Dimensionality-driven metal-insulator-transition in spin-orbit coupled SrIrO_3
P. Schütz, D. Di Sante, L. Dudy, J. Gabel, M. Stübinger, M. Kamp, Y. Huang, M. Capone, M.-A. Husanu, V. Strocov, G. Sangiovanni, M. Sing, R. Claessen
DDimensionality-driven metal-insulator-transition in spin-orbit coupled SrIrO P. Sch¨utz, D. Di Sante, L. Dudy, J. Gabel, M. St¨ubinger, M. Kamp, Y. Huang, M. Capone, M.-A. Husanu,
5, 6
V. Strocov, G. Sangiovanni, M. Sing, and R. Claessen Physikalisches Institut and R¨ontgen Center for Complex Material Systems (RCCM),Universit¨at W¨urzburg, Am Hubland, D-97074 W¨urzburg, Germany Institut f¨ur Theoretische Physik und Astrophysik,Universit¨at W¨urzburg, Am Hubland, D-97074 W¨urzburg, Germany Van der Waals - Zeeman Insitute, University of Amsterdam,Science Park 904, 1098 XH Amsterdam, The Netherlands CNR-IOM-Democritos National Simulation Centre and International Schoolfor Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy National Institute of Materials Physics, Atomistilor 405 A, 077125 Magurele, Romania Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland (Dated: October 17, 2018)Upon reduction of the film thickness we observe a metal-insulator transition in epitaxially sta-bilized, spin-orbit coupled SrIrO ultrathin films. By comparison of the experimental electronicdispersions with density functional theory at various levels of complexity we identify the leadingmicroscopic mechanisms, i.e., a dimensionality-induced re-adjustment of octahedral rotations, mag-netism, and electronic correlations. The astonishing resemblance of the band structure in the two-dimensional limit to that of bulk Sr IrO opens new avenues to unconventional superconductivityby ”clean” electron doping through electric field gating. Although typically viewed as disparate properties, theinterplay between strong spin-orbit coupling (SOC) andelectronic correlations in high- Z d transition metaloxides can lead to exotic quantum states of matterlike Kitaev spin liquids [1, 2] and topological phases[3, 4]. Sr IrO , the quasi-two-dimensional member( n = 1) of the layered-perovskite Ruddlesden-Popperseries Sr n +1 Ir n O n +1 , has attracted special attention asa possible parent material for exotic superconductivitysince it exhibits a SOC-driven Mott insulating state [5],which largely reproduces the fermiology of hole-dopedcuprates upon electron-doping [6, 7]. In contrast, itsmetastable three-dimensional ( n = ∞ ) counterpartSrIrO exhibits a semimetallic state [8] believed to bein proximity to a dimensionality-driven metal-insulatortransition (MIT) [9].In this Letter, we investigate the electronic and struc-tural properties of epitaxially-grown ultrathin perovskiteSrIrO films by tuning the film thickness with atomicprecision. We observe the opening of a distinct chargegap at the chemical potential and concurrent changesin the film crystalline structure when approaching thetwo-dimensional limit. In a combined experimentaland theoretical approach using soft x-ray angle-resolvedphotoelectron spectroscopy (SX-ARPES) and ab initio density functional theory (DFT and DFT+ U ) calcu-lations we investigate the evolution of the electronicband structure across the film thickness-driven MIT andshed light on the complex interplay between electroniccorrelations, structural degrees of freedom, magnetism,and dimensionality.SrIrO thin films were heteroepitaxially grown onTiO -terminated SrTiO (001) substrates by pulsed laser deposition (PLD) from a polycrystalline SrIrO target. The films adopt a pseudo-tetragonal perovskitestructure with an in-plane lattice constant locked tothat of SrTiO ( a = 3 .
905 ˚A) and an out-of-plane latticeconstant of 3 .
