This journal is© the Owner Societies 2018 Phys. Chem. Chem. Phys.

Cite this:DOI: 10.1039/c7cp07677k

Metamagnetism stabilized giant magnetoelectriccoupling in ferroelectric xBaTiO3–(1 � x)BiCoO3

solid solution†

Lokanath Patra, ab Zhao Pan,cd Jun Chen, c Masaki Azuma e andP. Ravindran*abfg

In order to establish the correlation between the magnetoelectric coupling and magnetic instability,

we have studied the structural, magnetic, and ferroelectric properties of BaTiO3 modified BiCoO3

i.e. xBaTiO3–(1 � x)BiCoO3 as a function of BaTiO3 concentration (x) and volume from a series of

general-gradient-corrected (GGA), GGA plus onsite Coulomb repulsion (U), full potential, spin-density-

functional band-structure calculations within the framework of density functional theory along with

synchrotron X-ray diffraction and magnetic measurement studies. G-type antiferromagnetic ordering

was found to be energetically favorable among all the considered magnetic configurations for x o 0.45

and higher concentrations stabilize with nonmagnetic (NM) states. We observe metamagnetic spin state

transitions associated with paraelectric to ferroelectric transitions as a function of volume and x using

synchrotron diffraction and computational studies, indicating a strong magnetoelectric coupling. Specifically

for x = 0.33 composition, a pressure induced high spin (HS) to low spin (LS) transition occurs when the

volume is compressed below 2.5%. Our orbital-projected density of states show a HS state for Co3+ in

the ferroelectric ground state for x o 0.45 and the corresponding paraelectric phase is stable in the NM

state due to the stabilization of LS state as evident from our fixed-spin-moment calculations and

magnetic measurements. The nature of chemical bonding has been studied using partial density of

states, electron localization function, and Born effective charge analysis. High values of spontaneous

ferroelectric polarizations are predicted for lower x values which inversely vary with x because of the

reduction of tetragonality (c/a) with increase in x which indicates the presence of both spin–lattice

and ferroelectricity–lattice coupling. Our partial polarization analysis shows that not only the lone pair at

Bi sites but also the d0-ness of Ti4+ ions contribute to the net polarization. Moreover, we find that the

HS–LS transition point and magnetoelectric coupling strength can be varied by x.

1 Introduction

The research on perovskite materials (ABO3) with both high Curietemperature (TC) and excellent ferroelectric(magnetic) performanceare widespread in industrial and scientific fields because of theirapplication in magnetic memories, sensors, actuators, transducers,and so on within a wide temperature range.1–4 Magnetoelectric(ME) multiferroics with coupled (anti-)ferroelectric and (anti-)-ferromagnetic ordering have become popular as they haveproperties to develop tunable devices.5–9 Bi-Based multiferroicshave become a center of attraction due to the high value ofelectric polarization,10,11 and Bi3+ is more environment-friendlythan Pb2+. In addition, magnetic oxides with stereochemicallyactive Bi3+ lone pair have become an area of interest, with thegoal of forming the ferromagnetic–ferroelectric coupling. Recently,Bi-based perovskites i.e. BiMO3 (M = cations with an averagevalence of 3+) have been found to form solid solution with BaTiO3,

a Department of Physics, Central University of Tamil Nadu, Thiruvarur 610101,

India. E-mail: raviphy@cutn.ac.inb Simulation Center for Atomic and Nanoscale MATerials,

Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610101, Indiac Department of Physical Chemistry, University of Science and Technology Beijing,

Beijing 100083, Chinad State Key Laboratory of Refractories and Metallurgy,

Wuhan University of Science and Technology, Wuhan 430081, Chinae Materials and Structures Laboratory, Tokyo Institute of Technology,

4259 Nagatsuta, Midori, Yokohama 226-8503, Japanf Department of Materials Science, Central University of Tamil Nadu, Thiruvarur,

Tamil Nadu, 610101, Indiag Center for Materials Science and Nanotechnology and Department of Chemistry,

University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway

† Electronic supplementary information (ESI) available: SXRD data for x = 0.1–0.5composition, ZFC/FC magnetization curves for x = 0.10, 0.20, 0.40 compositions,M–H loops for x = 0.10, 0.20, 0.40 compositions, Site and angular-momentumprojected DOS for 0.33BT–0.67BCO for G-AFM configuration obtained from GGAcalculations (U = 0 eV), polarization vs. tetragonality curve, and optimized atomicpositions for x = 0.33 composition. See DOI: 10.1039/c7cp07677k

Received 14th November 2017,Accepted 13th February 2018

DOI: 10.1039/c7cp07677k

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so that the high-temperature ferroelectric properties areoptimized.12–14 Furthermore, the B-site cations also introduce newproperties. BaTiO3-Based perovskite compounds are significantmultifunctional materials, which have been extensively researchedin the last half century.15–17 The physical properties of manycompounds, such as ferroelectric, piezoelectric, and other propertiescan be manipulated through the chemical modification usingBaTiO3.18 For example, investigations on the BaTiO3 modifiedBiFeO3 multiferroic solid solution (BFOBT) give interestingresults. This series results in excellent ME properties and highTC (TC of 580–690 1C).19 Kumar et al.20 reported that BFOBTsystem goes from a rhombohedral to cubic symmetry for0.1 o x o 0.7, and then to a tetragonal symmetry for x o 0.1.A non-centrosymmetric tetragonal symmetry was reported byKim et al.21 by neutron diffraction studies for x o 0.6. In fact,the chemical modification of modified Bi-based magneticperovskites using BaTiO3 leads to complex structural changes.

