We present an ab initio study of pure and doped TiO₂ in the rutile and anatase phases. The main purpose of this work is to determine the role played by different defects and different crystal structures in the appearance of magnetic order. The calculations were performed for varying impurity and vacancy concentrations in both TiO₂ structures. For Co impurities the local magnetic moment remained almost independent of the concentration and distribution while for Cu this is not the case, there is magnetism for low concentrations that disappears for the higher ones. Impurity–impurity interactions in both structures favor linear ordering of them. Magnetism in undoped samples appears for certain vacancy concentrations and structural strain.Facultad de Ciencias ExactasInstituto de Física La Plat

Errico, Leonardo Antonio

Weissmann, Mariana

Physica B Condensed Matter

Servicio de Difusión de la Creación Intelectual

ARTICLE IN PRESS0921-4526/$ - sedoi:10.1016/j.phCorrespondiE-mail addrePhysica B 398 (2007) 179–183www.elsevier.com/locate/physbThe role of vacancies, impurities and crystal structurein the magnetic properties of TiO2Mariana Weissmanna,, Leonardo A. ErricobaDepartamento de Fı́sica, Comisión Nacional de Energı́a Atómica, Av. del Libertador 8250, 1429 Buenos Aires, ArgentinabDepartamento de Fı́sica—Instituto de Fı́sica La Plata (CONICET), Facultad de Ciencias Exactas,Universidad Nacional de La Plata, C.C. N? 67, 1900 La Plata, ArgentinaAbstractWe present an ab initio study of pure and doped TiO2 in the rutile and anatase phases. The main purpose of this work is to determinethe role played by different defects and different crystal structures in the appearance of magnetic order. The calculations were performedfor varying impurity and vacancy concentrations in both TiO2 structures. For Co impurities the local magnetic moment remained almostindependent of the concentration and distribution while for Cu this is not the case, there is magnetism for low concentrations thatdisappears for the higher ones. Impurity–impurity interactions in both structures favor linear ordering of them. Magnetism in undopedsamples appears for certain vacancy concentrations and structural strain.r 2007 Elsevier B.V. All rights reserved.PACS: 75.50.Pp; 71.20.Nr; 75.20.Dd; 71.15.MbKeywords: Diluted magnetic semiconductors; Titanium dioxide; Ab initio calculations1. IntroductionDiluted magnetic semiconductors and insulators, espe-cially those having room-temperature (RT) ferromagnet-ism, have attracted great interest in the last years due totheir potential applications in spintronic devices [1]. Manysystems, such as GaN:Mn [2], GaN:Cr [3], ZnO:Co [4],ZnO:Mn [5], TiO2:Co [6,7], or CdGeP2:Mn [8], have beenreported to have RT ferromagnetism. In particular, thefirst report of robust RT ferromagnetism by Matsumoto etal. [6] generated a tremendous interest in Co-doped TiO2films. However, a large spread of Curie temperatures andmagnetizations were reported since then (e.g., see Ref. [9]).The growth conditions, the substrate structure andtemperature, the amount of oxygen present, all seem toinfluence the ferromagnetic behavior. Theoretical andexperimental studies have been intensively performed[10], but a consensus on the origin of the experimentallyobserved ferromagnetic coupling has not yet been reached.e front matter r 2007 Elsevier B.V. All rights reserved.ysb.2007.04.015ng author.ss: weissman@cnea.gov.ar (M. Weissmann).The use of these systems in spintronic devices has todaytwo types of limitations: the first one is the preparation of ahomogeneous solid solution of the dopant in the oxidehost, avoiding phase segregation. The second one isunderstanding the mechanism associated with the ferro-magnetic ordering [10–12].In the present work, we present a computational ab initiostudy of un-doped rutile and anatase TiO2 with oxygenvacancies and of TiO2 doped with a magnetic ion (Co) anda non-magnetic one (Cu). We put special care in thestructural relaxations and in the effects of impurityconcentration. We have not studied here cases