Anisotropic superconductivity and Fermi surface reconstruction in the spin-vortex antiferromagnetic superconductor CaK(Fe 0.95 Ni 0.05 ) 4 As 4
José Benito Llorens, Edwin Herrera, Víctor Barrena, Beilun Wu, Niclas Heinsdorf, Vladislav Borisov, Roser Valentí, William R. Meier, Sergey Bud'ko, Paul C. Canfield, Isabel Guillamón, Hermann Suderow
AAnisotropic superconductivity and Fermi surface reconstruction in the spin-vortexantiferromagnetic superconductor CaK(Fe . Ni . ) As Jos´e Benito Llorens, Edwin Herrera, V´ıctor Barrena, Beilun Wu, Niclas Heinsdorf, Vladislav Borisov,
2, 3
RoserValent´ı, William R. Meier, Sergey Bud’ko, Paul C. Canfield, Isabel Guillam´on, and Hermann Suderow Laboratorio de Bajas Temperaturas y Altos Campos Magn´eticos,Departamento de F´ısica de la Materia Condensada,Instituto Nicol´as Cabrera and Condensed Matter Physics Center (IFIMAC),Unidad Asociada UAM-CSIC, Universidad Aut´onoma de Madrid, E-28049 Madrid, Spain Institut f¨ur Theoretische Physik, Goethe-Universit¨at Frankfurt,Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden Ames Laboratory, Ames and Department of Physics & Astronomy, Iowa State University, Ames, IA 50011
High critical temperature superconductivity often occurs in systems where an antiferromagneticorder is brought near T = 0 K by slightly modifying pressure or doping. CaKFe As is a su-perconducting, stoichiometric iron pnictide compound showing optimal superconducting criticaltemperature with T c as large as 38 K. Doping with Ni induces a decrease in T c and the onset ofspin-vortex antiferromagnetic order, which consists of spins pointing inwards to or outwards fromalternating As sites on the diagonals of the in-plane square Fe lattice. Here we study the bandstructure of CaK(Fe . Ni . ) As (T c = 10 K, T N = 50 K) using quasiparticle interference with aScanning Tunneling Microscope (STM) and show that the spin-vortex order induces a Fermi surfacereconstruction and a fourfold superconducting gap anisotropy. Iron pnictide superconductors mostly crystallize in atetragonal structure. Optimal T c appears in a phase dia-gram that shows structural, nematic or magnetic order inthe vicinity of superconductivity[1–5]. Whereas most Fe-based superconductors need doping (or pressure) to reachmaximal T c values, CaKFe As is superconducting withthe highest critical temperature in the pure stoichiomet-ric compound with T c ≈
38 K[6, 7]. Elastoresistivity,nuclear magnetic resonance (NMR) and neutron scatter-ing experiments reveal magnetic fluctuations[8–10]. Con-trary to other pnictide superconductors, there are neitherstructural modifications of the crystal when cooling norstrong electronic anisotropy in form of nematicity[7, 11].The superconducting gap exchanges sign in differentpockets of the Fermi surface and has s ± symmetryas many other iron pnictides[12–15]. Electron countand other physical properties such as T c and pairingsymmetry are similar to the nearly optimally doped(Ba . K . )Fe As [12, 16], where the magnetic order ofBaFe As is suppressed by hole doping with K.Following this idea, electron doping by substitutingFe with Co or Ni leads to antiferromagnetic order inCaKFe As (Fig. 1(a))[17]. The crystal structure is com-posed of Fe As layers that are separated alternativelywith Ca and K. Thus, As sites in each layer are not equiv-alent, because their distance to the Fe plane differs dueto being close either to Ca or to K. The distance betweenAs1 and Ca is different than the distance between As2and K (upper left inset in Fig. 1(a)). This eliminates theglide symmetry in the Fe As planes that exists in com-pounds such as BaFe As . As a consequence, antiferro-magnetic order is non-collinear, with spins at each of thefour Fe sites in the crystal structure pointing inwards to (or outwards from) the As sites, giving a hedgehog spin-vortex crystal (SVC, brown arrows in upper left inset inFig. 