It is to be noted that, in BFOBT solid solutions, there are twocompeting mechanisms for ferroelectricity exist together, i.e.,the lone pair of the Bi atoms that shifts the Fe/Ti ion and alsothe Ti–O covalency that brings off-center displacements. In fact,these are the individual mechanisms for ferroelectricity inBiFeO3 and BaTiO3 compounds, respectively. However, thereare some drawbacks for (1 � x)BiFeO3–xBaTiO3 system. Firstly,it shows high dc conductivity because of a electron hoppingmechanism assisted by phonon between Fe2+ and Fe3+ as bothcoexist in this compound.22 Therefore, we have to improve itsresistivity by methods like sintering in an oxygen atmosphereand chemically modifying the compound.19 Secondly, chemicaldoping has been deliberately utilized to enhance the electricalproperties in BiMO3-based solid solutions. Nevertheless, inmost of the cases, the dopants added or substituted into the(1 � x)BiFeO3–xBaTiO3 system results in lowering the TC andthus limiting the temperature range of its use.22,23

It may be noted that BiCoO3 (BCO) is isostructural withtetragonal BaTiO3 (BT) (space group P4mm) where the Co3+

(3d6) ion prefers to be in a high-spin state at ambient condi-tions with a magnetic moment of 2.75 mB per Co. The Co3+

atoms make a high spin (HS)–low spin (LS) transition around5% volume compression indicating the presence of metamag-netism in the system. Due to the presence of strong tetragonaldistortion, corner-shared CoO5 pyramids form isolated layersand the presence of lone pair electrons from the Bi3+ ion bringsoffcenter displacement resulting ferroelectricity. BiCoO3 produceslarger ferroelectric polarization than BaTiO3 as the tetragonality(c/a, where c and a are lattice parameters) of BiCoO3 is muchlarger (1.27) than that of BaTiO3.24,25 Our previous first-principlesBerry-phase calculations for BiCoO3 evaluated the spontaneouselectric polarization as high as 179 mC cm�2. In addition, amongall the possible collinear magnetic orderings considered for ourtotal energy calculations, the magnetic phase was found to bestabilized with the C-AFM ordering. Further, neutron powderdiffraction (NPD) experiment confirms the C-AFM insulatingstate of BiCoO3 with the Neel temperature (TN) of 470 K.24 It isinteresting to note that the antiferromagnetic ferroelectric groundstate tetragonal P4mm structure changes to a non-magnetic cubic

paraelectric Pm%3m structure under volume compression. So, wehave concluded that BiCoO3 is having strong coupling betweenmagnetic and electric order parameters. This giant electro-magnetic coupling is resulting from metamagnetism originatingfrom HS–LS state transition of Co3+ ion. So, tetragonal phase ofBiCoO3 is a promising candidate to use as ME material forvarious applications. However, difficulty in synthesizing thiscompound in large quantity (this material is usually synthe-sized by high pressure high temperature technique) hamper itsuse. This motivated us to look for ME behavior in compositeMEs based on BiCoO3.

One can tune the properties of complex transition metaloxides by cation substitutions,26 where the B-site could exhibitfascinating cooperative electric order parameters i.e. spin, orbitaland electron order. The coupling between lattice and these orderparameters could bring out novel physical phenomena, in whichlattice is coupled with ferroelectric, ferromagnetic, and orbitaldegrees of freedom resulting colossal magnetoresistance,27 highTC superconductivity,28 multiferroism29 etc. The flexibility inthe crystal structure of bismuth-based perovskites provides anopportunity to explore unusual physical properties by chemicalmodification at A and/or B-sites. Hence, in this work, thestructural and the ME properties of composite ferroelectricxBaTiO3–(1 � x)BiCoO3 were investigated using ab initio totalenergy calculations. On one hand, these compounds are attrac-tive due to the absence of toxic Pb content and on the otherhand, they enhance physical properties compared with conven-tional ferroelectric materials. Further, as we have predictedgiant ME coupling in BiCoO3, the coupling can be tuned byvarying the x and through that identify potential new materialswith desired ME coupling strength. This motivated us to takethe present study.

2 Experimental andcomputational details2.1 Sample preparation

All samples were prepared with a cubic anvil-type high-pressureapparatus. Stoichiometric mixture powder of BaO, TiO2,Bi2O3, and Co3O4 was sealed in a gold capsule and reactedat 6 GPa and 1473 K for 30 min. A 10 mg amount of theoxidizing agent KClO4 (about 10 wt% of the sample) was addedto the top and bottom of the capsule in a separate manner. Theacquired sample was crushed and washed with distilled waterto remove the remaining KCl. After high pressure synthesis, thesamples were carefully grounded and annealed at 673 K for1 hour and slowly cooled to room temperature. The X-raydiffraction (XRD) patterns were collected with the Bruker D8ADVANCE diffractometer for phase identification at ArgonneNational Laboratory.

2.2 Magnetic measurement

The temperature dependence of the magnetic susceptibility(ZFC/FC) was measured with a SQUID magnetometer (QuantumDesign, MPMS XL) in an external magnetic field of 1000 Oe.

