Ab initio calculations of the atomic and electronic structure of CaTiO3 (001) and (011) surfaces
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J u l Ab initio calculations of the atomic and electronic structure of CaTiO (001) and (011)surfaces R. I. Eglitis and David Vanderbilt
Department of Physics and Astronomy, Rutgers University,136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA (Dated: July 30, 2008)We present the results of calculations of surface relaxations, energetics, and bonding propertiesfor CaTiO (001) and (011) surfaces using a hybrid B3PW description of exchange and correlation.We consider both CaO and TiO terminations of the non-polar (001) surface, and Ca, TiO and Oterminations of the polar (011) surface. On the (001) surfaces, we find that all upper-layer atomsrelax inwards on the CaO-terminated surface, while outward relaxations of all atoms in the secondlayer are found for both terminations. For the TiO -terminated (001) surface, the largest relaxationsare on the second-layer atoms. The surface rumpling is much larger for the CaO-terminated thanfor the TiO -terminated (001) surface, but their surface energies are quite similar at 0.94 eV and1.13 eV respectively. In contrast, different terminations of the (011) CaTiO surface lead to verydifferent surface energies of 1.86 eV, 1.91 eV, and 3.13 eV for the O-terminated, Ca-terminated, andTiO-terminated (011) surface respectively. Our results for surface energies contrast sharply withthose of Zhang et al. [Phys. Rev. B , 115426 (2007)], where the authors found a rather differentpattern of surface energies. We predict a considerable increase of the Ti-O chemical bond covalencynear the (011) surface as compared both to the bulk and to the (001) surface. PACS numbers: 68.35.Ct, 68.35.Md, 68.47.Gh
I. INTRODUCTION
Oxide perovskites are in demand for a variety of in-dustrial applications as a result of their diverse physi-cal properties.
For example, CaTiO is a cubic per-ovskite that is widely used in electronic ceramic ma-terials and as a key component of synthetic rock toimmobilize high-level radioactive waste. Thin films ofABO perovskite ferroelectrics are important for manyapplications. In particular, the titanates are interestingmaterials regarding their electrochemical properties andare promising as components for electrodes and sensors.Surface properties of CaTiO are important for cataly-sis and for epitaxial growth of high T c superconductors.For all these applications, the surface structure and theassociated surface electronic and chemical properties areof primary importance.In view of this technological importance, it is surprisingthat there have been so few ab initio studies of CaTiO surface atomic and electronic structure. For the CaTiO (001) surface we are only aware of the work of Wang etal. and Zhang et al. In contrast, several other ABO perovskite (001) surfaces have been widely studied. Forexample, ab initio andclassical shell-model studies were published for the(001) surfaces of SrTiO . The (001) surfaces of cu-bic perovskites have also been extensively investigatedexperimentally. For example, the SrTiO (001) sur-face relaxations and rumplings have been studied bymeans of low energy electron diffraction (LEED), reflec-tion high-energy electron diffraction (RHEED), mediumenergy ion scattering (MEIS), and surface x-ray diffrac-tion (SXRD) measurements. The status of thedegree of agreement between theory and experiment for these SrTiO surfaces is summarized in Ref. [7].ABO perovskite (011) surfaces are considerably less-well studied than (001) surfaces, both experimentallyand theoretically. However, there has been a surge ofrecent interest, focusing mainly on SrTiO , in whichSTM, UPS, XPS, and Auger spectroscopies as wellas LEED studies have been carried out. Onthe theory side, the first ab initio calculations for SrTiO (011) surfaces were performed by Bottin et al. , whocarried out a systematic study of the electronic andatomic structures of several (1 ×
1) terminations of the(011) polar orientation of the SrTiO surface. Theyfound that the electronic structure of the stoichiomet-ric SrTiO and O terminations showed marked differ-ences with respect to the bulk as a consequence of thepolarity compensation. Later, Heifets et al. performed ab initio Hartree-Fock (HF) calculations for four possi-ble non-polar terminations (TiO, Sr, and two kinds Oterminations) of the SrTiO (011) surface. The authorsfound that the surface energy of the O-terminated (011)surface is close to that of the (001) surface, suggestingthat both (011) and (001) surfaces can coexist in poly-crystalline SrTiO . Most recently, we performed an abinitio study of SrTiO (011) surfaces using a hybridHartree-Fock (HF) and density-functional theory (DFT)exchange-correlation functional, in which HF exchangeis mixed with Becke’s three-parameter DFT exchangeand combined with the nonlocal correlation functional ofPerdew and Wang (B3PW). Our calculations indi-cated a remarkably large increase in the Ti-O bond cova-lency at the TiO-terminated (011) surface, significantlylarger than for the (001) surfaces.Regarding other ABO (011) surfaces, Heifets et al. investigated the atomic structure and charge redistribu-tion of different terminations of BaZrO (011) surfacesusing density-functional methods. They found that theO-terminated (011) surface had the smallest cleavage en-ergy among (011) surfaces, but that this value was stilltwice as large as the cleavage energy needed for the for-mation of a pair of complementary (001) surfaces. More-over, we recently performed ab initio B3PW calculationsfor the technologically important BaTiO and PbTiO (011) surfaces. Our calculated surface energies showedthat the TiO -terminated (001) surface is slightly morestable than the BaO- or