We report \emph{ab initio} predictions on the proper multiferroic
(ferromagnetic, insulating and ferroelectric) character of PbTiO$_{3}$ doped
with vanadium. V impurities coupled ferromagnetically carry a magnetization of
1 $\mu_{\rm B}$ each. The coupling is expected to be strong, since the
paramagnetic solution is higher by 150 meV/vanadium, and no stable
antiferromagnetic solution was found. The electronic gap in the doped system is
about 0.2-0.3 eV in GGA, hence the system is properly multiferroic. V doping
increases the spontaneous polarization in PbTiO$_{3}$, with an approximate
percentual rate of 0.7 $\mu$C/cm$^{2}$.Comment: 4 pages, 3 figures, 1 tabl

Fiorentini, Vincenzo

Ricci, Francesco

Journal of Physics : Conference Series

English

arXiv

F Ricci

V Fiorentini

Crossref

Journal of Physics Conference Series

Multiferroicity in V-doped PbTiO<sub>3</sub>

We report ab initio predictions on the proper multiferroic (ferromagnetic, insulating and ferroelectric) character of PbTiO3 doped with vanadium (V). Ferromagnetically coupled V impurities carry a magnetization of 1 μB each. The coupling is expected to be strong, since the paramagnetic solution is higher by 150 meV/vanadium, and no stable antiferromagnetic solution was found. The electronic gap in the doped system is about 0.2-0.3 eV in the generalized gradient approximation (GGA), hence the system is properly multiferroic. V doping increases the spontaneous polarization in PbTiO3, with an approximate percentual rate of 0.7 μC/cm 2