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2.3 First-principle calculations

All the calculations given in this work are based on the projectoraugmented wave (PAW) method30 as implemented in the Viennaab initio simulation package (VASP).31 To determine ground-statestructures for xBaTiO3–(1 � x)BiCoO3, the structure is optimizedby minimizing the force as well as stress. During the calcula-tions, the ionic positions and the shape of the crystal wererelaxed for various volumes of the unit cell until they attain anenergy convergence criterion of 10�6 eV per cell and the forceconvergence criterion of 1 meV Å�1. As the generalized gradientapproximation (GGA)32 considers the effects of local gradients ofthe charge density, it gives better equilibrium structural para-meters than the local density approximation (LDA). A smallchange in structural parameters can lead to large change inpolarization. So, we have used GGA for all our calculations to getcorrect structural parameters and atom positions. GGA with thePerdew–Burke–Ernzerhof (PBE)33 has been used for all of ourcalculations presented in this paper and this functional gavegood structural parameter for close relevant system BiFeO3.10 Wehave also included a Hubbard U (Ueff = 6 eV) to the Hamiltonianmatrix to correctly account for the strong correlation effect of Co3d electrons. A very high 800 eV plane-wave cutoff energy wasused in the present work. The calculations were performed using6 � 6 � 6 Monkhorst–Pack k-point mesh34 centered at theirreducible Brillouin zone for the ferroelectric P4mm. We haveused same energy cutoff and k-point density for all the calcula-tions. The computations were performed in paramagnetic (PM),ferromagnetic (FM) and three antiferromagnetic (AFM) i.e. A-typeantiferromagnetic (A-AFM), C-type antiferromagnetic (C-AFM),and G-type antiferromagnetic (G-AFM) configurations.35 The Borneffective charges are calculated using Berry phase method.36,37 Wehave used a uniform 8 � 8 � 8 k-point mesh in the Berry-phasecalculations for BiCoO3 and the same density of k-point is used forall the other compositions. In order to study metamagnetismpresent in the system, the total energy as a function of themagnetic moment was calculated for different volumes usingthe fixed-spin-moment method.38

3 Results and discussions3.1 Structural details

It is well known that BiCoO3 has a tetragonal perovskitestructure with space group P4mm24 so as tetragonal BaTiO3

39

but with more electrical polarization.11 In our previous work,pressure driven spin transition was observed in BiCoO3 wherethe ground state ferroelectric P4mm state changes to para-electric Pm%3m state around 5% volume compression. Also, theparaelectric phase is stabilized with a non-magnetic solutionwith Co3+ in LS state where a magnetic solution with Co3+ in HSstate was found to be the ground state for ferroelectric phaseshowing the magnetic and electric order parameter is stronglycoupled. Giant ME coupling was also found in BiCoO3 which isoriginating from the HS–LS transition of Co3+ ions.11 We havesubstituted BaTiO3 in BiCoO3 to get composite ferroelectricswith composition xBaTiO3–(1 � x)BiCoO3 where the A site is

occupied by Bi and Ba and B site is occupied by Co and Ti. Assmall compositions would require large supercells heavy com-putation time, we have performed first-principle calculationsfor selected compositions i.e. x = 0.25, 0.33, 0.5, 0.67, 0.75 and 1.To understand the pressure dependence of the lattice para-meters and spin state transition for 0.33BT–0.67BCO, the totalenergy was calculated as a function of volume for the fullyrelaxed experimental structure. In cobaltites, the HS to LS transi-tion can be obtained by doping,40 temperature driven route, andpressure driven route.11

A series of xBaTiO3–(1 � x)BiCoO3 compounds for x = 0.1to 0.5 as single phase were prepared using the above mentionedpreparation methods. Fig. 1 shows the XRD patterns for0.1BT–0.9BCO compounds which was collected by high-energysynchrotron X-ray diffraction (SXRD) of wave length 0.117 Å.The structure refinement of xBaTiO3–(1 � x)BiCoO3 was donewith the starting structural model (space group P4mm) which isbased on the crystal structure of BaTiO3 where the atomicpositions of Ba/Bi is fixed at (0, 0, 0), Ti/Co at (0.5, 0.5, zTi/Co),O1 at (0.5, 0.5, zO1) and O2 at (0.5, 0, zO2). The SXRD pattern for0.1BT–0.9BCO was fitted well by this model. 0.2BT–0.8BCO and0.3BT–0.7BCO also showed similar SXRD patterns. The SXRDpatterns for other compositions can be found in the ESI.†Fig. 2(a) and (b) show the scanning electron microscope (SEM)micrographs for 0.2BT–0.8BCO and 0.4BT–0.6BCO compositions(scale bar 3 mm and 10 mm, respectively). Though due to theincorporation of BT into BCO, inhomogeneous grain growthhas occurred, there are no noticeable difference can be seen forx = 0.2 and 0.4 compositions. However, large grains of 45 mmwith small amount of small grains of 1–2 mm in boundaryare observed.

Our experimental crystal structures data obtained from SXRDmeasurements were optimized using VASP and the calculatedlattice parameters match well with the experimental results.

Fig. 1 Rietveld full profile refinement of SXRD patterns of tetragonal0.1BT–0.9BCO at room temperature. Observed (black circle), calculated(red line), and their difference profiles (bottom line) are shown. The Braggreflection positions are indicated by the green ticks.

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In the present calculations we have used periodic supercells torepresent the substitution effect computationally i.e. for acomposition 0.33BT–0.67BCO we have used ordered 1 � 1 � 3supercells where one third of the Bi ions in BiCoO3 lattice wereperiodically replaced with Ba such that the Ti as a neighborfor Ba to mimic experimental situation. Similar approach wasused to simulate other compositions considered in this work.The 1 � 1 � 2 and 1 � 1 � 3 supercells are given in Fig. 3(a)and (b), respectively. In case of 0.33BT–0.67BCO, the ratiobetween Bi and Ba atoms at A-sites and the ratio between Coand Ti atoms at B-sites is kept as 2 : 1. We have used similar kindof methodology to simulate other compositions. The results

obtained from the total energy versus volume calculations forferroelectric and paraelectric phases of 0.33BT–0.67BCO aregiven in Fig. 4. The curve was fitted to the Birch–Murnaghanequation of states (EOS)41 and the corresponding equilibriumvolume and calculated lattice parameters matches well with ourcorresponding experimental values. The bulk modulus and itspressure derivative are found to be 105 GPa and 26.6, respec-tively for 0.33BT–0.67BCO. The calculated total energy curvesfor ferroelectric phase show two minima and one saddle

Fig. 2 The scanning electron microscope (SEM) images for (a) 0.2BT–0.8BCO and (b) 0.4BT–0.6BCO.