PbO-terminated (001) surfacefor both materials, and that O-terminated BaTiO andTiO-terminated PbTiO (011) surfaces have surface en-ergies close to that of the (001) surface.The only existing ab initio study of CaTiO (011) polarsurfaces was performed by Zhang et al. In addition tothe (001) surfaces, they studied four possible non-polarterminations of the (011) surface, namely the TiO, Ca,asymmetric A-type O, and symmetric B-type O termina-tions. The results indicated that the most favorable sur-faces are the CaO-terminated (001) surface, the A-typeO-terminated (011) surface, and the TiO -terminated(001) surface, in that order.With the sole exception of the calculation onCaTiO by Zhang et al. , all of the first-principlesand shell-model studies of ABO perovskite surfaceenergies have found that the lowest-energy (001) surface is lower in energy than any of the(011) terminations. Zhang et al. , on the contrary, re-ported a surface energy of 0.837 eV for their “A-type”O-terminated (011) surface of CaTiO , to be comparedwith 1.021 eV for the TiO -terminated (001) surface. Be-cause this result contrasts sharply with the other previouscalculations, we were particularly motivated to check thisresult independently in our current study.In this study, we have performed predictive ab initio calculations for CaTiO (001) and (011) surfaces, usingthe same B3PW approach as in our previous work. As in the work of Zhang et al. , we do not explicitlyinclude octahedral rotations in the surface calculations,even though such rotations are likely to be more impor-tant for CaTiO than for many other perovskites; we dis-cuss and justify this approximation at the end of Sec. II.In contradiction to the work of Zhang et al. , we findthat the pattern of surface energies of CaTiO is similarto that of other perovskites. In particular, we find thatthe O-terminated CaTiO (011) surface is higher in en-ergy than either of the TiO - or CaO-terminated (001)surfaces. We also report the surface relaxations and rum-plings and the charge redistributions and changes in bondstrength that occur at the surface.The manuscript is organized as follows. In Sec. II wepresent our computational method and provide detailsof the surface slab models on which the calculations wereperformed. The results of our calculations for surfacestructures, energies, charge distributions, and bond pop-ulations are reported in Sec. III. Finally, we discuss theresults and present our conclusions in Sec. IV. II. COMPUTATIONAL METHOD ANDSURFACE SLAB CONSTRUCTION
To perform the first-principles DFT-B3PW calcula-tions we used the CRYSTAL-2003 computer code, which employs Gaussian-type functions (GTFs) localizedat atoms as the basis for an expansion of the crystallineorbitals. The features of the CRYSTAL-2003 code thatare most important for this study are its ability to cal-culate the electronic structure of materials within bothHartree-Fock and Kohn-Sham Hamiltonians and its abil-ity to treat isolated 2D slabs without artificial repetitionalong the z -axis. However, in order to employ the linearcombination of atomic orbitals (LCAO)-GTF method, itis desirable to have optimized basis sets (BS). The BS op-timization for SrTiO , BaTiO , and PbTiO perovskiteswas developed and discussed in Ref. [44]. Here we em-ploy this BS, which differs from that used in Refs. [12,13]by inclusion of polarizable d -orbitals on O ions. It wasshown that this leads to better agreement of the cal-culated lattice constant and bulk modulus with experi-mental data. For the Ca atom we used the same BS asin Ref. [45].Our calculations were performed using the hybridexchange-correlation B3PW functional involving a hy-brid of non-local Fock exact exchange, LDA exchange andBecke’s gradient corrected exchange functional, com-bined with the nonlocal gradient corrected correlationpotential by Perdew and Wang. The Hay-Wadt small-core effective core pseudopotentials (ECP) were adoptedfor Ca and Ti atoms. The small-core ECP’s replaceonly the inner core orbitals, while orbitals for sub-valenceelectrons as well as for valence electrons are calculatedself-consistently. Oxygen atoms were treated with theall-electron BS.The reciprocal space integration was performed bysampling the Brillouin zone of the five-atom cubic unitcell with an 8 × × and an 8 × The CaTiO (001) surfaces were modeled with two-dimensional slabs consisting of several planes perpendic-ular to the [001] crystal direction. To simulate CaTiO (001) surfaces, we used slabs consisting of seven alter-nating TiO and CaO layers, with mirror symmetry pre-served relative to the central layer. The 17-atom slabwith CaO-terminated surfaces and the 18-atom slab withTiO -terminated surfaces are shown in Figs. 1(a) and (b)respectively. These slabs are non-stoichiometric, withunit-cell formulae Ca Ti O and Ca Ti O , respec-tively. These two (CaO and TiO ) terminations are theonly possible flat and dense (001) surface terminationsof the perovskite structure. The sequence of layers with (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) a)b) TiOCa
FIG. 1: (Color online.) Side view of CaTiO (001) surfaces.(a) CaO-terminated surface. (b) TiO -terminated surface,with definitions of surface rumpling s and the near-surfaceinterplanar separations ∆ d and ∆ d . (001) orientation, and the definitions of the surface rum-pling s and the interplane distances ∆ d and ∆ d , areillustrated in Fig. 1.The problem in modeling the CaTiO (011) polar sur-face is that, unlike the CaTiO (001) neutral surface, itconsists of charged O-O and CaTiO planes, as illustratedin Fig. 2. Assuming nominal ionic charges of O − , Ti ,and Ca , a simple cleavage would create a negatively-charged O-O surface and a positively-charged CaTiOsurface, leading either to an infinite macroscopic dipolemoment perpendicular to the surface for a stoichiomet-ric slab terminated by planes of different kinds (O andCaTiO) as in Fig. 3(a), or to a net infinite charge for anon-stoichiometric symmetric slab as shown in Figs. 3(b)and (c). It is known that such crystal terminations makethe surface unstable. In proper first-principles calcu-lations on slabs of finite thickness, charge redistributions