1(b))[17, 18]. The magnetic wavevector is the sameas for the usual spin density wave antiferromagnetic orspin-charge magnetic order[18–21]. This SVC order pro-duces a characteristic pattern of hyperfine fields at the Assites depicted in the inset of Fig. 1(b). The As1 sites havean alternating field up and down along the c axis (red cir-cles and crosses). Critically, the hyperfine field is zero atAs2 due to canceling contributions from surrounding Femoments[17, 22]. There is robust experimental evidencefor the presence of the SVC within the superconductingphase[17, 23–26]. However, the electronic band structureis yet unknown. Here we study the local density of statesof CaK(Fe . Ni . ) As (T SV C = 50 K and T c = 10K) via Scanning Tunneling Microscopy (STM). We de-termine the band structure in the magnetic phase andshow that the superconducting gap is highly anisotropicdue to magnetism.We study single crystals of CaK(Fe . Ni . ) As which have been obtained using the method of Ref. [11,17]. Samples were mounted into a dilution refrigeratorSTM as described in Ref.[27]. We provide further de-tails of crystals, low temperature cleaving mechanism anddata analysis in Ref.[28].Fig. 1(b) shows a typical surface obtained forCaK(Fe . Ni . ) As which resembles surfaces ob-tained in pure CaKFe As [13]. We identify atomicallyflat areas over a scanning window several µ m in size, sep-arated by atomic size trenches (black lines in Fig. 1(b)).Fig. 1(c) displays the tunneling conductance G = dI/dV .The superconducting gap manifests as the usual, strongreduction of the tunneling conductance for voltages of or- a r X i v : . [ c ond - m a t . s up r- c on ] S e p
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Ni doping T ( K ) SC SVC
AFM
SC + SVC AFM
CaK(Fe Ni x ) As (a) (b)
200 nm -6 -4 -2 0 2 4 60.00.40.81.2 N o r m a li z ed c ondu c t an c e Voltage (mV) ( m e V ) T/T c (c) CaFe
As2
KAs1
FIG. 1. (a) Schematic phase diagram of Ni doped CaKFe As , with a dashed vertical line indicating the Ni concentrationdiscussed here. Crystalline structure of CaK(Fe . Ni . ) As is shown in the upper left inset. (b) STM topographic image ofthe surface of CaK(Fe . Ni . ) As . The difference between black and white corresponds to a height change of 0.3 nm. Inthe inset we show a view from the top of the structure, indicating Fe (brown) and As (As1 in blue and As2 in green) atomsand with arrows indicating the spin-vortex magnetic order. Note that the magnetic moments point towards As1, giving afinite hyperfine field pointing upwards along the c-axis (red circles with a cross) and from As1 atoms, giving a hyperfine fieldpointing downwards along the c-axis (red circle with a dot)[17]. At As2 the field cancels. (c) The temperature dependence ofthe tunneling conductance is shown as open circles in the main panel. Curves are taken (from bottom to top), at 0.3 K, 0.8 K,1.4 K, 4 K and 7 K. Lines are fits using the density of states obtained for a distribution of value of the superconducting gap.The bottom right inset shows as black open circles the temperature dependence of the superconducting gap value, extractedfrom the maximum in the derivative of the density of states as a function of temperature normalized to T c . The dashed line isa guide to the eye. Bottom left inset provides an image of the vortex lattice taken at 0.3 K and 2 T. Color scale shows the zerobias conductance which goes from the normal state value (red) to its value at zero field (blue). White lines are the Delaunaytriangulation of vortex positions, which are shown as black dots. Black scale bar is 30 nm long. Further images and details areprovided in Ref. [28]. der of a few mV, which disappears at about T c . The zerobias density of states is finite and the coherence peaksare strongly smeared. Under magnetic fields we observeda disordered hexagonal vortex lattice (lower left inset ofFig. 1(c) and Ref.[28]). To estimate the superconductinggap at zero field in CaK(Fe . Ni . ) As , we constructa superconducting density of states N ( E ) allowing for alarge distribution of values of the superconducting gap(details in Ref. [28]) which gives the tunneling conduc-tance as solid lines in the main panel of Fig. 1(c). Thelower right inset of Fig. 1(c) shows the energy at whichthe derivative of N ( E ), dNdE , has a maximum. We obtain1 . T c ≈