Fig. 3 (a) The 1 � 1 � 2 and (b) 1 � 1 � 3 supercell to simulate x = 0.5 and0.33 concentrations with their corresponding Co/Ti–O coordination.

Fig. 4 The total energy vs. volume curves for ferroelectric and para-electric phases of 0.33BT–0.67BCO.

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point. This kind of feature was already observed in BiCoO3 andthis was associated with the metamagnetism originating fromspin state transition. Similar to BiCoO3 a pressure-inducedmetamagnetic transition is observed in 0.33BT–0.67BCO wherethe Co3+ transforms from magnetic HS (ferroelectric) state tonon-magnetic low-spin(paraelectric) state which can be seen inthe discontinuity in E vs. V curve shown in Fig. 4. It is interestingto note that the equilibrium volume for the paraelectric phaseand the volume at which the local minimum is formed in thecase of ferroelectric phase, are almost equal. If we reduce thevolume further ferroelectric and the paraelectric curves coincideand this indicates the presence of ferroelectric to paraelectricphase transition in the system. A metamagnetic transition refersto nonmagnetic materials which change to (anti)ferromagneticmaterials with application of a sufficiently large amount ofmagnetic field. These types of band magnetism are mainlyobserved in Co-based materials. Similar metamagnetic behavioris also observed in the total energy curves of LaCoO3 previously.40

The lattice parameters a (c) of xBaTiO3–(1 � x)BiCoO3 linearlyincrease (decrease) with increase the value of x which results in adecrease in tetragonality (c/a). Fig. 5(a) shows the change inlattice parameters w.r.t. x as obtained from the optimized crystalstructures. The substitution of Ba2+ for Bi3+ and Ti4+ for Co3+ leadto these structural parameters changes. As the ionic radii of Ba2+

(1.56) ions are larger than the that of the Bi3+ (1.17), these cationsubstitutions induce isostatic pressure (chemical pressure) onthe lattice. The reduction in tetragonality results in an octahedralcoordination rather than a pyramidal structure (as shown in theinset of Fig. 5(a)) for higher x values in xBaTiO3–(1 � x)BiCoO3

solid solution. This large lattice distortion is associated withreduction in the lone pair electron concentration coming fromBi3+ ion and also the increase in d0 ions interactions from Ti4+

ion that gives covalency with increasing value of x. The latticestrain reduces with increasing content of BaTiO3 which is dueto a decreasing trend in the quantity of Bi ions i.e. the decrease

of lone pair electrons in the system, which implies thereduction of a strain of structure. This is evident from ourcalculated c/a ratio as a function of x.

Our high resolution synchrotron diffraction data measure-ments made as a function of x show that tetragonal to cubicphase transition occurs around x = 0.4 composition (see Fig. S1of the ESI†). To verify this, we have performed energy vs.c/a calculations for 0.5BTBCO composition. To perform thiscalculation, we have doubled the unit cell along c-axis to get a1 � 1 � 2 supercell. If the crystal is cubic, one should getminimum energy for c/a = 2. However, the total energy vs. c/acurve showing minimum value at c/a = 2.05 for the compositionx = 0.5 as evident from Fig. 5(b). It may be noted that smallcomposition variations and high temperature synthesis pro-cesses can stabilize the paraelectric phase (i.e. a phase withc/a = 2) over the ferroelectric phase as our experimental resultssuggest. However drastic reduction of tetragonality with xindicate that the system is going towards the paraelectric phasewith increase in x.

3.2 Electronic and magnetic structure

As shown in Fig. 6(a), the zero field cooled (ZFC) measurementcurve is deviated from field cooled (FC) curve at around 120 Kfor 0.3BT–0.7BCO. This type of deviation can also be explainedfrom superparamagnetism. Usually, when particle size dropsdown below 20 nm the material shows superparamagneticbehavior. But as we have mentioned earlier, the grain sizesare in mm range. So, we can conclude that the presence ofirreversibility (the difference between FC and ZFC curves) can’tbe explained by superparamagnetic behavior as the particlesizes are not small enough to reach the superparamagneticlimit.42 It may be noted that metamagnetism due to spin statetransition of Co3+ ions from HS state to LS state. Lattice strain,particle size, impurities and temperature effects can influencethe metamagnetic behavior and this may also explain the

Fig. 5 (a) Evolution of lattice parameters of xBaTiO3–(1 � x)BiCoO3 as a function of x. The rapidly decreasing a-axis and the slowly increasing c-axismake the tetragonality (c/a) to decrease continuously with the substitution of BaTiO3. The inset shows the pyramidal environment changing to octahedralenvironment of Co/Ti surrounded by O atoms due to reduction in tetragonality. The A- and B-sites are occupied by Bi/Ba and Co/Ti, respectively.(b) Total energy as a function of c/a for 0.5BT–0.5BCO in the ferroelectric P4mm phase.