99 ˚A. Due to collective rotations of theIrO octahedra ( a + b − b − in Glazer notation with the a -axis along the [100] or [010] direction of the substrate[8, 10]) the real-space unit cell is enlarged by 2 × √ × √ ab initio simulation package [14] within the projector-augmented-plane-wave (PAW) method [15, 16], using the generalizedgradient approximation (GGA) as parametrized by thePBE GGA functional [17]. Spin-orbit coupling was self-consistently included [18] and the Coulomb repulsion U and exchange interaction J of Ir d orbitals were treatedwithin the rotationally invariant DFT+ U scheme ofLiechtenstein et al. [19].Figure 1 shows the experimental and theoretical bandstructures along the high-symmetry lines Γ-X-M-Γ andZ-R-A-Z obtained from SX-ARPES on a 9 unit cells (uc)thick metallic SrIrO film and paramagnetic DFT(+ U )calculations for the bulk material. As starting point forthe analysis of the photoemission data we consider asimplified tetragonal perovskite structure compressivelystrained to the SrTiO substrate ( a ⊥ /a STO ≈ . U andexchange-coupling J on the DFT(+ U ) band structure a r X i v : . [ c ond - m a t . s t r- e l ] J un FIG. 1. (Color online) (a) Real and (b) reciprocal space structure of strained, tetragonal SrIrO without octahedral rotations.(c), (d) E vs k dispersions along the high-symmetry lines Γ-X-M-Γ and Z-R-A-Z measured by SX-ARPES ( hν = 745 eV and hν = 660 eV, respectively) and compared to DFT+ U calculations. The band structure was calculated for the tetragonal settingand projected onto a J eff = (1 / , /
2) basis with (c) U = 0 eV and J = 0 eV and (d) U = 3 . J = 0 . U and exchange coupling J . and Fermi surface topology. The resulting bands areprojected onto a J eff = (1 / , /
2) basis that can berepresented as a linear combination of Ir 5 d t g -orbitalsand a mixture of up and down spin states. As seenin Fig. 1 (c) and (e) DFT calculations already capturesome of the low-energy spectral features. However,most noteworthy, they predict an Ir 5 d e g electronpocket around Γ and an Ir J eff = 3 / U , which would bea magnetic insulator at variance with experiment, wediscard magnetism for this 9 uc film. In this framework, U mainly acts to shift orbitals with different occupationsrelative to each other. We chose its value to match theposition of the ARPES bands, thereby pushing the bandsabove (below) the chemical potential, whereupon the e g electrons are being predominantly transferred into the J eff = 3 / J eff = 1 / U and J are significantlylarger than ab initio estimates using the constraintrandom phase approximation (cRPA) [20, 21]. A moreaccurate treatment of the many-body processes basedon dynamical mean field theory (DMFT) would mostlikely account for the experimental features with smallervalues of the interaction (for DMFT studies for Sr IrO see Refs. 22 and 23).Despite the overall good agreement a closer inspectionof the theoretical DFT+ U band structure still reveals subtle remaining differences to the experimental data.In particular, the narrow band at the chemical potentialbetween X- and M-point and the spectral weight nearthe R-point are not captured in the DFT+ U calculationsin Fig. 1 (d). Indeed, previous ARPES studies usingultraviolet light have reported distinct narrow bandsnear the chemical potential resulting from backfoldingdue to octahedral rotations [8]. As shown in Fig. 2 (a)collective rotations of IrO octahedra introduce aperiodic perturbation of the crystal potential, thatenlarges the real-space unit cell by 2 × √ × √ ≈
400 meV and resolve the aforementioned discrepanciesbetween experiment and theory by exhibiting Fermicrossings around the X- and R-point. Note that due tothe breaking of translational symmetry the magnitudeof octahedral rotations may be enhanced at the surfaceof thicker films, which could explain the more evidentobservation of a backfolded band structure in highlysurface-sensitive ARPES measurements using He I light[8, 25] as opposed to bulk-sensitive photoemission in thesoft x-ray regime [26, 27].