with bothimpurities and vacancies, as in that situation there is chargecompensation and possibly few charge carriers.2. Method of calculationThe spin-polarized electronic-structure calculations pre-sented in this work were performed with two different abinitio codes, Wien2K [13] and Siesta [14]. The Wien2K is animplementation of the full-potential linearized-augmentedplane-wave method (FP-LAPW [15]). Exchange andARTICLE IN PRESSaabbccO1 O1O1 O1O2O2Fig. 1. Bulk structures of anatase (top) and rutile (bottom) TiO2. Blackand white balls represent Ti and O, respectively.M. Weissmann, L.A. Errico / Physica B 398 (2007) 179–183180correlation effects are treated within density-functionaltheory using the local spin density approximations (LSDA[16]). The atomic spheres radii (Ri), used for Ti and O were1.01 and 0.85 Å, while for Co and Cu we used Ri ¼ 1.06 Å.The parameter RKmax ¼ Rmt  Kmax, which controls the sizeof the basis set in these calculations, was chosen as 7 (Rmt isthe smallest muffin tin radius and Kmax the largest wavenumber of the basis set). We introduced local orbitals toinclude Ti-3s and 3p, O-2s and Co- and Cu-3p orbitals. Thenumber of k-points was increased until convergence wasreached.The Siesta code uses a linear combination of numericalreal-space atomic orbitals as basis set and norm-conservingpseudopotentials [17]. Although both contain the LSDAapproximation, the Siesta code is much faster for relaxa-tion of the structures and gives the results in terms ofatomic orbitals, so that one can separate the contributionof each orbital to the magnetic moment. The disadvantageis that pseudopotentials and basis sets have to be provedadequate for each calculation. On the contrary, theWien2K code can be converged in the number of planewaves and the number of k-points, leaving no parametersfree. But the disadvantage is that the charge in theinterstitial region cannot be separated in the differentsymmetries. Our usual strategy was to relax the structureswith the Siesta code and then use those atomic positions asinput for the Wien2K calculation. The total energy wasalways lower than that of the un-relaxed cases.3. Results and discussionsTitanium dioxide crystallizes in three different struc-tures: anatase (tetragonal, I41/amd, a ¼ b ¼ 3.782 Å,c ¼ 9.502 Å), rutile (tetragonal, P42/mnm, a ¼ b ¼4.5854 Å, c ¼ 2.9533 Å), and brookite (rhombohedrical,Pbca a ¼ b ¼ 5.436 Å, c ¼ 9.166 Å) [18]. However, onlyrutile and anatase have applications and are of interesthere. Their unit cells are shown in Fig. 1. In both struc-tures, the basic ‘‘building bricks’’ consist of a titaniumatom surrounded by six oxygen atoms in a more or lessdistorted octahedral configuration. In both structures, thetwo bonds between the titanium and the oxygen atoms atthe apices of the octahedron are slightly longer.3.1. Effect of vacancies in un-doped TiO2Different experimental and theoretical works suggestthat oxygen vacancies play an important role in the originof ferromagnetism of doped TiO2 [10]. In addition,ferromagnetism was discovered recently in thin films ofpure TiO2 [19] and other non-magnetic oxides [19,20]. Oneof the mechanisms proposed in order to explain theobserved ferromagnetism is based in the presence ofintrinsic oxygen vacancies, which act as donors, leadingto n-type doping of the material. In order to analyze theeffect of oxygen vacancies in doped TiO2, we first studiedthe reduced pure system, TiO2d, taking into account thestructural distortions produced by the vacancies using thesuper-cell (SC) method. We employed a small SC consist-ing of two unit cells of the rutile structure stacked along thec-axis and we removed an oxygen atom (Ti4O7) from thisSC.TiO2 is an ionic crystal; therefore, an oxygen vacancyproduces a large structural relaxation due to the repulsionof nearby titanium ions, and leaves a big hole in its place.In effect, the cations nearest neighbors to the vacancy siteare repelled from it. To study this relaxation, we used boththe Wien2K code, with the mini routine, and the Siestacode with the conjugate