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irreversibility in the magnetization. Fig. 6(b) shows the magneticfield dependence of the magnetization (M–H curves), atdifferent temperatures for 0.3BT–0.7BCO. It can be seen thatthe induced magnetization continuously rises (but does notsaturate) with the increase of the applied magnetic field (until10 kOe). The curves without any spontaneous magnetizationindicates the paramagnetic/antiferromagnetic nature of thesample. It may also be noted that as the xBaTiO3–(1 � x)BiCoO3

solid solution is a magnetically diluted system from BiCoO3,it is expected to experience similar magnetic interaction asBiCoO3, which is well known to be an antiferromagneticallyordered below its Neel temperature TN B 470 K. Therefore, thedeviation at around 120 K (Neel temperature) indicates a occur-rence of an antiferromagnetic ordering in the 0.3BT–0.7BCOcomposition. However, our spin polarized total energy calcula-tions show beyond doubt that G-AFM is the ground state for0.33BT–0.67BCO and the nonmagnetic phase is 120 meV higherin energy than the ground state(Table 1). This is also a typicalbehavior of the well-known antiferromagnetic ordering in theBiFeO3–PbTiO3 system.43–45 The Neel temperature for other0.1BT–0.9BCO, 0.2BT–0.8BCO and 0.4BT–0.6BCO are mentionedin the Fig. S2(a)–(c), respectively in the ESI.† The detailedmagnetic structure of 0.33BT–0.67BCO was determined by our

total energy calculations and discussed below. (See Fig. S3(a)–(c)for the M–H curve for 0.1BT–0.9BCO, 0.2BT–0.8BCO and0.4BT–0.6BCO, respectively in the ESI†).

The magnetic moment and the relative total energies ofvarious spin configurations with respect to the ground stateconfiguration are summarized in Table 1. Our calculationshows that 0.33BT–0.67BCO is found to be a G-type antiferro-magnetic insulator with both inter- and intra-layer antiferro-magnetic spin arrangements. This magnetic ordering is originatedby superexchange interactions in the Co3+–O–Co3+ arrangement.The magnetic moments and the band gaps are increased when weinclude U to our calculations. But it is found that 0.33BT–0.67BCOretains the G-AFM configuration irrespective of the U value. So it isclear that GGA is sufficient to obtain the ground state magneticconfiguration and the insulating behavior in 0.33BT–0.67BCO.Similar behavior was also found for 0.25BT–0.75BCO. From GGAcalculations, the total energy of G-AFM is 39, 53 and 84 meV lowerthan that of the C-AFM, A-AFM and F configurations, respectively.In order to understand the role of various magnetic configurationson the electrical properties of 0.33BT–0.67BCO, we have analyzedthe total and orbital projected density of states (DOS) for thissystem in all the magnetic orderings considered. It can be seenfrom the optimized crystal structure that Co is surrounded by 5oxygen atoms in a square pyramidal configuration (see Fig. 7).Generally Co 3d splits into non-degenerate b2g(dxy), doublydegenerate eg(dxz, dyz), non-degenerate a1g(dz2) and b1g(dx2–y2) inpresence of an ideal square pyramidal environment. Generally,the xy orbitals are higher in energy than that of the doublydegenerate yz and zx orbitals under a centrosymmetric tetra-gonal crystal field with c/a 4 1.46

But due to the non-centrosymmetric displacement presentin the system, the energy arrangement among the t2g orbitalsgets modified which results in the full occupation of xy orbitalwith an insulating energy gap above it (see Fig. 8 inset). Thepresence of Bi 6s lone-pair electrons (see Fig. 9 for the electron-localization-function (ELF)) and orbital-projected DOS for Co(see Fig. 10) indicate that the formal valence of 3+ can be

Fig. 6 (a) ZFC/FC magnetization for 0.3BT–0.7BCO. (b) M–H loops taken at various temperatures for 0.3BT–0.7BCO.

Table 1 The calculated total energies DE (meV f.u.�1) relative to thelowest energy states, the magnetic moments at Co site mCo (mB), totalmagnetic moments mTot (mB), band gap Eg (eV) values for different magneticconfigurations as a function of Ueff (eV) for 0.33BT–0.67BCO

Ueff G-AFM C-AFM A-AFM F NM

0 E 0 39 53 84 120mCo 2.588 2.537 2.779 2.818 —mTot 3.049 2.949 3.249 3.563 —Eg 0.35 0.32 0.27 0.19 Metal

6 E 0 81 104 101 —mCo 3.14 3.21 3.01 3.23 —mTot 3.25 3.45 3.24 3.52 —Eg 0.7 0.58 0.42 0.3 —

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assigned for the Co ions. According to the Pauli exclusionprinciple, the transfer of an electron to the neighboring ion isallowed in an antiparallel direction only. So, in an ideal case,the Co3+ ions in a cubic perovskite-like lattice with HS state willprefer to form the G-AFM ordering which is consistent with ourresults. The G-type AFM configuration is shown in Fig. 7 whereeach magnetic Co3+ ion is surrounded by other four Co3+ ionswith spins ordered antiferromagnetically to the central Co3+

ion. Fig. 8 shows the variation in the magnetic moment at theCo-site as a function of volume in the G-AFM state. From thiscurve it may be noted that when we compress the volume above5%, suddenly the magnetic moment at both Co and O1 sitereduces to zero showing the magnetic to nonmagnetic transi-tion in 0.33BT–0.67BCO. This effect is explained later with ourfixed spin moment (FSM) plots. Like LaCoO3, 0.33BT–0.67BCOalso has Co ions in the 3+ states. So a nonmagnetic solution canbe expected for 0.33BT–0.67BCO similar to LaCoO3. But due to

the presence of lone pair electrons at Bi site, anisotropy in theexchange interaction can also be expected. It is to be noted thatthe G-AFM state is stable with an energy which 120 meV per f.u.lower than the energy of NM state in 0.33BT–0.67BCO consis-tent with the expectation. This suggests that Bi lone pairelectrons plays a crucial role in the ferroelectric behaviors aswell as in the magnetic properties.

Fig. 7 The magnetic structure in a 2 � 2 � 2 supercell of tetragonal(space group P4mm) 0.33BT–0.67BCO with G-type magnetic configu-ration. The polyhedra shows the square-pyramidal environment of Co/Tiwith neighboring O atoms.

Fig. 8 Variation of magnetic moment at Co and O1 sites (as the O2 sitepossess negligible magnetic moment, it is not shown here) with volume forferroelectric 0.33BT–0.67BCO. The insets show the schematic diagramsfor the Co3+ in the HS and LS spin configurations.