FIG. 2. (Color online) (a) Real-space lattice structure ofSrIrO including octahedral rotations ( a + b − b − in Glazer no-tation with the a -axis orthogonal to the film surface normal)and strain. The orthorhombic unit cell (blue) is enlarged by2 × √ × √ U band structure calculatedin the orthorhombic setting and unfolded into the tetragonalBrillouin zone. The metastable, pseudo-cubic perovskite phase ofSrIrO can be regarded as the n = ∞ member of theSr n +1 Ir n O n +1 = ([SrIrO ] n ,SrO) Ruddlesden-Popperseries. These compounds essentially consist of n SrIrO perovskite layers, which are intercalated by SrO layersand laterally shifted with respect to each other such thatno Ir-O-Ir bonds persist between neighboring [SrIrO ] n blocks [28]. As shown above perovskite SrIrO can bestabilized as epitaxial thin films, that essentially exhibitbulk electronic and structural properties [10, 29] abovea thickness of at least 9 uc, i.e., paramagnetism andmetallicity with a partially filled J eff = 1 / n = 2) and single-layer ( n = 1)compounds Sr Ir O and Sr IrO are insulators thatexhibit a complex collinear and canted antiferromagneticorder, respectively. The intriguing variety of physicalproperties within this family of compounds is com-monly explained by a dimensional crossover from thetwo-dimensional ( n = 1) to the three-dimensional limit( n = ∞ ). It is thus tempting to tune the dimensionalityin SrIrO thin films by reducing the number of mono-layers and trace the electronic and structural changes.Figure 3 (a) shows photoemission spectra (He I, hν = 21 . films with thicknesses of m = 4 , , , ). Thickerfilms ( m ≥
4) exhibit a metallic density of states with apronounced Fermi-Dirac cut-off at the chemical potentialas expected in the three-dimensional limit. Intriguingly, at m = 3 the Fermi cut-off disappears and upon furtherreduction of the film thickness a distinct charge gapopens. Hence, in analogy to the Ruddlesden-Popperiridates the films undergo a metal-insulator transition asfunction of dimensionality as also observed in transportmeasurements [30]. As shown in the inset of Fig. 3 (a)magnetic DFT+ U calculations for m SrIrO layers on4 SrTiO layers ( m //4) similarly show a decreasingcharge gap in the k integrated density of states (DOS)as m is increased. Note that in the presence of magneticordering the increasing film thickness alone does nottrigger a transition from insulating to metallic in ourcalculations.The photoemission gap opening is accompanied by astructural transition as inferred from low energy (LEED)and reflection high-energy electron diffraction (RHEED)from the film surface. As seen in Fig. 3 (b) the surfaceperiodicity changes from √ × √ m ≤
3) to 2 × m ≥
4) with respect to the pseudo-tetragonal unit cell.Here, the doubling of the surface periodicity in the thickfilms simply reflects the complex rotational patternof IrO octahedra in the bulk as shown in Fig. 3 (c),where the top layer of a SrIrO film with a + b − b − bulkstructure is depicted. However, for atomically thinfilms rotations about the [100] and [010] directions aresuppressed since the SrIrO film forms a corner-sharedoctahedral network with the SrTiO substrate, whichis a cubic perovskite without octahedral rotationsat room temperature ( a a a ). Thus, only rotationsabout