya D T Adroja A DHillier A M Strydom W Kockelmann B D Rainford andK A McEwen Phys Rev B 90 014513 (2014)

[14] J Auer and H Ullmaier Phys Rev B 7 136 (1973)[15] V Moshchalkov M Menghini T Nishio Q H Chen A V

Silhanek V H Dao L F Chibotaru N D Zhigadlo and JKarpinski Phys Rev Lett 102 117001 (2009)

[16] E Babaev J Carlstroumlm M Silaev and J M Speight PhysicaC (Amsterdam) 533 20 (2017)

[17] T Bauch E Babaev M G Blamire C Brun A Buzdin JCarlstroumlm T Cren O Dobrovolskiy J Ge V N Gladilinet al Superconductors at the Nanoscale From Basic Researchto Applications (de Gruyter Berlin 2017)

[18] T Reimann M Schulz D F R Mildner M Bleuel A BrucircletR P Harti G Benka A Bauer P Boumlni and S MuumlhlbauerPhys Rev B 96 144506 (2017)

[19] Y Wang R Lortz Y Paderno V Filippov S Abe U Tutschand A Junod Phys Rev B 72 024548 (2005)

[20] J-Y Ge J Gutierrez A Lyashchenko V Filipov J Li andV V Moshchalkov Phys Rev B 90 184511 (2014)

[21] D J Rebar Exploring Superconductivity in Chiral StructuredAuBe PhD thesis Louisiana State University and Agriculturaland Mechanical College 2015

[22] A V Tsvyashchenko V A Sidorov A E Petrova L NFomicheva I P Zibrov and V E Dmitrienko J Alloys Compd686 431 (2016)

[23] P Lejay I Higashi B Chevalier J Etourneau and PHagenmuller Mater Res Bull 19 115 (1984)

[24] V K Anand A D Hillier D T Adroja A M Strydom HMichor K A McEwen and B D Rainford Phys Rev B 83064522 (2011)

[25] N Kimura H Ogi K Satoh G Ohsaki K Saitoh H Iida andH Aoki JPS Conf Proc 3 01501-1 (2014)

[26] N Kimura N Kabeya K Saitoh K Satoh H Ogi K Ohsakiand H Aoki J Phys Soc Jpn 85 024715 (2016)

[27] S J Ray A S Gibbs S J Bending P J Curran E BabaevC Baines A P Mackenzie and S L Lee Phys Rev B 89094504 (2014)

[28] E D Mun S L Budrsquoko H Ko G J Miller and P C CanfieldJ Magn Magn Mater 322 3527 (2010)

[29] M J Winiarski and M Samsel-Czekała Solid State Commun179 6 (2014)

[30] A P Pikul and D Gnida Solid State Commun 151 778(2011)

[31] M Nakashima K Tabata A Thamizhavel T C KobayashiM Hedo Y Uwatoko K Shimizu R Settai and Y OnukiJ Phys Condens Matter 16 L255 (2004)

[32] H Kotegawa K Takeda T Miyoshi S Fukushima H HidakaT C Kobayashi T Akazawa Y Ohishi M Nakashima AThamizhavel et al J Phys Soc Jpn 75 044713 (2006)

[33] E D Mun S L Budrsquoko A Kreyssig and P C CanfieldPhys Rev B 82 054424 (2010)

[34] M A Avila M Sera and T Takabatake Phys Rev B 70100409(R) (2004)

[35] F R Arantes D Aristizaacutebal-Giraldo S H Masunaga F NCosta F F Ferreira T Takabatake L Mendonccedila-FerreiraR A Ribeiro and M A Avila Phys Rev Mater 2 044402(2018)

[36] K Dewhurst S Sharma L Nordstrom F Cricchio FBultmark H Gross C Ambrosch-Draxl C Persson CBrouder R Armiento et al ELK [httpelksourceforgenet](2016)

[37] J P Perdew A Ruzsinszky G I Csonka O A Vydrov G EScuseria L A Constantin X Zhou and K Burke Phys RevLett 100 136406 (2008)

[38] See Supplemental Material at httplinkapsorgsupplemental101103PhysRevB99224505 for the tables with the latticeparameters and the elastic module

