Electronic, magnetic and multiferroic properties of magnetoelectric NiTiO3

Accepted Manuscript Electronic, magnetic and multiferroic properties of magnetoelectric NiTiO3 Chao Xin, Yi Wang, Yu Sui, Yang Wang, Xianjie Wang, Kun Zhao, Zhiguo Liu, Bingsheng Li, Xiaoyang Liu PII: DOI: Reference:

S0925-8388(14)01296-1 http://dx.doi.org/10.1016/j.jallcom.2014.05.189 JALCOM 31378

To appear in: Received Date: Revised Date: Accepted Date:

7 April 2014 23 May 2014 26 May 2014

Please cite this article as: C. Xin, Y. Wang, Y. Sui, Y. Wang, X. Wang, K. Zhao, Z. Liu, B. Li, X. Liu, Electronic, magnetic and multiferroic properties of magnetoelectric NiTiO3, (2014), doi: http://dx.doi.org/10.1016/j.jallcom. 2014.05.189

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Electronic, magnetic and multiferroic properties of magnetoelectric NiTiO3 Chao Xina, Yi Wangb, Yu Suia,*, Yang Wangb, Xianjie Wanga, Kun Zhaoa, Zhiguo Liua, Bingsheng Lib and Xiaoyang Liuc a

Department of Physics, Harbin Institute of Technology, Harbin 150001, People’s Republic

of China b

Natural Science Research Center, Academy of Fundamental and Interdisciplinary Sciences,

Harbin Institute of Technology, Harbin 150080, People’s Republic of China c

State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of

Chemistry, Jilin University, Changchun 130012, P R China

Abstract The structural, electronic, magnetic, and ferroelectric properties of NiTiO3 are predicted through ab initio calculations based on the density functional theory (DFT). The theoretical structure parameters matched well with those obtained experimentally. The electronic structure results show that the antiferromagnetic (AFM) phase of LiNbO3 (LN)-type NiTiO3 has a direct band gap of 2.16eV. The calculated local magnetic moment of Ni ion is 1.61µ B. The calculated Born effective charges (BECs, denoted by tensor Z*) show that the Z* of Ti and O atoms are significantly and anomalously large. Interestingly, ferroelectric spontaneous polarization is predicted to be along [111] direction with a large magnitude of 97µC/cm2 . B-site Ti ions in 3d0 state dominate ferroelectric polarization of multiferroic NiTiO3, whereas

*

Author to whom correspondence should be addressed. Electronic mail: [email protected]. 1

A-site Ni ions having partially filled eg orbitals are considered to contribute to the antiferromagnetic properties of NiTiO3. Furthermore, the current study also found that the polar lattice distortion can induce weak ferromagnetism. Keywords: Multiferroic; Antiferromagnetic; Weak ferromagnetism; Ferroelectric polarization 1. Introduction Magnetoelectric (ME) multiferroic materials have spontaneous magnetic and electronic order in the same phase [1]. With this coexistence, they have the spontaneous magnetization switched on by an applied magnetic field and the spontaneous polarization tuned by an electric field. Owing to the coupling between magnetic and ferroelectric orders, this can lead to ME effect, in which magnetization can be switched on by an applied electric field and vice versa [2]. The ME effect produces various possibilities in the realization of the mutual control and detection of electrical polarization and magnetism [6]. Multiferroic composite structures in bulk forms are explored as high sensitivity ac magnetic field sensors and electrically tunable microwave devices such as filters, and phase shifters. One can also explore multiple state memory elements, where data are stored in both electric and magnetic polarizations. Besides the application aspects of this technology, the fundamental physics of magnetoelectric coupling is also important for understanding the novel physical phenomena. Many efforts have been devoted to theoretically investigate multiferroic materials over the last decade [7]. It is recognized that ferroelectricity and ferromagnetism are rarely found in the same system because the conventional off-center distortion of the B ion in d0 state responsible for polar behavior is usually inconsistent with the partially filled d orbitals, which