10 K, ∆ ≈ . As , where atwo-gap structure with a few states at the Fermi level isfound[12, 13].When zooming into a small region we observe strongelectronic scattering due to defects. The field of viewshown in the topographic constant current image ofFig. 2(a)) is atomically flat. There are atomic size de-fects (black spots) and there is a wavy background. Wecan then build tunneling conductance maps G ( V, x, y ) at each point ( x, y ) of the field of view. A representative ex-ample is shown in Figs. 2(b-f) for a few bias voltages V . G ( V ) is quite homogeneous and does not change muchclose to atomic size defects but we can identify clearlya wavy background whose wavelength changes with V.The contribution of scattered electrons to the G ( V ) isproportional to the densities of states of initial and finalstates, i.e. the joint density of states, and the scatter-ing wavelength is equal to the difference q between ini-tial and final scattering wavevectors[13, 29]. The Fouriertransform of the tunneling conductance images is shownin Fig. 2(g-k). We identify three main scattering vec-tors, q α , q β and q γ . The largest scattering vector, q γ , isslightly anisotropic, being larger along the Γ- X directionthan along Γ- M (notation of Brillouin zone directionsfollows the one proposed for pnictide superconductors inRef. [30]). The Fourier amplitude at the three scatter-ing vectors decreases close to the Fermi level due to theopening of the superconducting gap (Figs. 2(i)).When plotting the bias voltage dependence of the scat-tering pattern along the high symmetry directions Γ- X and Γ- M (Figs. 3(a) and (b) respectively), we observethat all scattering vectors q decrease in size when in-creasing the bias voltage above the Fermi level. Thequalitative behavior is very similar for both high sym-
20 nm -18 mV -7 mV 0 mV 16 mV7 mV (a) (c)(b) (e)(d) q γ q β q α
20 nm0.05 nm -1 (f)(g) (h) (i) (j) (k) FIG. 2. (a) Topography of the area where we have made the quasiparticle interference experiment shown in (b-k). The colorscale bar is given in the bottom right and the gray scale by the bar at the right. The image has been taken at a bias voltageof 30 mV and a current of 1 nA at zero magnetic field and at 0.3 K. (b-f) Tunneling conductance as a function of the positionfor a few representative bias voltages (given in each panel). The lateral scale bar is provided in (d). (g-k) Fourier transform,symmetrized taking into account the in-plane square lattice, of (b-f) shown in the first Brillouin zone. In (g) we mark the outermain scattering vector (black dashed circle) as well as the two inner scattering vectors (purple and green dashed circles). Thelateral scale bar is given in (i) and grey scale goes from low (black) to large (white) scattering intensity. metry directions, although the values of q γ are slightlylarger for Γ- X than for Γ- M . The reduction of the inten-sity inside the superconducting gap is band dependent.The superconducting gap is most clearly observed for thelargest scattering vector q γ .In Fig. 3(c) we show the scattering intensity aroundzero bias and at q γ as a function of the angle, with θ = 0 ◦ for Γ- X and θ = 45 ◦ for Γ- M . We find a fourfold mod-ulation of the superconducting density of states which isnot present in the stoichiometric compound and followsthe symmetry of the SVC[12, 13]. The superconductinggap is larger along the direction where the hyperfine fieldon the As1 sites cancels (Γ- X , orange lines in Fig. 3(c)),whereas it is smaller when the hyperfine field remains fi-nite (Γ- M , green lines in Fig. 3(c)), suggesting a compet-ing scenario between superconductivity