gradient procedure. In the firstcase, the symmetry around the vacant site is maintained onrelaxing while in the second case it is not. The final atomicpositions are different: in one case the vacancy-sitedistances to its Ti nearest neighbors are 2.16 and 2.34 Å;in the other they are 1.97 and 2.40 Å (all are larger than theoxygen–Ti nearest-neighbor distances in stoichiometricTiO2 of 1.94 and 1.98 Å). The energies of the two relaxedunit cells with one vacancy differ by less than 104Ry, butalthough they were both calculated with the Wien2K codeup to convergence one of them leads to zero magneticmoment while the other has 1.6mB/SC. This surprisingresult is obtained when the cell size is kept fixed at theexperimental value and suggests that strain may be thereason for obtaining ferromagnetism in un-doped oxidefilms. This strain could be due to the substrate, to the fastgrowth in an oxygen-poor atmosphere or to interstitialatoms nearby. Calculations with a larger unit cell and onlyone vacancy, both in rutile and anatase structures, wereperformed but there was no magnetic moment. WeARTICLE IN PRESSFig. 2. (Top) Charge density for the (1 1 0) plane of the rutile structure ofTiO2 in the 48-atom SC; (middle) spin density for the same plane with oneCo impurity per SC; (bottom) spin density for the same plane with one Cuimpurity per SC.M. Weissmann, L.A. Errico / Physica B 398 (2007) 179–183 181conclude that the appearance of a magnetic momentdepends on the vacancy concentration and on the strainof the structure.3.2. Effect of concentration and distribution of impuritiesFor this study, we restricted ourselves to one magnetic(Co) and one non-magnetic impurity (Cu) with no oxygenvacancies. In the case of the rutile phase, the first SCconsidered consisted of two unit cells of TiO2 stacked alongthe c-axis with one Ti atom replaced by the impurity. Theresulting 12-atom SC (Ti3RO8) has dimensions a0 ¼ b0 ¼ a,c0 ¼ 2c. The impurity concentration in this SC is 25%. Thesecond SC employed consisted of 8 units cells of TiO2,corresponding to an impurity concentration of 6.25%. Theresulting 48-atom SC (Ti15RO32) has dimensionsa0 ¼ b0 ¼ 2a, c0 ¼ 2c. In the case of the anatase phase, weperformed calculations with the simple 12-atom unit celland also with a 48-atom SC (Ti15RO32, a0 ¼ b0 ¼ 2a,c0 ¼ c).We found that the presence of Co impurities induceslocal geometrical distortions (contractions) in the firstoxygen neighbors (ONN) of the impurities. The bondlengths Co–ONN are reduced by about 0.05 Å. In the caseof Cu, the structural distortions induced by the impurityare anisotropic, the Cu–O1 bond lengths are shorter whilethe Cu–O2 distances are enlarged by about 0.04 Å.Results for the magnetic moments are summarized inTable 1. We see that the same magnetic moment of 1.0mBper Co atom in the SC was found for Co in both structuresand concentrations, but that for Cu there is no magneticmoment in the small unit cells while it is 1.0mB/SC in thelarger systems. The appearance of magnetism in Cu-dopedTiO2 agrees with experimental results [21]. The samedependence of the magnetic moment on concentration ofCu was also found in calculations for ZnO [22]. Thisconcentration dependence shows again, as for the un-doped system, that the variety of results obtainedexperimentally for different samples also appears in abinitio calculations, even though these are performed forbulk materials and at 0K.Table 1 also shows that Co spin-polarization occursmainly at the impurity sites while the ONN are polarizedonly up to 0.06mB/ONN, but that in the case of Cu theTable 1Magnetic moments in the muffin tin sphere of the impurities (mimp) and inthe super-cell (mSC) for the two concentrations and structures studiedRutile Anatasemimp/mSC (mB) mimp/mSC (mB)TiO2:Co, 12-atom SC 0.63/0.98 0.73/1.01TiO2:Co, 48-atom SC 0.64/1.14 0.73/0.96TiO2:Cu, 12-atom SC 0.00/0.00 0.00/0.00TiO2:Cu, 48-atom SC 0.47/1.01 0.37/0.97magnetic moment is delocalized. In Fig. 2, we present thecharge and spin densities for the rutile structure in the(1 1 0) plane, where this difference in