the surface normal ( a a b + / − in Glazer notation)may prevail in thin films ( m ≤ √ × √ IrO and Sr Ir O alsoexhibit octahedral rotations exclusively about the c -axisreducing their space group symmetry from I /mmm to I /acd and Bbcb , respectively [31–34].Figure 4 (a) shows the SX-ARPES bandmap of a 1uc SrIrO film grown on Nb:SrTiO in comparison tothe DFT+ U band structure of a 1 // //SrTiO slab along the pseudo-tetragonal high-symmetry lineΓ-X-M-Γ. In excellent agreement with each other theexperimental and theoretical data exhibit a flat bandbehavior with a valence band maximum at the M-point.Interestingly, as seen in the k -integrated DOS of the1//4 slab in Fig. 4 (b), only the antiferromagneticsolution yields an insulating ground state, whereasthe paramagnetic solution remains metallic like in thethree-dimensional limit. This finding is in line with theenhanced spin fluctuations near the thickness-drivenMIT recently observed in magnetoconductance mea-surements of samples identical to ours [30]. Similarly,the dimensionality-induced metal-insulator transitionsobserved in Ruddlesden-Popper iridate crystals [1, 34–37] and [(SrIrO ) m , SrTiO ] superlattices [38] areaccompanied by a magnetic transition. Intriguingly, theantiferromagnetic DFT+ U band structure of the 1//4 FIG. 3. (Color online) (a) Ultraviolet photoelectron spectroscopy (UPS) of SrIrO films with thickness m (bare Nb:SrTiO , m = 1 , , , U slab calculations of m SrIrO layers on 4 SrTiO layers ( m //4). (b) LEED and RHEED patterns of an insulating ( m = 3) and a metallic ( m = 4)SrIrO film exhibit a structural transition from a √ × √ × √ × √
2/ 2 × a a b + / − / a + b − b − IrO octahedral rotations in the film. SrIrO slab shows a striking similarity to that of bulkSr IrO shown in Fig. 4 (c).For a deeper understanding of the driving mechanismbehind the metal-insulator-transition one needs to takeinto account the subtle interplay between the dominant,comparably strong physical interactions ( U , W , SOC)in 5 d transition metal oxides, which leaves the electronicand magnetic ground state highly susceptible to smallexternal perturbations. Here we have demonstrated thatthe SrIrO film thickness can be used as experimentalcontrol parameter to tune three physical properties,which cooperatively determine the system’s groundstate. Firstly, the effective Coulomb interaction U/W increases upon reduction of m since the coordination ofIr sites becomes smaller, hence providing less hoppingchannels (smaller W ) and less screening (bigger U )[21]. Secondly, the crystalline structure due to theIrO rotations deviates from the rotational pattern ofbulk SrIrO in the two-dimensional limit, since theoctahedral network with the cubic SrTiO substrateimposes constraints upon the in-plane rotations. Finally,the magnetic ordering is susceptible to the dimension-ality due to the strong competition between intra- andinterlayer coupling [34].The strong cooperative interplay between these degreesof freedom constitutes the complexity of the system.Specifically, octahedral rotations strongly affect themagnetic coupling in iridates due to pseudodipolarand Dzyaloshinsky-Moriya exchange interactions asevidenced by the locking of the Ir magnetic momentsto the rotated oxygen octahedra in Sr IrO [36]. In