and magnetism.We will analyze this observation further below.In what follows we investigate the origin of the threescattering vectors identified in Fig. 3(a,b). We havecalculated the electronic structure of CaKFe As andCaK(Fe . Ni . ) As in the tetragonal paramagneticphase within density functional theory as described inRef. [28]. The effect of Ni doping has been taken intoaccount with the Virtual Crystal Approximation (VCA).In Fig. 4(a) and (b) we show the respective Fermi sur-faces. As expected, upon Ni doping the inner hole pock-ets slightly shrink in CaK(Fe . Ni . ) As (Fig. 4(b))as compared to the pure compound (Fig. 4(a)) with theoverall structure of the Fermi surface remaining simi-lar. Our measurements (e.g. Fig. 3(a,b)) show, how-ever, that the scattering pattern is very different. InCaKFe As [13] the scattering pattern consists of a sin-gle scattering vector, associated to interband scattering between two hole bands centered at the Brillouin zonethat increases strongly in size when increasing the biasvoltage. In CaK(Fe . Ni . ) As there are three vec-tors whose size decreases much less drastically above theFermi level. The SVC magnetic order invokes a foldingof the band structure along the AFM wavevector due tothe doubling of the unit cell (see inset in Fig. 4(c)).We assume that folding is the main consequence of theSVC in the bandstructure. The folded electron bandsare shown in Fig. 4(c) and the Fermi surface in Fig.4(d)). The bands at the edges of the unfolded Brillouinzone are now centered around Γ, providing a clearly de-fined set of bands coexisting in the same Brillouin zoneregion as the hole pockets centered at Γ. In the calcu-lated bands we identify three scattering vectors betweenhole and electron bands whose size corresponds to theobserved q α , q β and q γ vectors (arrows in Figs. 4(c,d)).Their value decreases with increasing bias voltage as isalso found experimentally Fig. 3(a,b). Thus, the recon-structed Fermi surface provides an accurate descriptionof the band structure of CaK(Fe . Ni . ) As .We discuss now the observed fourfold modulationof the superconducting gap in CaK(Fe . Ni . ) As (Fig. 3(c)) which is not present in the stoichiomet-ric compound[12, 13]. NMR experiments, M¨ossbauerspectroscopy and muon spin rotation/relaxation stud-ies have shown evidence for the coexistence be-tween superconductivity and the magnetic order inCaK(Fe . Ni . ) As [23–25]. It has been also re-ported that, similar to what is found in 122 compoundsBa − x M x Fe As with M = Co, Ni and Rh[31–33] andBa(Fe − x K x ) As [34], the ordered magnetic moment isgradually suppressed when entering in the superconduct- -0.4 -0.2 0.0 0.2 0.4-30-20-100102030 B i as V o l t a g e ( m V ) q( p /a) -0.4 -0.2 0.0 0.2 0.4-30-20-100102030 B i as V o l t a g e ( m V ) q( p /a) (a) Angle q ( o ) E ( q γ ) ( m e V ) (c) q α q β q γ (b)
45 90 135 180 225 !" − !$ !" − !%
FIG. 3. (a) Scattering intensity for the two main symmetrydirections, Γ- X (left panel) and Γ- M (right panel). Opencircles mark the evolution of the scattering vectors with biasvoltage. Scattering vectors q α , q β and q γ are shown in black,violet and green. Color scale goes from low (blue) to high(red) scattering intensity. (b) Scattering intensity as a func-tion of the angle with respect to the in-plane a axis for energiesclose to the Fermi level in q γ . Color scale goes from blue (lowintensity) to cyan (high intensity). The vertical light greenand orange lines highlight the Γ- M and Γ- X directions respec-tively. The black dashed curve is a guide to the eye. The rightinset shows a schematic representation of the lattice, with Featoms in brown (and their spins represented by arrows), As1in blue and As2 in green and the main symmetry directionsas light green and orange lines. ing phase, suggesting that superconductivity and mag-netism are competing for the same electrons in the iron-based superconductors[24–26, 35]. Our results show