[39] S P Murarka Silicides for VLSI Applications (Academic PressNew York 2012)

[40] M K Niranjan V S Kumar and R Karthikeyan J Phys D47 285101 (2014)

[41] J-Y Lin H-M Hsu and K-C Lu CrystEngComm 17 1911(2015)

[42] M Tinkham Introduction to Superconductivity (McGraw-HillNew York 1996)

[43] W L McMillan Phys Rev 167 331 (1968)

224505-13


[44] V H Tran and M Sahakyan Sci Rep 7 15769 (2017)[45] M Sahakyan and V H Tran J Phys Condens Matter 28

205701 (2016)[46] G-Y Chen X Zhu H Yang and H-H Wen Phys Rev B 96

064524 (2017)[47] F Gross B S Chandrasekhar D Einzel K Andres P J

Hirschfeld H R Ott J Beuers Z Fisk and J L Smith ZPhys B 64 175 (1986)

[48] R Ribeiro-Palau R Caraballo P Rogl E Bauer and IBonalde J Phys Condens Matter 26 235701 (2014)

[49] J R Waldram Superconductors of Metals and Cuprates(Institute of Physics Publishing Bristol 1996)

[50] A D Becke and K E Edgecombe J Chem Phys 92 5397(1990)

[51] A Savin R Nesper S Wengert and T F Faumlssler AngewChem Int Ed Engl 36 1808 (1997)

[52] G-H Sung and D-B Kang Bull Korean Chem Soc 24 325(2003)

[53] A Junod D Bichsel and J Muller Helvetica Physica Acta 52580 (1979)

224505-14


In this paper we present a detailed characterization of twononmagnetic compounds of the RNiSi3 series (those with R =Y Lu) expected to show many of the same features as YNiGe3

with Tc = 046 K [30] We report on the discovery via re-sistivity magnetization and specific-heat measurements ofbulk type-I superconductivity in single crystals of YNiSi3 andLuNiSi3 with critical temperatures Tc = 136(3) K for YNiSi3

and Tc = 161(2) K for LuNiSi3 We also present densityfunctional theory (DFT) calculations to obtain the electronicproperties of these compounds

II METHODS

YNiSi3 and LuNiSi3 single crystals were synthesized viathe Sn-flux method originally used to grow YbNiSi3 [34] Aproportion of 11345 (YLuNiSiSn) was used as detailedin previous work [35] wherein the crystalline structures wereverified by powder x-ray diffraction (PXRD) analysis andwavelength dispersive electron-probe microanalysis (EPMA)of the single crystals conducted in a JEOL JXA-8200 mi-croanalyzer The crystal compositions were determined byaveraging over ten different points of a polished sample

Resistivity between 004 and 4 K was measured with astandard four-probe ac method in a homemade system insidea commercial Cambridge Magnetic Refrigeration mFridgemF-ADR50 with applied magnetic fields in two orientationsparallel or perpendicular to the crystal plate main surfacesSpecific heat between 037 and 5 K was measured on crystalswith total mass of about 7 mg under applied fields parallelto the plates using the 2τ thermal relaxation method in theQuantum Design Physical Property Measurement System

Magnetic susceptibility was measured in a Quantum De-sign Magnetic Property Measurement System magnetometerwith an iQuantum 3He insertmdashin this case the field wasperpendicular to the plate surfaces Proper evaluation of themagnetization measurements in SCs must take into accountthe demagnetization factor (N) due to the sample shape sincethe volumetric susceptibility of a bulk SC must approach χ simminus1 below the critical temperature In our case the platelikeshape of the crystal made it simple to estimate N sim 05 forYNiSi3 and N sim 07 for LuNiSi3 with the magnetic fieldapplied perpendicular to the main surface of the sample(H b)

Spin-polarized first-principles DFT calculations includingspin-orbit coupling (SOC) in a second-variational schemehave been carried out using the full-potential augmented-plane wave method with local orbitals (FP-APW + lo)as implemented in the ELK code [36] For the exchange-correlation energy functional we have used the generalizedgradient approximation and its PBEsol parametrization [37]The muffin-tin (MT) radii of Y Lu Ni and Si are set toRY