TiOCa (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) z, [110] y, [−110]x, [00−1] [110], CaTiO [110], O (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) FIG. 2: (Color online.) Sketch of the cubic CaTiO perovskitestructure showing two (011) cleavage planes that give rise tocharged CaTiO and O (011) surfaces. (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1) a)b)c) d)f)e) FIG. 3: (Color online.) Possible (011) surface slab mod-els considered in the text. [(a)-(c)] Slabs obtained by sim-ple cleavage, yielding mixed, O-terminated, and CaTiO-terminated polar surfaces, respectively. [(d)-(f)] Slabs withnonpolar TiO-terminated, Ca-terminated, and O-terminatedsurfaces, respectively. near the surface arising during the self-consistent fieldprocedure could, in principle, compensate at least par-tially for these effects. However, previous careful studiesfor SrTiO have demonstrated that the resultingsurfaces have a high energy, and that the introduction ofsurface vacancies provides an energetically less expensivemechanism for compensating the surfaces.For these reasons, we limit ourselves here to non-polarCaTiO (011) surfaces that have been constructed bymodifying the composition of the surface layer. Remov-ing the Ca atom from the upper and lower layers ofthe 7-layer symmetric CaTiO-terminated slab generatesa neutral and symmetric 16-atom supercell with TiO-terminated surfaces as illustrated in Fig. 3(d). Remov-ing both the Ti and O atoms from the upper and lowerlayers of the 7-layer symmetric CaTiO-terminated slabyields a neutral and symmetric 14-atom supercell withCa-terminated surfaces as shown in Fig. 3(e). Finally,removing the O atom from the upper and lower layersof the 7-layer symmetric O-O terminated slab, we ob-tain the neutral and symmetric 15-atom supercell withO-terminated surfaces shown in Fig. 3(f). The stoichiom-etry of these surface terminations, and the number ofbonds cleaved, are comprehensively discussed for the caseof SrTiO in Ref. [29].Before leaving this Section, it is worth discussing the TABLE I: Calculated effective charges Q and bond popula-tions P (in e ) for bulk CaTiO .Ion or bond Property ValueCa Q Q − Q P P P − issue of the tilting of TiO octahedra in CaTiO . Xrayand neutron diffraction studies have not definitively es-tablished the phase-transition sequence at higher tem-perature, but clearly show that the crystal adopts anorthorhombic structure with space group P bnm below ∼ This room-temperature ground statehas a 20-atom unit cell and is a slight modification fromthe ideal perovskite structure involving a pattern of tiltsof the TiO octahedra according to the a − a − c + patternin Glazer’s notation. The octahedral tilts have alsobeen studied using first-principles calculations.
Be-cause these tilts are substantial ( ∼ ◦ ), it is possiblethat they may have some impact on the surface structureand energetics. However, we have not included octahe-dral tilts in the work presented here for several reasons.First, we want to compare with previous calculations,which have universally not included octahedral tilts. Sec-ond, the CRYSTAL-2003 code package does not providefor efficient structural optimization as would be neededto study these tilts, and the larger surface unit cells thatwould be required would make the calculations impracti-cal. But finally and most importantly, we estimate thatthe energy scale of the tilts ( ∼ III. RESULTS OF CALCULATIONSA. CaTiO bulk atomic and electronic structure As a starting point of our calculations, we calculatedthe CaTiO bulk lattice constant and found it to be3.851 ˚A, slightly smaller than the experimental value of3.895 ˚A. We used the theoretical bulk lattice constantin the following surface structure calculations. To char-acterize the chemical bonding and covalency effects, weused a standard Mulliken population analysis for the ef-fective atomic charges Q , bond populations P , and otherlocal properties of the electronic structure as describedin, e.g., Refs. [59,60]. Our calculated effective chargesand bond populations for bulk CaTiO are presented in TABLE II: Computed atomic relaxation (in percent of thebulk lattice constant a ) for the TiO - and CaO-terminatedCaTiO (001) surfaces. Positive values indicate outward dis-placements.CaO-terminated TiO -terminatedLayer Ion This study Ion This study1 Ca − − − − Table I. The bond population of the Ti–O bond is clearlymuch larger than that of the Ca–O bond, consistent withpartial Ti–O covalency, and the small but negative O–Opopulation indicates a repulsive overlap of oxygen shellsin bulk CaTiO . B. CaTiO (001) surface structure The atomic displacements obtained using the ab initio