turn, the symmetry breaking due to octahedral rotationsprovides further spin-dependent hopping terms in the J eff basis that additionally increase the kinetic energy W [37]. This tendency is reflected in the (albeit small)resistivity drop at T = 105 K [39], where the SrTiO substrate undergoes a structural transition involv-ing a a c − -rotations of the TiO octahedra [40, 41],which can induce in-plane tiltings in the SrIrO filmdepending on the domain structure in the SrTiO .On the other hand changes in U/W will affect themagnetic ordering by altering the required criticalon-site Coulomb repulsion U for a magnetic transitionto antiferromagnetic order [37]. The underlying reasonfor this extraordinary dimensionality-dependence is thespatially three-dimensional J eff = 1 / d systems.This is in stark contrast to typical 3 d systems like thecuprates, where the planar e g orbitals host the S = 1 / IrO as a potential parent materialfor exotic superconductivity, the analogy between mono- FIG. 4. (Color online) (a) SX-ARPES bandmap of a SrIrO monolayer grown on Nb:SrTiO and DFT+ U bandstructure ofa 1 // //SrTiO slab along the pseudo-tetragonal high-symmetry line Γ-X-M-Γ. (b) DFT+ U k -integrated density ofstates (DOS) of the 1 // ≈ U band structure calculation for bulk Sr IrO . layer SrIrO and bulk Sr IrO may open a promisingexperimental avenue towards electron doping withoutthe introduction of disorder through electrostatic orion-liquid gating, possibly pushing the system into anovel, spin-orbit driven superconducting phase.This work was supported by the Deutsche Forschungs-gemeinschaft (SFB 1170 ToCoTronics [1] G. Jackeli and G. Khaliullin, Physical Review Letters , 017205 (2009).[2] W. Witczak-Krempa, G. Chen, Y. B. Kim, and L. Ba-lents, Annual Review of Condensed Matter Physics , 57(2014).[3] D. Pesin and L. Balents, Nature Physics , 376 (2010).[4] X. Zhang, H. Zhang, J. Wang, C. Felser, and S.-C.Zhang, Science , 1464 (2012).[5] B. Kim, H. Jin, S. Moon, J.-Y. Kim, B.-G. Park,C. Leem, J. Yu, T. Noh, C. Kim, S.-J. Oh, J.-H. Park,V. Durairaj, G. Cao, and E. Rotenberg, Physical ReviewLetters , 076402 (2008). [6] Y. K. Kim, O. Krupin, J. D. Denlinger, A. Bostwick,E. Rotenberg, Q. Zhao, J. F. Mitchell, J. W. Allen, andB. J. Kim, Science , 187 (2014).[7] Y. K. Kim, N. H. Sung, J. D. Denlinger, and B. J. Kim,Nature Physics , 37 (2016).[8] Y. F. Nie, P. D. C. King, C. H. Kim, M. Uchida, H. I.Wei, B. D. Faeth, J. P. Ruf, J. P. C. Ruff, L. Xie, X. Pan,C. J. Fennie, D. G. Schlom, and K. M. Shen, PhysicalReview Letters , 016401 (2015).[9] S. J. Moon, H. Jin, K. W. Kim, W. S. Choi, Y. S. Lee,J. Yu, G. Cao, A. Sumi, H. Funakubo, C. Bernhard, andT. W. Noh, Physical Review Letters , 226402 (2008).[10] J. M. Longo, J. A. Kafalas, and R. J. Arnott, Journal ofSolid State Chemistry , 174 (1971).[11] See Supplemental Material.[12] V. N. Strocov, T. Schmitt, U. Flechsig, T. Schmidt,A. Imhof, Q. Chen, J. Raabe, R. Betemps, D. Zimoch,J. Krempasky, X. Wang, M. Grioni, A. Piazzalunga, andL. Patthey, Journal of Synchrotron Radiation , 631(2010).[13] V. N. Strocov, X. Wang, M. Shi, M. Kobayashi, J. Krem-pasky, C. Hess, T. Schmitt, and L. Patthey, Journal ofSynchrotron Radiation , 32 (2013).[14] G. Kresse and J. Furthm¨uller, Physical Review B ,11169 (1996).