MT = 27777 RLuMT = 27495 RNi

MT = 20563 and RSiMT =

20563 au respectively The parameter RMT|G + k|max gov-erning the number of plane waves in the FP-APW + lo methodis chosen to be 95 The Brillouin zone (BZ) is sampled with auniformly spaced k grid of 8 times 8 times 8 for the structural relax-ation and 16 times 16 times 16 for the calculation of the dispersionrelation E (k) the total and site projected densities of states(DOS) and the Fermi surface (FS)

III EXPERIMENTAL RESULTS

Previous work on the series RNiSi3 [35] showed by PXRDanalysis that these compounds crystallize in the orthorhombicspace group Cmmm The experimental lattice constants aregiven in Table I of the Supplemental Material [38] Elementalanalysis using EPMA revealed average sample compositionsof Y096(11)Ni100(19)Si309(18) and Lu100(1)Ni068(2)Si313(2) withan upper limit of sim500 ppm Sn impurities in both crystalsLuNiSi3 crystals thus form with significant Ni vacancies asobserved in the RNiGe3 series [28] This effect is small forYNiGe3 but is more pronounced for heavier rare earths as inthe case of LuNiGe3 There were some small NiSi2 crystallitesattached to the surface of the crystals (a diamagnetic non-superconducting metallic silicide [39ndash41]) that could be easilyremoved by polishing Besides Sn (Tc = 37 K) no othersuperconducting impurity was detected so we may claim thatthe superconducting transitions presented below are due tothese new intermetallic compounds

In the following sections we describe the characteristicsof the superconductivity in YNiSi3 and LuNiSi3 throughmagnetization specific-heat and resistivity experiments

A YNiSi3

Figure 1 shows the magnetic characterization ofYNiSi3χ (T ) [Fig 1(a)] was measured under an appliedfield of μ0H = 2 mT following a zero-field-cooled warmingprotocol At 131(2) K there is a relatively sharp transitionwith χ rising from the value of minus1 as expected bythe complete field expulsion of a bulk SC Figure 1(b)shows the M(H ) curves at several temperatures below thesuperconducting transition They are marked by a type-I SCbehavior with M = minusH at low fields and an abrupt jump atHc The transition in some type-I SC can be broadened bythe presence of impurities inhomogeneities and even a highdemagnetization effect however the type-I behavior of thissample is very clear attesting to the quality of the crystal

The critical fields extracted from the curves in Fig 1(b)were used to plot the phase diagram displayed in Fig 1(c)The points were fitted by the empirical parabolic law [42]

Hc(T ) = Hc(0)

[1 minus

(T

Tc

)2] (1)

yielding an estimated critical field μ0Hc(0) = 96(2) mTFigure 2(a) shows the dependence of the total heat-capacity

(Cp) on T for YNiSi3 at zero field and with H ranging from5 mT up to 1 T a field well above that in which the super-conductivity is suppressed At zero field there is a jump at135(5) K agreeing with the bulk superconductivity observedin the magnetization measurements The data also seem toshow a double peak which could be a sign of a doubletransition over a narrow temperature range but the resolutionis not sufficient to allow a definitive conclusion For thecurves measured under applied fields the transition tempera-ture shifts to lower T with values comparable to the criticaltemperatures observed in Fig 1(b) The jumps in Cp(T )in 5 and 6 mT are higher than in zero field suggesting afirst-order transition for H = 0 Figure 2(b) shows the de-pendence of CpT with T for the same data displayed in

224505-2








θD =(

n12π4R

5β

)13

(2)

224505-3



N (EF) = 3γN

π2k2BNA

(3)












CSGel = A1γNTc exp

(minusSG0 kBT

) (5a)

CDGel = A2γNTc

[f exp

(minusDG10 kBT

)+ (1 minus f ) exp

(minusDG20 kBT

)] (5b)


(minusSGNF0 kBT

) + γ2T (5c)




SG 67(7) 24(1)DG 15(1) 13(1) 45(2) 011(1)SGNF 10(1) 35(2) 24(1)ANI 055(6) 54(3) 095(9) 067(7)

gap [24546]