RICCI, FRANCESCO

FIORENTINI, VINCENZO

Archivio istituzionale della ricerca - Università di Cagliari

Multiferroicity in V-doped PbTiO3F Ricci and V FiorentiniCNR-IOM and Dept. of Physics, University of Cagliari, Cittadella Universitaria, 09042Monserrato (CA), ItalyE-mail: frankyricci@gmail.com, vincenzo.fiorentini@gmail.comAbstract. We report ab initio predictions on the proper multiferroic (ferromagnetic, insulat-ing and ferroelectric) character of PbTiO3 doped with vanadium (V). Ferromagnetically coupledV impurities carry a magnetization of 1 µB each. The coupling is expected to be strong, sincethe paramagnetic solution is higher by 150 meV/vanadium, and no stable antiferromagnetic so-lution was found. The electronic gap in the doped system is about 0.2-0.3 eV in the generalizedgradient approximation (GGA), hence the system is properly multiferroic. V doping increasesthe spontaneous polarization in PbTiO3, with an approximate percentual rate of 0.7 µC/cm2.1. IntroductionModern technology uses extensively ferroic materials –i.e. having a spontaneous and permanentorder parameter of one kind or another– with fairly exotic properties. For example, commoditydata-storage devices exploit ferromagnets with giant magnetoresistance in magnetic random-access memories, in a continued push toward increased information density and reduceddimensions and writing energy. Besides their traditional use in sensors and actuators,ferroelectrics –with their permanent and switchable electrical polarization– are the building blockof non-volatile, high speed, random-access memories which promise performances superior tosemiconductor flash memories.While their existence has been known since the 1960s, multiferroics, i.e. materials wherepolarization P and magnetization M coexist [1, 2], have enjoyed a renaissance in recent years,because of great improvements in growth techniques and new theoretical approaches. Thecoexistence of several order parameters and their mutual coupling may open the way to newdevice concepts, including the electrical addressing of magnetic memories without magnetic fieldsand their generating currents; the creation of multi-layer multi-state logical devices, exploitingcombinations of polarization and magnetization; and magnetoelectric sensors. However, mostof the current multiferroics lack suﬃciently strong polarization or magnetization, or suﬃcientmagnetoelectric coupling, or the correct kind of magnetic order (ferromagnets are desired, butantiferromagnets are much more common).Some of the diﬃculties of single-phase multiferroics are bypassed by “metamultiferroics” builtof multilayer heterostructures of ferromagnets and ferroelectrics [3], as for example in multiferroictunnel junctions (MFTJ), where ferromagnetic electrodes are separated by a ferroelectricinsulating barrier. The resistance against tunneling across the junction depends on the relativeorientation of magnetization of the two electrodes (magnetoresistance) and on the direction offerroelectric polarization of the insulating layer (electroresistance). This enables in principle a4th Young Researcher Meeting, Trieste 2013 IOP PublishingJournal of Physics: Conference Series 470 (2013) 012013 doi:10.1088/1742-6596/470/1/012013Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd 14-level switchable resistance using external electric and magnetic fields. Of course, a furthermagnetic degree of freedom in the insulating-barrier material could potentially duplicate thenumber of states, and any chance of locally tuning the magnetization would add further designleeway. Following this line of thought, in this paper we report an ab initio investigation stronglysuggesting that PbTiO3 (PTO) doped with V (V:PTO) is a ferromagnetic small-gap insulator,hence a proper multiferroic. This is particularly interesting in view of the giant electroresistanceeﬀect predicted in tunnel junctions with PTO as ferroelectric tunnel layer [4].2. V doping of PTOHere we report the first principles prediction of a multiferroic state of lead titanate dopedwith magnetic vanadium. PTO is a well-known tetragonal perovskite with a high spontaneouspolarization (86 µC/cm2) of displacive origin. PbVO3 also happens to be tetragonal, and withan even higher spontaneous polarization (152 µC/cm2). Previous studies have shown its groundstate to be an antiferromagnetic insulator (C-type), making it not especially interesting as amultiferroic. Motivated by our previous study of V-doped ferroelectric titanates [5], we examinethe magnetic properties of vanadium diluted within the robust PTO ferroelectric.Ab initio calculations are performed within density functional theory in the generalizedgradient approximation (GGA) by Perdew-Wang using the PAW method [6, 7] as implementedin the VASP code [8]. Standard cutoﬀ is used for the plane wave basis, and the k-point meshfor the bulk is 8×8×8 (appropriately rescaled for defect super cells). The Berry phase techniqueis used to calculate the polarization change upon V doping, using strings of 16 points in thepolarization direction.-3 -2 -1 0 1E-EF (eV)-20-10010203040Density of States (a. u.)majority spinminority spinV doped PTO-0.6 -0.4 -0.2 0 0.20246810maj. dxy orbital of VFigure 1. Density of states for V:PTO. Positive curve is majority spin, negative is minorityspin. Fermi energy is at 0 eV. Inset shows a zoom of the gap peak. The dotted line is a V d-up.After studying PTO and PVO in the respective ferroelectric phases, we substituted V for oneTi in a 2×2×2 tetragonal supercell of ferroelectric PTO, i.e. dopant concentration ∼12.5%. Aselection of structure parameters (lattice constants, distance of V or Ti from neighbouring Oalong the polar axis) are collected in table 1. V has one excess electron compared to Ti, so it is,as expected, spin-polarized with a moment of 1 µB. Orbital angular momentum is assumed tobe quenched. Figure 1 displays the key result, i.e. the density of states (DOS) of ferromagneticV:PTO. As we can observe, a fully occupied peak appears in the gap of PTO, placed so thata gap of about 0.2 eV survives. This DOS feature