Fig. 9 Isosurface (at a value of 0.75) of the valence electron localizationfunction of 0.5BT–0.5BCO in the ferroelectric P4mm structure.

Fig. 10 The orbital-projected density of Co 3d states for the ferroelectric(left) phase in the ground state G-AFM configuration and the paraelectric(right) phase in the NM configuration for 0.33BT–0.67BCO.

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The total DOS for different magnetic configurations of0.33BT–0.67BCO are shown in Fig. 11. The total DOS forFM configuration shows semiconducting behavior with a verysmall band gap in the minority spin channel. In case of AFMconfigurations, due to the exchange potential produced by theexchange interaction, there is a shift in energy of Co 3d bandtowards lower energy site producing a wider band gap (seeTable 1) as shown in Fig. 11. It is hereby found that not onlythe spin polarization but also the magnetic ordering plays animportant role in determining the ground state structure. Toaccount for the strong correlation effect due to the localized Co3d electrons, we have considered the correlation effect throughincluding a Hubbard U into the Hamiltonian matrix, andcalculated the energies for the considered magnetic configura-tions using Ueff value of 6 eV. Fig. 12 shows the partial DOSfor ground state G-AFM configuration obtained with GGA+Ucalculations. It can be seen that a sharp peak can be seenaround �11.5 eV which is corresponding to Bi 6s states. InBaTiO3, the Ti d and O p strongly hybridize making the chargesredistribute between the two states, resulting in a fraction of Tid states to be occupied.47,48 The Bi 6p, Co 3d, Ti 3d and O 2pstates are distributed from �7 eV to Fermi energy (EF) forminga broad band. This indicates the strong hybridization effect ofCo 3d–O 2p, Bi 6p–O 2p and Ti 3d–O 2p states. The p states ofBa atoms and the 2s states for O1 and O2 are well-localizedand are present around �11 eV and �18 eV, respectively. It iswell known that, in magnetic perovskites, the hybridizationbetween Co 3d and the surrounding oxygen ligands often leadto superexchange interactions. The partial DOS curves plotted

with U = 0 (GGA) is given in Fig. S4 of the ESI.† It can be seenthat the DOS curves shows almost similar features except thestates with GGA+U get more localized to produce a bandgaplarger than that of in the case of GGA. The localization ofd electrons produces a larger magnetic moment which can beseen from Table 1.

As the Bi 6s, Bi 6p and O 2p states are occupied, thehybridization between them is unexpected at the first sight.But these issues have an important role on the properties ofxBaTiO3–(1 � x)BiCoO3. So, they can be understood as follows.As it can be seen from the partial DOS (PDOS) plot shown inFig. 12 that Bi 6p–O and 2p states are energetically degenerateindicating the presence of hybridization between them. As theBi lone pairs are 6s electrons, one could expect a sphericaldistribution around the atom. But Fig. 9 confirms the presenceof a lobe at the Bi site. A lobe type structure can be formedonly when there is a hybridization interaction between the lonepair and the orbitals of neighboring ions. Moreover, Watsonand Parker49,50 have suggested that lone pairs can form lobeshaped structure due to the p character from the anions. So, toform a lobe, there must be some hybridization between thelone pair 6s electrons and o p states. Bi 6s and O 2p orbitals canhybridize if they are energetically degenerate. From Fig. 12, itcan be seen that though O p electrons gives major contributionto the top of the valence band, finite O p electrons can be foundaround �10 eV. Interestingly, the Bi 6s electrons are alsopresent around �10 eV. So, it is confirmed that there is ahybridization interaction between O p and Bi 6s electrons dueto which the lone pair electrons are distributed to form a lobe.

Fig. 11 Calculated total DOS for 0.33BT–0.67BCO in FM, A-AFM, C-AFMand G-AFM configurations.

Fig. 12 Site and angular-momentum projected DOS for 0.33BT–0.67BCOfor G-AFM configuration obtained from GGA+U calculations withUeff = 6 eV.

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It can be seen from Fig. 9 that negligible still finite value of ELFpresent between the atoms indicates the presence of noticeablecovalency in the material though ionic bonding is dominant.Also, the maximum ELF distribution can be seen at O siteswhich indicates the charger transfer interaction from Bi/Ba andCo/Ti sites to O sites. Moreover, the presence of finite ELFbetween Ti/Co and O shows the covalent bonding which isconsistent with our non-integer Born effective charges forthe constituents.

Table 1 shows that the calculated magnetic moment at theCo site obtained from GGA and GGA+U calculations for variousmagnetic orderings considered for our study. Our GGA calcula-tions show that the value of the magnetic moment variesbetween 2.537 mB and 2.818 mB per Co atom. Due to the presenceof a hybridization interaction with the neighboring O ions, Coatoms possesses non-integer magnetic moment values. One canexpect induced magnetic moment at O sites due to hybridizationinteraction. In our calculations for FM configuration, we foundan induced magnetic moment of 0.35 mB O sites which have asimilar polarization direction as that of the Co sites. So we getthe net total moment considerably larger than Co moments in0.33BT–0.67BCO (see the total moment in Table 1). When weinclude U, there is an increase in the magnetic moments for allthe configurations because the Co 3d states get more localized.The spin state of Co3+ has been always a topic of interest for thescientific community from the last few decades due to exoticbehavior arising from spin state transitions. In general, theoctahedral CoO6 coordination environments stabilize with Co3+

ions in a low-spin (LS) state where the pyramidal CoO5 coordina-tion environments prefers to be in a high-spin (HS) or inter-mediate spin (IS) state. In case of pure ionic compound, the Co3+