B3PW method for TiO - and CaO-terminated CaTiO (001) surfaces are shown in Table II. According to the re-sults of our calculations, atoms of the first surface layerrelax inwards, i.e. towards the bulk, for both TiO andCaO-terminated (001) surfaces. The latter result is indisagreement with the previous calculations of Wang etal. , who calculated that the first-layer oxygen atoms onthe (001) surface should relax outwards by 0.7% of thebulk lattice constant a . According to our calculations,they move inwards by 0.42% of a . Our calculated in-ward relaxation of the first-layer oxygen atoms on theCaO-terminated CaTiO (001) surface is in line with pre-vious ab initio studies dealing with BaTiO , PbTiO ,and BaZrO (001) surfaces, but contrasts withthe outward relaxation of first-layer oxygen atoms on theSrO-terminated SrTiO (001) surface. According tothe results of our current calculations, outward relax-ations are found for all atoms in the second layer forboth CaO and TiO terminations of the CaTiO (001)surface.Table II shows that the relaxations of the surface metalatoms are much larger than those of the oxygens on boththe TiO - and CaO-terminated CaTiO (001) surfaces,leading to a considerable rumpling of the outermost sur-face plane. For the TiO -terminated case, we found muchlarger displacements in the second layer than in the firstlayer. This behavior contrasts with the atomic relaxationpattern of the TiO -terminated BaTiO (001) surface,where the upper-layer Ti relaxation is generally largerthan the second-layer Ba relaxation. However, it isin line with the only existing ab initio study of the TiO -terminated CaTiO (001) surface, as well as with other ab initio studies dealing with related BO -terminatedABO (001) surfaces, such as PbTiO and BaZrO , TABLE III: Calculated surface rumpling s , and relative dis-placements ∆ d ij between the three near-surface planes, forthe CaO- and TiO -terminated CaTiO (001) surface. Unitsare percent of the bulk lattice constant.CaO-terminated TiO -terminated s ∆ d ∆ d s ∆ d ∆ d − − where the second-layer anion (Pb or Ba) relaxations werelarger than the upper-layer (Ti or Zr) ones.In order to compare the calculated surface structureswith experimental results, the surface rumpling s (therelative oxygen displacement relative to the metal atomin the surface layer) and the changes in interlayer dis-tances ∆ d and ∆ d (where 1, 2 and 3 label the near-surface layers) are presented in Table III. Our calcula-tions of the interlayer distances are based on the posi-tions of the relaxed metal ions (Fig. 1), which are knownto be much stronger electron scatters than the oxygenions. The amplitude of the surface rumpling on theCaO-terminated surface is predicted to be almost fivetimes larger than that for the TiO -terminated (001) one.From Table III, one can see that both CaTiO (001) sur-faces show a reduction of interlayer distance ∆ d and anexpansion of ∆ d . The reduction of interlayer distance∆ d is twice as large for the CaO-terminated surfacethan it is for the TiO -terminated surface. Our calcu-lations dealing with the surface rumpling s , reduction ofinterlayer distances ∆ d , and expansion of interlayer dis-tances ∆ d are in qualitative agreement with the onlyexisting ab initio study dealing with CaTiO (001) sur-face structures. To the best of our knowledge there are no experimentalmeasurements with which we can compare our caculatedvalues of s , ∆ d , and ∆ d on the CaTiO (001) sur-faces. Even when such data do exist, it is sometimes con-tradictory, as is the case for the SrO-terminated SrTiO (001) surface, where existing LEED and RHEED ex-periments contradict each other regarding the sign of∆ d .The calculated atomic displacements, effective staticcharges, and bond populations between nearest metaland oxygen atoms are given for the TiO - and CaO-terminated (001) surfaces in Table IV. The major effectobserved here is a strengthening of the Ti-O chemicalbond near the surface. Recall from Table I that theTi and O effective charges (2.330 e and − e , respec-tively) in bulk CaTiO are much smaller than expectedin an ideal ionic model, and that the Ti-O bond pop-ulation is 0.084 e . Table IV shows that the Ti-O bondpopulation for the TiO -terminated (001) surface is con-siderably larger than the associated bulk value. Compar-ing with the very small bulk Ca-O bond populations of0.006 e from Table I, we see that the Ca-O bond popu-lations near the CaO-terminated (001) surface in TableIV are more than three times larger than in the bulk, TABLE IV: Calculated absolute magnitudes of atomic dis-placements D (in ˚A), effective atomic charges Q (in e ), andbond populations P (in e ) between nearest metal-oxygenpairs, for the for the TiO - and CaO-terminated CaTiO (001) surfaces.Layer Property Ion TiO -terminated Ion CaO-terminated1 D Ti − − Q P D O − − Q − − P D Ca 0.106 Ti 0.043 Q P D O 0.041 O 0.000 Q − − P D Ti — Ca — Q P D O — O — Q − − P but more than five times smaller than the Ti-O bondpopulations on the TiO -terminated (001) surface. C. CaTiO (011) surface structures As explained in Sec. II, non-polar TiO-, Ca-, and O-terminated surfaces can be constructed for the CaTiO (011) surface as in Figs. 3(d)-(f) respectively. Details ofthe relaxed structures obtained from our calculations forthese three terminations are given in Tables V and VI.On the TiO-terminated (011) surface, the upper-layerTi atoms move inwards by 7.14% of the bulk latticeconstant a , whereas the O atoms move outwards by4.67% (Table V), leading to a large surface rumpling of11.81% (Table VI), in excellent agreement with the cor-responding surface rumpling of 12.10% calculated earlierby Zhang et al. The second-layer oxygen atoms moveinwards by less than 1% of a . The displacement mag-nitudes of the atoms in the third layer are larger thanin the second layer, but smaller than in the top layer.The ∆ d values in Table VI show that the reduction ofthe distance between the first and second layers is threetimes larger than the corresponding expansion betweenthe second and third layers.On the Ca-terminated (011) surface, Table V showsthat the Ca atoms in the top layer move inwards verystrongly, while the O atoms in the second layer only moveoutwards very weakly. The pattern of oxygen displace- TABLE V: Calculated atomic relaxations of the CaTiO (011)surfaces (in percent of the bulk lattice constant a ) for thethree surface terminations. Positive signs correspond to out-ward displacements.Layer Ion ∆z ∆yTiO-terminated surface1 Ti − − − − − − − − − − − − − − − − ments is similar to that