is obviously related to the excess V electronoccupying antibonding conduction states. Indeed, as shown in the inset, the main contributionto that peak is that of spin-up d orbitals of V. Thus, PTO doped with vanadium is a small-gap4th Young Researcher Meeting, Trieste 2013 IOP PublishingJournal of Physics: Conference Series 470 (2013) 012013 doi:10.1088/1742-6596/470/1/0120132Table 1. Cell parameters for V doped PTO, bulk PTO and PVO. Theoretical values arecalculated for this work in GGA approximation. Experimental values are from references [9, 10]V:PTO PTO (Theor. / Expt.) PVO (Theor. / Expt.)a 7.848 3.924 / 3.895 3.806 / 3.804c 8.351 4.175 / 4.171 4.979 / 4.677V-Otop 1.709 - 1.700 / 1.677V-Odown 2.377 - 3.278 / 3.01Ti-Otop 1.792 1.795 / 1.75 -Ti-Odown 2.380 2.380 / 2.42 -ferromagnetic insulator thanks to the unpaired electron of dopant vanadium. The gap of PTO isof course underestimated due to the known gap error of semi-local functionals [12]; it may wellbe that the small V-related gap is also somewhat larger than calculated due to the same eﬀects(self-interaction, xc discontinuity, etc.).In the cell just discussed, V is ferromagnetic by construction, being coupled to its periodicimages. To study an antiferromagnetic configuration we consider two V’s at the sameconcentration in a 2√2×2√2×2 tetragonal cell. The two V are placed in that cell as far aspossible from each other. While the ferromagnetic configuration is stable, the antiferromagneticconfiguration is not. The V moments disappear and the system converges to a metallic Pauliparamagnet of zero moment, which is about 300 meV higher in energy than the ferromagnet.Of course, this prevents the evaluation of a coupling parameter for magnetic models, but theferromagnet seems quite stable nevertheless.Figure 2. Majority spin density of the spin-polarized electron of V in the basal plane (iso-level:10−3 e/Å3). The state is anti-bonding with first-neighbor O’s, has dxy-like nodal structure, andpropagates through dxy-like Ti states. Charge paths along the vertical axis are negligible.Inspection of the charge density of the impurity state (Fig. 2) suggests a dxy-like nodalstructure and coupling of V’s via V-O-Ti-O-... paths in the basal plane, whereas hardly anydensity is to be found along the vertical axis. While the V-centered state is, as expected, anti-bonding with first neighbors, the bonding O-V states (which mimic those of the substituted Ti)appear to make for a larger charge accumulation in the V-O bond region (Fig. 3), matching theshorter V-O bond length compared to Ti-O (1.71 vs 1.79 Å).Following Ref.[11], the equilibrium concentration is [V]=Ns exp (−Ef (V) /kTg), where Ns isthe density of Ti sites and Tg the growth temperature. Assuming that the solubility limit forV in PTO is PVO, i.e. that high V contents will eventually cause phase separation of PVO,the formation energy is Ef (V)=E(V:PTO)–(n–1)E(PTO)–E(PVO)≈1.23 eV, involving the total4th Young Researcher Meeting, Trieste 2013 IOP PublishingJournal of Physics: Conference Series 470 (2013) 012013 doi:10.1088/1742-6596/470/1/0120133Figure 3. Total charge density (in arbitrary units) in the vertical plane across a Ti-O bondin PTO (left) and a V-O bond in V:PTO. A slightly larger bond charge can be appreciated inV:PTO.energy of the doped supercell of V:PTO comprising n unit cells, and of the unit cells of PTOand PVO. Since Ns=1.25·1023cm−3, at a typical Tg=650 K we find a logarithmic concentrationlog10 [V] ≈13.4, which may increase perhaps to about 16 due to vibrational entropy (V is heavierthan Ti). This thermodynamic solubility limit is relatively low, but it may well not applywhenever kinetics or non-equilibrium phenomena become dominant, as it happens in modernepitaxial growth techniques.Finally, we estimated the changes in polarization induced by V doping. At 12.5% V we finda polarization increase of 8.3 µC/cm2, which agrees nicely with 8.25 µC/cm2 obtained by linearinterpolation between the bulk values of PTO and PVO mentioned previously. Therefore, interms of polarization, V does not seem detrimental, but in fact benign.3. ConclusionsIn summary, we presented an ab initio prediction of the proper multiferroicity of V-doped PTO.The gap is about 0.2-0.3 eV and the magnetization is 1 µB/V, or 1.5×1022 spins/cm3 at ourchosen V density. We predict the polarization to increase linearly with V concentration at thepercentual rate of 0.7 µC/cm2. Presumably this will only apply at relatively low concentrations,since the antiferromagnetic character of PVO will eventually take over.Note – During review we have become aware of a very recent study [13] of transition-metal dopingin a perovskite ferroelectric (BaTiO3), reporting results in general agreement with the ones justpresented.References[1] Wang K F, Liu J M and Ren Z F, Advances in Physics vol. 58, No. 4, 321-448 (2009).[2] Velev J P, Jaswal S S and Tsymbal E Y, Phil. Trans. R. Soc. A 369, 3069-3097 (2011).[3] Velev J P, Duan C-G, Burton J D, Smogunov A, Niranjan M K, Tosatti E, Jaswal S S and Tsymbal E Y,Nano Lett. 9, 427 (2009)[4] Ricci F, Filippetti A and Fiorentini V, In preparation[5] Scarrozza M, Filippetti A and Fiorentini V, Phys. Rev. Lett. 109, 217202 (2012).[6] Blöchl P E, Phys. Rev. B 50, 17953 (1994)[7] Kresse G and Joubert D, Phys. Rev. B 59, 1758 (1999).[8] Kresse G and Furthmüller J, Phys. Rev. B 54, 11169 (1996).[9] Rodriguez J A, Etxeberria A, Gonzalez L and Maiti A, J. Chem. Phys. 117, 2699 (2002).[10] Ming X, Yin J-W, Wang X-L, Wang C-Z, Huang Z-F and Chen G, Solid State Sci. 12, 938 (2010).[11] Van de Walle C G, Laks D B, Neumark G F and Pantelides S T, Phys. Rev. B 47, 9425 (1993).[12] See e.g. Godby R W and Garcia-Gonzalez P, in A Primer in Density Functional Theory, Springer LectureNotes in Physics; Fiolhais C, Nogueira F and Marques M A L eds. (Springer, Berlin 2003), Ch. 5, p.185.[13] Chandra H K, Gupta K, Nandy A K and Mahadevan P, Phys. Rev. B 87, 214110 (2013)4th Young Researcher Meeting, Trieste 2013 IOP PublishingJournal of Physics: Conference Series 470 (2013) 012013 doi:10.1088/1742-6596/470/1/0120134