[15] P. E. Bl¨ochl, Physical Review B , 17953 (1994).[16] G. Kresse and D. Joubert, Physical Review B , 1758(1999).[17] J. P. Perdew, K. Burke, and M. Ernzerhof, PhysicalReview Letters , 3865 (1996).[18] S. Steiner, S. Khmelevskyi, M. Marsmann, andG. Kresse, Physical Review B , 224425 (2016).[19] A. I. Liechtenstein, Physical Review B , R5467 (1995).[20] H. Zhang, K. Haule, and D. Vanderbilt, Physical ReviewLetters , 246402 (2013).[21] B. Kim, P. Liu, and C. Franchini, Physical Review B , 115111 (2017).[22] R. Arita, J. Kuneˇs, A. V. Kozhevnikov, A. G. Eguiluz,and M. Imada, Physical Review Letters , 086403(2012).[23] C. Martins, M. Aichhorn, L. Vaugier, and S. Biermann, Physical Review Letters , 266404 (2011).[24] W. Ku, T. Berlijn, and C.-C. Lee, Physical Review Let-ters , 216401 (2010).[25] Z. T. Liu, M. Y. Li, Q. F. Li, J. S. Liu, W. Li, H. F.Yang, Q. Yao, C. C. Fan, X. G. Wan, Z. Wang, andD. W. Shen, Scientific Reports , 30309 (2016).[26] A. Yamasaki, H. Fujiwara, S. Tachibana, D. Iwasaki,Y. Higashino, C. Yoshimi, K. Nakagawa, Y. Nakatani,K. Yamagami, H. Aratani, O. Kirilmaz, M. Sing,R. Claessen, H. Watanabe, T. Shirakawa, S. Yunoki,A. Naitoh, K. Takase, J. Matsuno, H. Takagi,A. Sekiyama, and Y. Saitoh, Physical Review B ,115103 (2016).[27] Recently, a Dirac-like feature in the band structure ofSrIrO has been discussed in the literature. For more de-tails related to our present work see Supplemental Mate-rial section VIII.[28] S. N. Ruddlesden and P. Popper, Acta Crystallographica , 54 (1958).[29] J. G. Zhao, L. X. Yang, Y. Yu, F. Y. Li, R. C. Yu,Z. Fang, L. C. Chen, and C. Q. Jin, Journal of AppliedPhysics , 103706 (2008).[30] D. J. Groenendijk, C. Autieri, J. Girovsky, M. CarmenMartinez-Velarte, N. Manca, G. Mattoni, A. M. R. V. L.Monteiro, N. Gauquelin, A. F. Otte, M. Gabay, S. Pi-cozzi, and A. D. Caviglia, to be published.[31] M. K. Crawford, M. A. Subramanian, R. L. Harlow, J. A.Fernandez-Baca, Z. R. Wang, and D. C. Johnston, Phys-ical Review B , 9198 (1994). [32] M. A. Subramanian, M. K. Crawford, and R. L. Harlow,Materials Research Bulletin , 645 (1994).[33] G. Cao, Y. Xin, C. S. Alexander, J. E. Crow,P. Schlottmann, M. K. Crawford, R. L. Harlow, andW. Marshall, Physical Review B , 214412 (2002).[34] J. W. Kim, Y. Choi, J. Kim, J. F. Mitchell, G. Jackeli,M. Daghofer, J. van den Brink, G. Khaliullin, and B. J.Kim, Physical Review Letters , 037204 (2012).[35] S. Boseggia, R. Springell, H. C. Walker, A. T. Boothroyd,D. Prabhakaran, D. Wermeille, L. Bouchenoire, S. P.Collins, and D. F. McMorrow, Physical Review B ,184432 (2012).[36] S. Boseggia, H. C. Walker, J. Vale, R. Springell, Z. Feng,R. S. Perry, M. M. Sala, H. M. Rønnow, S. P. Collins,and D. F. McMorrow, Journal of Physics: CondensedMatter , 422202 (2013).[37] J.-M. Carter, V. Shankar V., and H.-Y. Kee, PhysicalReview B , 035111 (2013).[38] J. Matsuno, K. Ihara, S. Yamamura, H. Wadati, K. Ishii,V. V. Shankar, H.-Y. Kee, and H. Takagi, Physical Re-view Letters , 247209 (2015).[39] D. J. Groenendijk, N. Manca, G. Mattoni, L. Kootstra,S. Gariglio, Y. Huang, E. van Heumen, and A. D. Cav-iglia, Applied Physics Letters , 041906 (2016).[40] G. Shirane and Y. Yamada, Physical Review , 858(1969).[41] A. M. Glazer, Acta Crystallographica Section B Struc-tural Crystallography and Crystal Chemistry28