found on the TiO-terminated(011) surface, in that the inward oxygen displacement inthe third layer is larger than the outward displacementin the second layer, but the Ti and Ca displacements inthe third layer are smaller than the second-layer oxygenatom displacements.The O-terminated (011) surface has sufficiently lowsymmetry that some displacements occur in the y aswell as in the z direction. The O atoms in the toplayer move mostly inwards ( ∼ ∼ y direction, andalso inwards, while the second-layer O atoms move verystrongly in the y direction (but in the opposite directioncompared to the top-layer O atoms) and rather stronglyoutwards. The third-layer O atoms move in the same di-rection as the second-layer O atoms along the y -axis, buttheir displacement magnitude are more than four timessmaller, and they also move slightly inwards. Table VIshows that there is a substantial contraction of the inter-layer distance ∆ d and only a very slight expansion of∆ d . TABLE VI: Surface rumpling s and relative displacements∆ d ij (in percent of the bulk lattice constant a ) for the threenear-surface planes on the TiO- and O-terminated CaTiO (011) surfaces.TiO terminated O terminated s ∆ d ∆ d ∆ d ∆ d − − D. CaTiO (001) and (011) surface energies In the present work, we define the unrelaxed surfaceenergy of a given surface termination Λ to be one-halfof the energy needed to cleave the crystal rigidly into anunrelaxed surface Λ and an unrelaxed surface with thecomplementary termination Λ ′ . For CaTiO , for exam-ple, the unrelaxed surface energies of the complementaryCaO- and TiO -terminated (001) surfaces are equal, asare those of the TiO- and Ca-terminated (011) surfaces.The relaxed surface energy is defined to be the energy ofthe unrelaxed surface plus the (negative) surface relax-ation energy. These definitions are chosen for consistencywith Refs. [12,30]. Unlike the authors of Refs. [29,31,63],we have made no effort to introduce chemical potentialshere. Thus, while the values of the surface energies E surf reflect the cleavage energies and thus give some informa-tion about trends in the surface energetics, they shouldbe used with caution when addressing questions of therelative stability of surfaces with different stoichiometriesin specific environmental conditions.To calculate the CaTiO (001) surface energies, westart with the cleavage energy for the unrelaxed CaO-and TiO -terminated surfaces. In our calculations thetwo 7-layer CaO- and TiO -terminated slabs, containing17 and 18 atoms respectively, represent together 7 bulkunit cells of 5 atoms each. Surfaces with both termina-tions arise simultaneously under cleavage. According toour definition, we assume that the relevant cleavage en-ergy is distributed equally between created surfaces, sothat both the CaO- and TiO -terminated surfaces endup with the same unrelaxed surface energy E (unr)surf = 14 [ E (unr)slab (CaO) + E (unr)slab (TiO ) − E bulk ] , (1)where E (unr)slab (CaO) and E (unr)slab (TiO ) are the unrelaxedCaO- and TiO -terminated slab energies, E bulk is the en-ergy per bulk unit cell, and the factor of 1/4 comes fromthe fact that we create four surfaces upon the cleavageprocedure. Our calculated unrelaxed surface energy forthese surfaces is 1.40 eV, as shown in Table VII. The cor-responding relaxation energies are calculated using E (rel) (Λ) = 12 [ E (rel)slab (Λ) − E (unr)slab (Λ)] , (2)where Λ = CaO or TiO and E (rel)slab (Λ) is the slab energyafter both sides of the slab have been allowed to relax. TABLE VII: Calculated cleavage, relaxation, and surface en-ergies for CaTiO (001) and (011) surfaces (in eV per surfacecell).Surface Termination E (unr)surf E rel E surf CaTiO (001) TiO − − (011) TiO 4.61 − − − We find relaxation energies of − − -terminated and CaO-terminated surfaces, re-spectively. The final surface energies are then obtainedas a sum of the cleavage and relaxation energies using E surf (Λ) = E (unr)surf (Λ) + E (rel) (Λ) . (3)The resulting surface energies of the two (001) surfacesare comparable, but that of the TiO -terminated surfaceis slightly larger than that of the CaO-terminated one(1.13 vs. 0.94 eV), as summarized in Table VII.In order to calculate the surface energies of the TiO-and Ca-terminated surfaces shown in Fig. 3(d) and (e),containing 16 and 14 atoms respectively, we start withthe cleavage energy for unrelaxed surfaces. The two 7-plane Ca- and TiO-terminated slabs represent togethersix bulk unit cells. The surfaces with both terminationsarise simultaneously under cleavage of the crystal, andthe relevant cleavage energy is divided equally betweenthese two surfaces, so we obtain cleavage energies accord-ing to E (unr)surf (Λ) = 14 [ E (unr)slab (Ca) + E (unr)slab (TiO) − E bulk ] (4)where Λ denotes Ca or TiO, E (unr)slab (Λ) is the energy ofthe unrelaxed Ca or TiO terminated (011) slab, E bulk is the energy per bulk unit cell, and again the factor of1/4 arises because four surfaces are created upon cleav-age. Our calculated cleavage energy for the Ca or TiO-terminated (011) surfaces of 4.61 eV is more than threetimes larger than the relevant cleavage energy for theCaO- or TiO -terminated (001) surfaces. Finally, thesurface energy E surf (Λ) is just a sum of the cleavage andrelaxation energies, as in Eq. (3).When we cleave the crystal along (011) in another way,as in Fig. 3(f), we obtain two identical O-terminated sur-face slabs containing 15 atoms. The cleavage energy of3.30 eV computed for this O-terminated surface is slightlysmaller than for the Ca or TiO-terminated (011) surfaces,but still more than twice as large as for the (001) sur-faces. The unit cell of the 7-plane O-terminated slab hasthe same contents as three bulk unit cells, so the relevantsurface energy is just E surf (O) = 12 [ E (rel)slab (O) − E bulk ] , (5) where