thatthis competition is also associated with the developmentof a strongly anisotropic superconducting gap.The SVC phase is the only magnetic phase of pnictidesuperconductors where glide symmetry is broken withinthe unit cell. The relation between glide symmetry andsuperconductivity is not direct, because the coherencelength is larger than the unit cell size. However, it maylead to a spin-current density wave, or d -density wavewith increasing temperature or disorder[36]. The chi-ral properties of a spin-current density wave are con-nected to a pattern of currents inside the unit cell. The d -density wave has been suggested to be related to sit-uations with hidden order parameters, such as the lowtemperature ordered phase of URu Si or the pseudogapin the cuprates[37–39]. By contrast to usual magnetic (a) (b)(c) (d) FIG. 4. Fermi surface of (a) pure CaKFe As and (b)CaK(Fe . Ni . ) As in the paramagnetic phase, obtainedas described in the text. (c,d) Band structure and Fermi sur-face of CaK(Fe . Ni . ) As in the folded AFM Brillouinzone. Folded bands are shown in blue. Black, violet andgreen arrows are the main scattering vectors shown in Fig.3.Convention for the names of directions of folded and unfoldedBrillouin zones (inset of (c)) follows Ref. [30]. fluctuations, which peak at horizontal directions on theBrillouin zone and favor repulsive interactions, fluctua-tions related to SVC peak at the corners of the Brillouinzone are attractive[36]. Thus, there are in principle noexpected modifications of s ± pairing in the SVC. How-ever, the absence of local inversion symmetry, with theassociated potential spin current d -density wave plaque-tte pattern is likely to have a strong influence on thesuperconducting properties and might produce the four-fold nodeless anisotropic gap observed here[36–39]. Lon-don penetration depth measurements in pure and elec-tron irradiated crystals of CaK(Fe . Ni . ) As havesuggested the presence of an anisotropic superconductinggap with s ± symmetry which is more sensitive to disor-der than in the stoichiometric compound [40]. This canalso explain the observation of a finite density of statesat zero bias in CaK(Fe . Ni . ) As .In conclusion, we have measured the spatial depen-dence of the tunneling conductance in the SVC state ofCaK(Fe . Ni . ) As and report direct evidence for astrong mutual influence between superconductivity andSVC antiferromagnetic order. Quasiparticle interfer-ence measurements supported by band structure calcu-lations demonstrate a Fermi surface reconstruction andanisotropic pairing through an in-plane fourfold mod-ulation of the superconducting gap. The comparisonto CaKFe As , where there is no antiferromagnetic or-der and the superconducting gap shows no in-planeanisotropy, strongly suggests that the SVC antiferromag-netic state is responsible for the anisotropic pairing inCaK(Fe . Ni . ) As . ACKNOWLEDGMENTS
This work was supported by the Spanish Re-search State Agency (FIS2017-84330-R, RYC-2014-15093, CEX2018-000805-M), by the European Re-search Council PNICTEYES grant agreement 679080and by EU program Cost CA16218 (Nanocohy-bri), by the Comunidad de Madrid through programNANOMAGCOST-CM (Program No. S2018/NMT-4321) and by the Deutsche Forschungsgemeinschaft(DFG, German Research Foundation) through TRR 288- 422213477 (project A05). The research was supportedby the U.S. Department of Energy (DOE), Office of BasicEnergy Sciences, Division of Materials Sciences and Engi-neering. Ames Laboratory is operated for the U.S. DOEby the Iowa State University under Contract No. DE-AC02-07CH11358. WRM was supported by the Gordonand Betty Moore Foundations EPiQS Initiative throughGrant GBMF4411. We acknowledge SEGAINVEX atUAM for design and construction of cryogenic equipmentand the computational resources of the computer centerof the Goethe University Frankfurt. We also thank R.´Alvarez Montoya, S. 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