CANIel (T ) = A4

N (EF)

πT

int 2π

0dφ

int π

0dθ sin θ

timesint hωD

0minus part f

partE

(E2 + 1

2β

d2(T θ )

dβ

)dE

(6a)


(T θ ) = 0(T )(1 + αprime cos 2θ ) (6c)

0(T ) = ANI0 tanh

[(πkBTc

ANI0


]

(6d)






224505-4










2= U minus T S

U (T ) =int Tc

T[Cs(T


S(T ) =int Tc

T



224505-5









radic2 and ξGL =




B LuNiSi3







224505-6






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14








θD =(

n12π4R

5β

)13

(2)

224505-3



N (EF) = 3γN

π2k2BNA

(3)












CSGel = A1γNTc exp

(minusSG0 kBT

) (5a)

CDGel = A2γNTc

[f exp

(minusDG10 kBT

)+ (1 minus f ) exp

(minusDG20 kBT

)] (5b)


(minusSGNF0 kBT

) + γ2T (5c)




SG 67(7) 24(1)DG 15(1) 13(1) 45(2) 011(1)SGNF 10(1) 35(2) 24(1)ANI 055(6) 54(3) 095(9) 067(7)

gap [24546]

CANIel (T ) = A4

N (EF)

πT

int 2π

0dφ

int π

0dθ sin θ

timesint hωD

0minus part f

partE

(E2 + 1

2β

d2(T θ )

dβ

)dE

(6a)


(T θ ) = 0(T )(1 + αprime cos 2θ ) (6c)

0(T ) = ANI0 tanh

[(πkBTc

ANI0


]

(6d)






224505-4










2= U minus T S

U (T ) =int Tc

T[Cs(T


S(T ) =int Tc

T



224505-5









radic2 and ξGL =




B LuNiSi3







224505-6






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14



N (EF) = 3γN

π2k2BNA

(3)












CSGel = A1γNTc exp

(minusSG0 kBT

) (5a)

CDGel = A2γNTc

[f exp

(minusDG10 kBT

)+ (1 minus f ) exp

(minusDG20 kBT

)] (5b)


(minusSGNF0 kBT

) + γ2T (5c)




SG 67(7) 24(1)DG 15(1) 13(1) 45(2) 011(1)SGNF 10(1) 35(2) 24(1)ANI 055(6) 54(3) 095(9) 067(7)

gap [24546]

CANIel (T ) = A4

N (EF)

πT

int 2π

0dφ

int π

0dθ sin θ

timesint hωD

0minus part f

partE

(E2 + 1

2β

d2(T θ )

dβ

)dE

(6a)


(T θ ) = 0(T )(1 + αprime cos 2θ ) (6c)

0(T ) = ANI0 tanh

[(πkBTc

ANI0


]

(6d)






224505-4










2= U minus T S

U (T ) =int Tc

T[Cs(T


S(T ) =int Tc

T



224505-5









radic2 and ξGL =




B LuNiSi3







224505-6






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14










2= U minus T S

U (T ) =int Tc

T[Cs(T


S(T ) =int Tc

T



224505-5









radic2 and ξGL =




B LuNiSi3







224505-6






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14









radic2 and ξGL =




B LuNiSi3







224505-6






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14






SG 55(6) 26(2)DG 94(9) 11(1) 43(2) 010(1)SGNF 63(6) 37(2) 22(1)ANI 050(5) 50(2) 096(9) 062(6)






224505-7













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14













224505-8






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14






D = hsqD

kB (8)

where s = ( 13s3

l+ 2

3s3t)minus13


3 Gρ


Gρ

is the


qD = 3radic










224505-9



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14



224505-10








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14








V DISCUSSION



224505-11





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14





YNiSi3 LuNiSi3






VI CONCLUSION


224505-12


ACKNOWLEDGMENTS













































224505-13












224505-14


ACKNOWLEDGMENTS













































224505-13












224505-14












224505-14

Superconductivity in monocrystalline YNiSi3 and LuNiSi3€¦ · superconductivity occurs in a...

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