E surf (O) and E (rel)slab (O) are the surface energy andthe relaxed slab total energy for the O-terminated (011)surface. The results are again summarized in Table VII.Unlike for the (001) surface, we see that different ter-minations of the (011) surface lead to large differencesin the surface energies. Here the lowest calculated sur-face energy is 1.86 eV for the O-terminated (011) surface,while the TiO-terminated (3.13 eV) is much more costlythan the Ca-terminated (011) surface (1.91 eV). E. CaTiO (011) surface charge distributions andchemical bondings We present in Table VIII the calculated Mulliken ef-fective charges Q , and their changes ∆ Q with respect tothe bulk values, for atoms near the surface for the various(011) surface terminations.On the TiO-terminated surface, the charge on the sur-face Ti atom is seen to be substantially reduced relativeto the bulk, while the metal atoms in the third layer losemuch less charge. The O ions in all layers except thecentral one also have reduced charges, making them lessnegative. The largest charge change (0.232 e ) is observedfor subsurface O atoms, giving a large positive change of0.464 e in the charge for that subsurface layer.On the Ca-terminated surface, negative changes in thecharges are observed for all atoms except for the oxygensin the central layer and the Ti atom in the third layer.The largest charge changes are for the surface Ca ionand the subsurface O ion. The largest overall change ina layer charge ( − e ) appears in the subsurface layeras well.For the O-terminated surface, the negative charge onthe surface oxygen is very strongly decreased. Corre-spondingly, the second layer becomes substantially morenegative (overall change − e ), with the change com-ing mostly on the Ti atom. The total charge density onthe third layer is almost unchanged. Negative changes incharge are observed on all central layer atoms, leading toa total charge change of − e in that layer.The interatomic bond populations for the three termi-nations of the (011) surface are given in Table IX. Themajor effect observed here is a strong increase of the Ti-Ochemical bonding near the TiO- and O-terminated sur-face as compared to bulk (0.084 e ) or to what was foundon the TiO -terminated (001) surface (0.114 e ). For theO-terminated surface, the O(I)-Ti(II) bond population isabout twice as large as in the bulk, and about half againas large as at the TiO -terminated (001) surface. Forthe TiO-terminated (011) surface, the Ti-O bond pop-ulations are larger in the direction perpendicular to thesurface (0.186 e ) than in the plane (0.128 e ). TABLE VIII: Calculated Mulliken atomic charges Q , andtheir changes ∆Q with respect to the bulk, in e , for the threeCaTiO (011) surface terminations. For reference, the bulkvalues are 2.330 e (Ti), − e (O), and 1.782 e (Ca).Atom (layer) Q ∆QTiO-terminated surfaceTi(I) 2.204 − − − − − − − − − − − − − − − − − − − − − − − − − IV. CONCLUSIONS
According to the results of our ab initio hybrid B3PWcalculations, all of the upper-layer atoms for the TiO -and CaO-terminated CaTiO (001) surfaces relax in-wards, while outward relaxations of all atoms in thesecond layer are found at both kinds of (001) termina-tions. These results are typical for other technologicallyimportant ABO perovskites such as BaTiO , PbTiO ,and BaZrO . However, they contrast with theonly previous ab initio study of CaTiO (001) surfacesby Wang et al. , where the authors found that the first-layer O atoms relax outwards on the CaO-terminated(001) surface. For the TiO -terminated (001) surface,our largest relaxation is on the second-layer atoms, noton the first-layer ones, this time in agreement with Wang et al. The stronger relaxation of the second-layer atomscompared to the first-layer ones was found by us ear-lier also for TiO -terminated PbTiO and SrTiO (001)surfaces. Our calculations of the CaO-terminated(001) surface shows a very strong inward relaxation of8.31% for the top-layer Ca atoms, in very good quan-titative agreement with the inward relaxation of 8.80%
TABLE IX: The A - B bond populations P (in e ) and the rel-evant interatomic distances R (in ˚A) for three different (011)terminations of the CaTiO surface. Symbols I-IV denote thenumber of each plane enumerated from the surface. The near-est neighbor Ti-O distance in the unrelaxed bulk is 1.926 ˚A.Atom A Atom B P R
TiO-terminated surfaceTi(I) O(I) 0.128 1.979O(II) 0.186 1.752O(II) Ti(III) 0.110 1.935Ca(III) 0.018 2.769O(III) − − − − − − − found by Wang et al. This inward relaxation of the sur-face Ca atoms on the CaO-terminated (001) surface ismuch stronger than was obtained for the AO-terminated(001) surfaces of other ABO perovskites (A = Sr, Ba,Pb, and Zr). Our calculated surface rumpling of 7.89% for theCaO-terminated (001) surface is almost five times largerthan that of the corresponding TiO -terminated sur-face, and is comparable with the surface rumpling of9.54% obtained for the CaO-terminated surface by Wang et al. This rumpling is larger than the rumplings ob-tained in previous ab initio calculations for the AO-terminated (001) surfaces of SrTiO , BaTiO , BaZrO ,and PbTiO . Our calculations predict a compression of the inter-layer distance between first and second planes, and anexpansion between second and third planes, for the (001)surfaces. Our value for ∆ d of − − et a. andis larger than the corresponding value for , BaTiO ,BaZrO , and PbTiO (001) surfaces. Asfor experimental confirmation of these results, we areunfortunately unaware of experimental measurements of∆ d and ∆ d for the CaTiO (001) surfaces. More-over, for the case of the SrO-terminated SrTiO (001)surface, existing LEED and RHEED experiments ac-tually contradict each other regarding the sign of ∆ d .In view of the absence of clear experimental