3d6 electrons will fill the energy levels either with a non-magneticLS state (b2

2g e4g a0

1g b01g) or with a magnetic HS state (b2

2g e2g a1

1g b11g)

having spin moments 0 and 4 mB, respectively. In the IS configu-ration (b2

2g e3g a1

1g b01g), one can expect a magnetic moment of 2 mB

per Co. The electrons in transition metals either participate inbonding or magnetism. Hence, it is expected that the calculatedmagnetic moments would be smaller than that for the pure ioniccase due to presence of covalent hybridization. So, the Co can beassigned a HS state in the ferroelectric phase with a calculatedspin moment of 3.05 mB f.u.�1. The cooperative magnetism in0.33BT–0.67BCO is originating from the partially filled andlocalized b2

2g e2g a1

1g b11g orbitals in Co3+ ions. Our orbital-

projected DOS in Fig. 10 is also in good agreement with ourexplanations and shows a LS and HS state of Co for the para-electric and ferroelectric phases, respectively. To examine thevolume dependence of the spin state transition, we have per-formed FSM calculations for 33% BaTiO3 doped BiCoO3 inwhich magnetic moment m is used as an external parameterand the total energy is calculated as a function of m. The FSMcurves for various unit cell volumes of 0.33BT–0.67BCO areplotted and shown in Fig. 13. It can be seen from the plotthat the energy difference between the HS and LS state is about0.2 eV f.u.�1. The curves show that the equilibrium volume and2.5% compressed volume are stabilized in HS state with momentaround B3.6 mB and if the volume compression is more than

2.5%, the system makes a HS–LS transition and the LS statebecomes more stable than HS state. This results suggest thepresence of stong magnetovolume effect in this material andhence the HS to LS transition of Co3+ also plays an importantrole in the giant volume contraction.

From the total energy calculations, we have found that theground state magnetic ordering for 0.33BT–0.67BCO and0.25BT–0.75BCO is G-type AFM where both the inter- andintra-planes are having antiferromagnetic ordering as shownin Fig. 7. For x = 0.5, 0.67, and 0.75 the ground state emergesto be non-magnetic with Co3+ ions in LS state. In order tounderstand the magnetic to nonmagnetic phase transition as afunction of compositions (see Fig. 14), the total energy ofxBaTiO3–(1 � x)BiCoO3 in the tetragonal structure is calculatedfor the G-type antiferromagnetic as well as the nonmagnetic caseas a function of x. Let us first analyze the possible electronicorigin of the stability of the magnetic tetragonal phase forx = 0.33 configurations. From the orbital-projected DOS given

Fig. 13 The fixed spin moment curves for 0.33BT–0.67BCO for variousvolumes. The horizontal dotted line represents the total energy for theNM case.

Fig. 14 Total energy difference between antiferromagnetic and nonmag-netic state of xBaTiO3–(1 � x)BiCoO3 as a function of x.

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in Fig. 10, it can be seen that, for the paraelectric phase in theNM configuration, the nonbonding t2g electrons are highlyconcentrated around the EF. As the one-electron energy increaseswith increasing concentration of electrons closer to EF, thepresent condition is not preferable for stability. So, a Peierls–Jahn–Teller-like instability51 is expected and the system prefersto lower its symmetry. In our case, 0.33BT–0.67BCO stabilizeswith a low symmetric tetragonal structure. However, for tetra-gonal antiferromagnetic phase, the t2g levels split into doublydegenerate a1g state and singly occupied b1g state. As a resultthere is a gain in the total energy of the system due to this crystalfield splitting along with exchange splitting. Hence, we get alower energy for the antiferromagnetic than the nonmagneticphase (Table 1). Also it can be seen from Fig. 11 that, the EF fallson gap in the DOS in the tetragonal structure of 0.33BT–0.67BCOin the G-AFM configuration. Moreover, EF is located on the gapwhich is a suitable condition for the structural stability. So,0.33BT–0.67BCO stabilizes in the G-type antiferromagnetictetragonal structure. For x = 0 and 0.25 also, our calculationssuggest that xBaTiO3–(1 � x)BiCoO3 will stabilize in the G-typeAFM structure with insulating behavior. It is also clear from thecomposition vs. total energy difference between nonmagnetic–magnetic configuration plot (see Fig. 14) that from magnetic tononmagnetic transition is taking place around x = 0.45. Thesystem is in the ferroelectric as well as magnetic in thecomposition range x o 0.45. So one could expect magneto-electric behavior in the system. However, x 4 0.45, the systemstabilizes in the nonmagnetic state with ferroelectric distortion.

The magnetic properties of xBaTiO3–(1 � x)BiCoO3 aredetermined by 2 factors i.e. the composition of the Co atomsand their distance with respect to O atoms. For higher x values,the overlap interaction between the A-site cation with neigh-bours increases which will suppress the magnetic interaction.Further one increase the x, the amount of d electrons in thesystem get reduced since Ti4+ ion in principle don’t have anyd electrons. This reduction in d-electron also contribute toweakening of exchange interaction. As a result, the spontaneousmagnetic ordering disappears when we go beyond x = 0.45. Alsofor higher x values not all Co atoms have enough Co atomsas neighbors to have exchange interaction which makes non-magnetic states stable at higher x values. It may be noted thatwhen we increase the BaTiO3 content, the nearest distancebetween B-site also increases and hence one can expect enhance-ment in magnetic interaction due to localization of electrons.However, due to the increase in covalency and decrease in the delectron concentration brings nonmagnetic state stable overmagnetic state for x 4 0.45. Moreover the tetragonality decreaseswith increase in x and hence the interatomic distance betweenB-site cations increases (for a tetragonal system, the distancebetween B-site cations = the length of the a-axis) which weakensthe super-exchange path and hinders the antiferromagneticinteractions.