spin localization isclearly evident. In Fig. 3, we present the charge and spindensities for the (0 0 1) plane in both structures. As can beseen, the hybridization is also very different for the twodifferent impurities and this, together with the differentspin localization raises the question if the mechanism forlong-range ferromagnetic order could be the same for Coand Cu.The densities of states (DOS) of these systems are shownin Fig. 4. In all cases, the impurity states (d states) aremainly located in the energy gap of TiO2 and the Ti and Ostates are not much affected by the doping. The features ofthe 48-atom SCs are also valid for the 12-atom SCs, theonly differences being the larger values of the DOS at theFermi levels and the increased structures from impurity-induced states. These results are in good agreement withprevious calculations, for example, those reported byJanisch and Spaldin [23] for the case of Co in anatase TiO2.Next we substituted a second Ti atom by an impurity inthe 48-atom SC, leading to an impurity concentration of12.5%, and allowing us to compare the energies of ferro-and antiferromagnetic orderings. We varied the positionsof the impurity atoms to study the preferred configurationsand the dependence of the magnetic moment on theimpurity distribution. We found that in all cases the lowestenergy corresponded to a ferromagnetic alignment, as wasfound in Ref. [22] for ZnO.Our results for the rutile structure show that if the Cuatoms are located at the shortest possible distance to eachARTICLE IN PRESSM. Weissmann, L.A. Errico / Physica B 398 (2007) 179–183182other, the system has its lowest energy and highestmagnetic moment. This corresponds to impurities locatedalong the c-axis of the rutile structure, where they are atFig. 3. Charge (top) and spin densities (middle and bottom) in the (0 0 1)plane of rutile (left) and anatase (right) for Co- and Cu-doped TiO2. Thereis one impurity in the 48-atom SC.-40-2002040-6 -4 -2 0 2-40-2002040EFTiO2:Co, rutile structureTiO2:Cu, rutile structureDOS (states/eV)Energy (eV)Fig. 4. Densities of states of Co- and Cu-doped rutile and anatase TiO2. EnergiSC.2.90 Å and form a row of impurities due to the periodicity.It would be very interesting to build experimentally theselinear structures and to find out if they validate theseresults. It is important to mention that when Cu impuritiesare considered, there is an increase of the magnetic momentfrom 1.1 to 3.2mB/SC (see Table 2). In the case of Coimpurities, the lowest energy distribution also correspondsto Co at the shortest possible distance, but the magneticmoment is nearly independent of the Co distribution in thehost. The magnetic moment in these cases is 2.0mB/SC, twotimes the magnetic moment corresponding to the case ofone Co impurity (see Table 2). This difference could be dueto the greater localization of spin in the case of Coimpurities.For the anatase structure, the nearest-neighbor positionsdo not form a row and the lowest energy for the pair ofimpurities is when they are second neighbors, forming arow along the a-axis at a distance of 3.78 Å from eachother. In the case of Cu there is a decrease of the magneticmoment, to 0.80mB/SC, while for Co we obtained similarresults to those found for the rutile structure.-60-40-200204060-6 -4 -2 0 2-60-40-200204060EFTiO2:Co, anatase structureTiO2:Cu, anatase structureDOS (states/eV)Energy (eV)es are referred to the Fermi level (EF). There is one impurity in the 48-atomTable 2Magnetic moments per SC (mSC) obtained for the systems Ti15R1O32 andTi14R2O32 (R: Co and Cu)Rutile AnatasemSC (mB) d (Å) mSC (mB) D (Å)TiO2:Cu, 1 Cu-impurity 1.01 — 0.97 —TiO2:Cu, 2 Cu-impurities 3.2 2.96 0.8 3.78TiO2:Cu, 2 Cu-impurities 1.8 5.90 2.0 5.46TiO2:Co, 1 Co-impurity 1.14 — 0.96 —TiO2:Co, 2 Co-impurities 2.0 2.96 2.0 3.78TiO2:Co, 2 Co-impurities 2.0 5.90 2.0 5.46Of all the possible configurations for the two impurities, we only show theone with lowest energy and the one where the impurities are farther apart.We denote with d the impurity–impurity distance.ARTICLE IN