determina-tions of these parameters, therefore, the first-principlescalculations are a particularly important tool for under-standing the surface properties.Turning now to the CaTiO (011) surfaces, we foundthat the inward relaxation of the upper-layer metalatom on the TiO-terminated (011) surface (Ti displace-ment of 7.14%) is smaller than on the CaO-terminated(001) surface (Ca displacement of 8.31%), in contrast towhat was found for the SrTiO , BaTiO , PbTiO , andBaZrO surfaces. However, the inward re-laxation by 16.05% of the upper-layer Ca atom on theCa-terminated (011) surface is about twice as large asthe inward relaxations of surface atoms obtained on theCaO-terminated (001) surface. Our calculated atomicdisplacements in the third plane from the surface forthe Ca, TiO, and O-terminated (011) surfaces are stillsubstantial. Our calculated surface rumpling s for theTiO-terminated (011) surface is approximately 1.5 timeslarger than that of the CaO-terminated (001) surface,and many times times larger than that of the TiO -terminated (001) surface. Also, our ab initio calculationspredict a compression of the interlayer distance ∆ d andan expansion of ∆ d for the TiO- and O-terminated(011) surfaces. This behavior seems to be obeyed by allprevious calculations of relaxations at (001) ABO per-ovskite surfaces ; we can conclude that thiseffect may be a general rule, requiring further experimen-tal studies and confirmation.A comparison of our ab initio B3PW calculations onthe TiO-terminated CaTiO (011) surface with the pre-vious ab initio calculation performed by Zhang et al. shows that the atomic displacement directions almost al-ways coincide, the only exception being the small third-layer Ti-atom inward relaxation of − , BaTiO , PbTiO ,and BaZrO cases. Just as they did forthe TiO-terminated (011) surface, our relaxation direc-tions for the Ca-terminated surface almost all coincidewith those obtained previously, the only exception be-ing again the displacement direction of the third-layerTi atom. We find that this atom moves slightly inwardsby 0.37%, whereas the previous work obtain an outwardrelaxation of 0.89%. For the O-terminated (011) surface, in most casesour calculated displacement directions are in qualitativeagreement with the results of Ref. [6]. In some cases,as for example for the second layer Ti and O atom dis-placements in the direction along the surface, our cal-culated displacement magnitudes for Ti (4.70%) and forO (8.05%) are in an excellent agreement with the cor-responding results (4.53% and 8.06% respectively) ofZhang et al. However, in many cases, our calculateddisplacement magnitude is smaller than that calculatedin Ref. [6]. Most disturbingly, in three cases there arealso some qualitative differences between our results andthose of Zhang et al. Specifically, the second-layer Caand Ti atoms move substantially inwards in our calcu-lations, but outwards in Ref. [6], and the third-layer Oatoms move in opposite directions in the two calculations.As for the surface energies, we find that both the CaO-and TiO -terminated (001) surfaces are about equallyfavorable, with surface energies of 0.94 and 1.13 eV re-spectively. These values are in excellent agreement withthe corresponding values of 0.824 and 1.021 eV respec-tively as computed by Zhang et al. in Ref. [6]. In con-trast, we see very large differences in surface energieson the (011) surfaces. Our lowest-energy (011) sur-face is the O-terminated one at 1.86 eV, with the Ca-terminated surface just behind at 1.91 eV, and the TiO-terminated surface is very unfavorable at 3.13 eV. Theseare all much larger, by about a factor of two or more,than for the (001) surfaces. This is the same orderingof (011) surface energies as was obtained by Zhang etal. , but these authors obtained quite different values of0.837, 1.671, and 2.180 eV for the O-, Ca-, and TiO-terminated (011) surfaces, respectively. The values forthe Ca- and TiO-terminated surface energies are onlymodestly smaller than ours, but the value for the O-terminated (011) surface energy presents a clear disagree-ment with the present work, being more than twice assmall as ours. In fact, according to their work, the O-terminated (011) surface is even lower in energy thanthe TiO -terminated (001) surface, and about equal tothat of the CaO-terminated (001) surface. In this re-spect, their result contrasts not only with our result for0CaTiO , but with all previous ab initio and shell-modelcalculations dealing with SrTiO , BaTiO , PbTiO , andBaZrO (001) and (011) surface energies, where the (001) surface energies are always smaller thanthe (011) surface energies.We do not understand the reason for this discrepancy.We have carried out test calculations of the cleavage en-ergies of the three (011) surfaces using the PBE-GGAexchange-correlation functional used by Zhang et al. ,but within the CRYSTAL-2003 code package, and wefind cleavage energies that are only about 15-25% largerthan theirs. The drastic difference, then, must be in therelaxation energy of the Ca-terminated surface, whichis − − ab initio calculations indicate a considerable in-crease in the Ti-O bond covalency near the TiO- and O- terminated (011) surfaces, as well as the TiO -terminated(001) surface. The Ti-O bond covalency at the TiO-terminated (011) surface (0.128 e ) is much larger thanthat for the TiO -terminated (001) surface (0.114 e ) orin bulk CaTiO (0.084 e ). The Ti-O bond populationson the TiO-terminated (011) surface are much larger inthe direction perpendicular to the surface than in theplane (0.186 vs. 0.128 e ). Our calculated increase of theTi-O bond covalency near the (011) surface, is in agree-ment with the resonant photoemission experiments. This should have an impact on the electronic struc-ture of surface defects (e.g., F centers), as well as onthe adsorption and surface diffusion of atoms and smallmolecules relevant for catalysis. V. ACKNOWLEDGMENTS