3.3 Born effective charge and spontaneous polarization

The Born effective charges (BEC, Z*) were calculated using theBerry phase approach generalized to spin-polarized systems.36,37

BECs are important to understand the piezoelectric and ferro-electric properties since they provide a clear idea about therelation between the lattice displacements and the electricfield. They also give an indication of long range Coulombinteractions whose competition with the short range forcesproduces a polarized ground state. A large Z* value suggeststhat even if the electric field generated by the atomic displace-ments is small, it can generate larger force resulting in thestabilization of polarized state. The averages of the calculateddiagonal components of Z* values for 0.33BT–0.67BCO areZBi* = 5.39, ZBa* = 3.13, ZCo* = 3.29, ZTi* = 5.30, ZO1* = �2.91,and ZO2* = �2.59. In case of a pure ionic picture, Bi, Ba, Co, Tiand O in xBaTiO3–(1 � x)BiCoO3 are 3+, 2+, 3+, 4+ and 2�,respectively. The value of Z* higher than formal oxidation stateof an ion shows the presence of covalency in the bondinginteraction of the ion with its neighbours. We found that theZ* of the constituents in xBaTiO3–(1 � x)BiCoO3 are signifi-cantly large which shows the large dynamic contribution of thecovalency effect which is superimposed to the static charge. It iscommon to get these type of abnormally larger BEC values thanformal oxidation state for the constituents in ferroelectriccompounds.52,53 The BEC for Co is only 10% higher withrespect to its static charge indicating a relatively smallercovalency effect than that from Ti (+32% higher than the formalvalency). This is because the electrons in Co atoms contributemore to magnetism rather than bonding. This is in consistentwith our conclusion from the deduced magnetic momentsat different atomic sites and also the bond length fromthe optimized structure of 0.33BT–0.67BCO (Co–O = 1.884 Å,Ti–O = 1.787 Å).

The BECs can also be used to calculate the spontaneouspolarization in xBaTiO3–(1� x)BiCoO3. It is well known that theparaelectric phase produces zero net polarization due to theabsence of off-center displacement. So, the spontaneous elec-tric polarization can be calculated by keeping the optimizedlattice parameters and atom positions of both the paraelectricand ferroelectric phase and calculate the displacements of ionswith respect to the paraelectric phase. The introduction ofBaTiO3 results in decreasing in length of c-axis and increasein length of a-axis, resulting the reduction of tetragonality (c/a).As a result, xBaTiO3–(1� x)BiCoO3 with higher value of x producesan octahedral rather than a pyramidal coordination. The spon-taneous polarization for 0.25BT–0.75BCO was calculated to beB90 mC cm�2 which is comparable to that of multiferroicBiFeO3

10 and much higher than typical piezoelectrics phasesuch as PbZr0.52Ti0.48O3 (54 mC cm�2)54 and PbTiO3–BiScO3

(40 mC cm�2).55 The analysis on the partial polarization showsthat not only the Bi3+ lone pairs contribute to the polarizationbut also there are contributions from the displacement of theions when going from paraelectric to ferroelectric phase due tothe strong Ba/Bi–O hybridization as well as the couplinginteraction between cations such as Ti/Co and Ba/Bi. Similarprocedure was followed to calculate polarization using thenominal ionic charges and it yielded a Ps of B50 mC cm�2,almost 45% less than the value obtained using the BECs. Thereduction in the value of polarization obtained using nominal

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ionic charges is related to the covalency effect. The calculatedpolarization values are found to decrease systematically inxBaTiO3–(1 � x)BiCoO3 with the increase in x as shown inFig. 15. This can be understood as follows. It is well known thatthe tetragonality has direct effect on electrical polarization ofthe tetragonal lattices. Due to the introduction of BaTiO3, c-axisdecreases and in a-axis increases, resulting the reduction oftetragonality (c/a). So there is a decreasing trend is seen in thepolarization value with increase in value of x (see Fig. S5 in theESI† for polarization vs. c/a plot). Also as we increase x, the Biatoms are replaced by Ba atoms at the A-site resulting areduction in the lone pair electron concentration in the latticeand consequently a decrease in polarization.

4 Conclusion

The present experimental and DFT calculation results indicatethat xBaTiO3–(1 � x)BiCoO3 possesses magnetoelectric behavior forx o 0.45, which simultaneously show the coexistence of ferro-electricity and antiferromagnetism. Volume contraction has beenobserved in xBaTiO3–(1 � x)BiCoO3 system at the ferroelectric-to-paraelectric phase transition point for BaTiO3 concentration o0.45where the Co3+ makes an HS–LS transition. For higher x values, itchanges to nonmagnetic ferroelectric phase with reduction inspontaneous polarization value because of reducing tetragonality.Hence, we have reported that metamagnetism/magnetic instabilitycan induce strong magnetoelectric coupling in materials. Theseresults show a possible way to design potential materials where themagnetic properties can be varied drastically i.e. one can go from amagnetic state to a nonmagnetic state, and vice versa by theapplication of an electric field as shown here. This kind of giantcoupling between the magnetic and electric order parameterscan be used to design spintronic devices. Also, it can be used todesign data-storage media which can be a good alternative tomagneto-optical disks where the slow magnetic writing process isreplaced by a fast magnetic inversion using electric fields. Thus, thestrong coupling between metamagnetism and giant magneto-electricity will encourage further study towards identifying potentialmultiferroics for various practical applications.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful to the Research Council of Norwayfor providing computing time at Norwegian supercomputerconsortium (NOTUR). This research was supported by theIndo–Norwegian Cooperative Program (INCP) via Grant No.F. 58-12/2014(IC). L. P. wishes to thank Prof. Helmer Fjellvågand Prof. Anja Olafsen Sjåstad for their fruitful discussions.L. P. also thanks Mr Ashwin Kishore MR for critical reading ofthe manuscript.

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