PRESSM. Weissmann, L.A. Errico / Physica B 398 (2007) 179–183 1834. ConclusionsFrom these calculations, we conclude that magnetism inun-doped transition metal oxide films is possibly due tovacancies and structural strain, produced either by thesubstrate or by the growth procedure. Slightly differentrelaxations with a fixed cell size, calculated with the samecode and precision and energetically degenerate, give verydifferent magnetic moments.For the doped system, we analyzed the case of amagnetic impurity (Co) and a non-magnetic one (Cu). Coimpurities have a localized magnetic structure, with 1mB/Coatom in the SC and a very small interaction among them.On the other hand, Cu impurities produce a magneticmoment for very small concentrations only, and it isdelocalized so that about 0.5mB can be attributed to Cu andthe rest to neighbor atoms.Concerning the impurity distribution in the host lattices,the impurities prefer to be located in rows, along the c-axisof the rutile structure and the a-axis of anatase. Themagnetic moment does not depend on the distance betweenCo atoms but it depends strongly for Cu. It would be veryinteresting to produce rows of impurities experimentally.The differences in the spin densities obtained between Coand Cu doping, and between rutile and anatase structures,raise the question if the mechanism for long-rangeferromagnetic order is the same for Co and Cu doping,and also if it is the same for un-doped films.AcknowledgmentsThis work was partially supported by ANPCyT underPICT98 03-03727 and 03-10698, by CONICET (underPIP006/98, PEI 6174, PIP6032 and PIP 6016), Fund.Antorchas, Argentina, and TWAS, Italy, RGA 97-057.M.W. and L.A.E. are members of Carrera del Investiga-dor, CONICET, Argentina. We are indebted to Dr. JavierGuevara for critical reading of the manuscript and helpfulsuggestions.References[1] H. Ohno, Science 281 (1998) 951.[2] M.E. Overberg, et al., Appl. Phys. Lett. 79 (2001) 3473.[3] M. Hashimoto, et al., Appl. Phys. Lett. 80 (2001) 4187.[4] K. Ueda, et al., Phys. Rev. Lett. 96 (2006) 17203.[5] P. Sharma, et al., Nat. Mater. 2 (2003) 673.[6] Y. Matsumoto, et al., Science 291 (2001) 854.[7] S.A. Chambers, et al., Appl. Phys. Lett. 79 (2001) 3467;S.A. Chambers, Mater. Today 5 (2002) 34.[8] G.A. Medvedkin, et al., Jpn. J., Part 2: Appl. Phys. 39 (2000) L949.[9] R. Janisch, P. Gopal, N.A. Spaldin, J. Phys.: Condens. Matter 17(2005) R657.[10] L.A. Errico, M. Renterı́a, M. Weissman, Phys. Rev. B 72 (2005)184425 and references therein.[11] K.M. Krishnan, A.B. Pakhomov, Y. Bao, P. Blomovist, Y. Chun,M. Gonzales, K. Griffin, X. Ji, B.K. Roberts, J. Mater. Sci. 41 (2006)793.[12] H. Weng, et al., Phys. Rev. B 69 (2004) 125219.[13] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvaniscka, J. Luitz,WIEN2K, an augmented plane wave+local orbitals program forcalculating crystal properties, K. Schwarz, Techn. University, Wien,Austria, 2001.[14] P. Ordejón, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) R10441;D. Sánchez-Portal, et al., Int. J. Quantum Chem. 65 (1997) 453.[15] O.K. Andersen, Phys. Rev. B 12 (1975) 3060;S.H. Wei, H. Krakauer, M. Weinert, Phys. Rev. B 32 (1985) 7792.[16] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244.[17] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993.[18] U. Diebold, Surf. Sci. Rep. 48 (2003) 53 and references therein.[19] N. Hong, et al., Phys. Rev. B 73 (2006) 132404.[20] M. Venkatesan, et al., Nature 430 (2004) 630;J.M.D. Coey, J. Magn. Magn. Mater. 290 (2005) 1405.[21] S. Duhalde, et al., Phys. Rev. B 72 (2005) R161313.[22] L.M. Huang, A.L. Rosa, R. Ahuja, Phys. Rev. B 74 (2006) 075206.[23] R. Janisch, N.A. Spaldin, Phys. Rev. B 73 (2006) 35201.

The role of vacancies, impurities and crystal structure in the magnetic properties of TiO₂

http://sedici.unlp.edu.ar/bitstream/handle/10915/132101/Documento_completo.pdf?sequence=1

The role of vacancies, impurities and crystal structure in the magnetic properties of TiO₂

Abstract

Similar works

Full text

Available Versions

Servicio de Difusión de la Creación Intelectual