The present work was supported by DeutscheForschungsgemeinschaft (DFG) and by ONR Grant No.N00014-05-1-0054. J. F. Scott,
Ferroelectric Memories (Springer, Berlin,2000). M. Dawber, K. M. Rabe, and J. F. Scott, Rev. Mod. Phys. , 1083 (2005). R. E. Cohen, Nature, , 136 (1992). A. E. Ring, S. E. Kesson, K. D. Reeve, D. M. Levins, E.J. Ramm, in: W. Lutze, R. C. Ewings (Eds.),
RadioactiveWaste Forms for the Further , (North Holland Publishing,Amsterdam, 1987). Y. X. Wang, M. Arai, T. Sasaki, and C. L. Wang, Phys.Rev. B , 035411 (2006). J. M. Zhang, J. Cui, K. W. hu, V. Ji, Z. Y. Man, Phys.Rev. B , 115426 (2007). R. I. Eglitis, and D. Vanderbilt, Phys. Rev. B , 195408(2008). S. Kimura, J. Yamauchi and M. Tsukada, Phys. Rev. B , 11049 (1995). Z. Q. Li, J. L. Zhu, C. Q. Wu, Z. Tang and Y. Kawazoe,Phys. Rev. B , 8075 (1998). R. Herger, P. R. Willmott, O. Bunk, C. M. Schlep¨utz, B.D. Patterson and B. Delley, Phys. Rev. Lett. , 076102(2007). N. Erdman, K. Poeppelmeier, M. Asta, O. Warschkow, D.E. Ellis and L. Marks, Nature , 55 (2002). E. Heifets, R. I. Eglitis, E. A. Kotomin, J. Maier, and G.Borstel, Phys. Rev. B , 235417 (2001). E. Heifets, R. I. Eglitis, E. A. Kotomin, J. Maier, and G.Borstel, Surf. Sci. , 211 (2002). K. Johnston, M. R. Castell, A. T. Paxton and M. W. Fin-nis, Phys. Rev. B , 085415 (2004). R. I. Eglitis, S. Piskunov, E. Heifets, E. A. Kotomin, andG. Borstel, Ceram. Int. , 1989 (2004). S. Piskunov, E. A. Kotomin, E. Heifets, J. Maier, R. I.Eglitis and G. Borstel, Surf. Sci. , 75 (2005). R. Herger, P. R. Willmot, O. Bunk, C. M. Schlep¨utz, B. D. Patterson, S. Delley, V. L. Schneerson, P. F. Lyman,and D. K. Saldin, Phys. Rev. B , 195435 (2007). C. H. Lanier, A. van de Walle, N. Erdman, E. Landree, O.Warschkow, A. Kazimirov, K. R. Poeppelmeier, J. Zegen-hagen, M. Asta and L. D. Marks, Phys. Rev. B , 045421(2007). Y. L. Li, S. Choudhury, J. H. Haeni, M. D. Biegalski, A.Vaudevarao, A. Sharan, H. Z. Ma, J. Levy, V. Gopalan,S. Trolier-McKinstry, D. G. Schlom, Q. X. Jia and L. Q.Chen, Phys. Rev. B , 184112 (2006). C. Cheng, K. Kunc, M. H. Lee, Phys. Rev. B , 10409(2000). J. Padilla and D. Vanderbilt, Surf. Sci. , 64 (1998). V. Ravikumar, D. Wolf and V. P. Dravid, Phys. Rev. Lett. , 960 (1995). E. Heifets, E. A. Kotomin, and J. Maier, Surf. Sci. ,19 (2000). N. Bickel, G. Schmidt, K. Heinz, and K. M¨uller, Phys. Rev.Lett. , 2009 (1989). T. Hikita, T. Hanada, M. Kudo, and M. Kawai, Surf. Sci. , 377 (1993). M. Kudo, T. Hikita, T. Hanada, R. Sekine, and M. Kawai,Surf. Interface Anal. , 412 (1994). Y. Kido, T. Nishimura, Y. Hoshido, and H. Mamba, Nucl.Instrum. Methods Phys. Res. B , 371 (2000). G. Charlton, S. Brennan, C. A. Muryn, R. McGrath, D.Norman, T. S. Turner, and G. Thorton, Surf. Sci. ,L376 (2000). F. Bottin, F. Finocchi, and C. Noguera, Phys. Rev. B ,035418 (2003). E. Heifets, W. A. Goddard III, E. A. Kotomin, R. I. Eglitis,and G. Borstel, Phys. Rev. B , 035408 (2004). E. Heifets, J. Ho, and B. Merinov, Phys. Rev. B , 155431(2007). R. I. Eglitis, and D. Vanderbilt, Phys. Rev. B , 155439 (2007). H. Bando, Y. Aiura, Y. Haruyama, T. Shimizu, Y. Nishi-hara, J. Vac. Sci. Technol. B , 1150 (1995). K. Szot, and W. Speier, Phys. Rev. B , 5909 (1999). J. Brunen, J. Zegenhagen, Surf. Sci. , 349 (1997). Q. D. Jiang, J. Zegenhagen, Surf. Sci. , 343 (1999). J. Zegenhagen, T. Haage, Q. D. Jiang, Appl. Phys. A ,711 (1998). R. Souda, Phys. Rev. B , 6068 (1999). Y. Adachi, S. Kohiki, K. Wagatsuma, M. Oku, J. Appl.Phys. , 2123 (1998). A. D. Becke, J. Chem. Phys. , 5648 (1993). J. P. Perdew, and Y. Wang, Phys. Rev. B , 8800 (1986);J. P. Perdew, and Y. Wang, ibid. , , 3399(E) (1989); J.P. Perdew, and Y. Wang, ibid. , , 13244 (1992). R. I. Eglitis, J. Phys.: Condens. Matter , 356004 (2007). V. R. Saunders, R. Dovesi, C. Roetti, M. Causa, N. M.Harrison, R. Orlando, C. M. Zicovich-Wilson,
CRYSTAL-2003 User Manual , University of Torino, Torino, Italy,2003. S. Piskunov, E. Heifets, R. I. Eglitis, and G. Borstel, Com-put. Mater. Sci. , 165 (2004). H. Shi, R. I. Eglitis, and G. Borstel, Phys. Rev. B ,045109 (2005). P. J. Hay, and W. R. Wadt, J. Chem. Phys. , 270 (1985);P. J. Hay, and W. R. Wadt, ibid. , 284 (1985); P. J. Hay,and W. R. Wadt, ibid. , 299 (1985). H. J. Monkhorst, and J. D. Pack, Phys. Rev. B , 5188(1976). C. Noguera, J. Phys.: Condens. Matter , R367 (2000). P. W. Tasker, J. Phys. C: Solid State Phys. , 4977(1979). A. Pojani, F. Finocchi, and C. Noguera, Surf. Sci. ,179 (1999). A. Granicher and O. Jakits, Nuove Cimento Suppl. , 480(1954). H. F. Kay and P. C. Bailey, Acta Crystallogr. , 437(1957). X. Liu and R. C. Liebermann, Phys. Chem. Minerals ,171 (1993). B. J. Kennedy, C. J. Howard, and B. C. Chakoumakos, J.Phys. Cond. Matt. , 1479 (1999). A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Crystal-logr. Cryst. Chem. , 3384 (1972). D. Vanderbilt and W. Zhong, Ferroelectrics , 181(1998). E. Cockayne and B. P. Burton, Phys. Rev. B , 3735(2000). Ferroelectrics and Related Substances , edited by K. H. Hell-wege, and A. M. Hellwege, Landolt-Bornstein, New Series,Group III, Vol. (Springer Verlag, Berlin, 1969). C. R. A. Catlow, and A. M. Stoneham, J. Phys. C: SolidState Phys. , 4321 (1983). R. C. Bochiccio, and H. F. Reale, J. Phys. B: At. Mol. Opt.Phys. , 4871 (1993). J. Padilla, and D. Vanderbilt, Phys. Rev. B , 1625(1997). B. Meyer, J. Padilla, and D. Vanderbilt, Faraday Discuss. , 395 (1999). K. Rapcewics, B. Chen, B. Yakobsen, J. Bernhok, Phys.Rev. B , 7281 (1998). J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996). R. Courths, B. Cord, H. Saalfeld, Solid State Commun. , 1047 (1989). R. I. Eglitis, N. E. Christensen, E. A. Kotomin, A. V.Postnikov, and G. Borstel, Phys. Rev. B56