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are a prerequisite for a magnetic ground state. The MTiO3 family of compounds with the LiNbO3 (LN)-type structure (space group R3c) stands out as a rare class of materials where the antisymmetric Dzyaloshinskii-Moriya (DM) interaction leads to weak ferromagnetism, as observed for instance in manganites and some rare-earth orthoferrites. The structure of this compound was initially predicted to be rhombohedral with R-3 symmetry, and then was confirmed by resent studies with x-ray diffraction investigations on the epitaxial film. The R-3 unit cell comprises two formula units and the RT lattice parameters are a=5.4385; α=55.1147º [9]. At high temperatures and pressures, NiTiO3 within R-3 phase transforms to a denser R3c phase through a cation reordering process. The R3c unit cell also comprises two formula units and the RT lattice parameters are a=5.4363; α=55.1136º [10]. Fennie et al. have proposed a strategy to design structures from symmetry principles, which provide that a polar lattice distortion induces weak ferromagnetism, and suggested that LiNbO3 (LN)-type materials crystallizing in the high-pressure form with a magnetic ion such as FeTiO3, MnTiO3, and NiTiO3, are candidates for multiferroic materials [11]. The prediction is thereafter validated by the synthesis of the high-pressure form of LN-type FeTiO3 which is ferroelectric at and below room temperature and weakly ferromagnetic below 120 K [12]. Recently, Varga et al [9], report the magnetic characteristics of epitaxial NiTiO3 films grown by pulsed laser deposition that are isostructural with acentric LiNbO3 (space group R3c). They also found that LN-type NiTiO3 is polar (and possibly ferroelectric) at room temperature and weakly ferromagnetic below 250K, down to at least 10K. However, the detailed structural, electronic, magnetic and dielectric properties of LN-type NiTiO3 have rarely been reported. Fundamental investigations are of importance for understanding the

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multiferroic materials and improving their practical applications. The aim of the present work is to calculate rigorously the ground-state structural, electronic, magnetic and lattice dielectric properties of NiTiO3 by using first-principles calculations to provide solid ground for further investigations. The rest of this article is organized as follows. After a brief description of the adopted first-principles calculation method and the approximations used in the calculations in Sec. 2, we first provide a detailed analysis of the ground-state structural and electronic properties in (Sec. 3.1) such as the lattice and electronic structures. Subsequently, we discuss the dielectric properties in Sec. 3.2 such as the BECs of multiferroic NiTiO3 . Finally, we draw a conclusion in Sec. 4. 2. Calculation details Our calculation is based on the first-principles density functional theory [13]. The Vienna ab initio simulation package (VASP) [14] was used with the projector augmented wave method (PAW) [16]. The Kohn–Sham equation [17] was solved using the generalized gradient approximation (GGA) [18] with the Hubbard parameter, U = 4.5 eV, J = 0.9. GGA+U has been found to be quite efficient in describing strongly correlated multiferroic systems [19] in comparison to the conventional local density approximation (LDA) and generalized gradient approximation (GGA). We employed the simplified, rotationally invariant approach introduced by Dudarev [21]. We included sixteen valence electrons for Ni (3p63d8 4s2), ten for Ti (3p63d24s2) and six for O (2s22p4) ions. A plane wave energy cutoff of 500 eV was used. The conjugate gradient algorithm [22] was used for the optimization of the structure. All the calculations were performed at 0 K. Structural optimization and calculation of the electronic band structure and density of states were carried out using a Monkhorst–Pack [23] 6 × 6 × 6

4

mesh. Spontaneous polarization was calculated using the Berry phase method [24] with 8 × 8 × 8 mesh. We started our calculations with the experimental structural parameters obtained from the x-ray diffraction spectra of crushed film of NiTiO3 obtained at room temperature [9]. In order to obtain the ground state structure, the ionic positions, lattice parameters and unit-cell shape were sequentially relaxed in such a way that the pressure on the optimized structure was almost zero and the Hellmann–Feynman forces were less than 0.01 eV / Å. 3. RESULTS AND DISCUSSION 3.1 Structure and electronic properties NiTiO3 in the LiNbO3 structure (LN-type) is a metastable compound that can be obtained by quenching from very high pressure and high temperature. At high temperatures and high pressures, ilmenite-type (IL-type) NiTiO3 transforms to a denser LN-type phase through a cation reordering process [25]. In order to explain the difference in the two phases: LN and IL, we plot the structure of the two phases, (see Fig. 1) including both rhombonedral and hexagonal representation. One can see that in ilmenite, there are two types of metal ions, which form alternating bilayers of Ni and Ti ions perpendicular to c axis, with –Ti–Ni–□–Ni–Ti– ordering along the threefold axes, reducing the symmetry to R-3. The Ni and Ti ions are octahedrally coordinated to O ions with three octahedral edges shared between cation octahedral of the same type (see the figure). Each cation octahedron shares on octahedral face with a cation of the other type in an adjacent bilayer whereas the face opposite is shared with an empty octahedral position (“hole”). The crystallographic cell contains two formula units of NiTiO3 with Ni ions at ±(0, 0, NiZ), Ti ions at ±(0, 0, TiZ) and oxygen ions at ±(Ox, Oy, Oz; -Oy, Ox-Oy, Oz; Oy-Ox, -Ox, Oz). The lithium niobate (LiNbO3 ) form differs by

5

having mixed Ni, Ti bilayers, and a threefold axis ordering of –Ni–Ti–□–Ni–Ti–. Experimental data reveal that both IL-type and LN-type NiTiO3 are antiferromagnetic (AFM). As a comparison, the data of IL-type NiTiO3 has also been calculated in this work. First, we determined the structural parameters of NiTiO3 in its two phases by relaxing simultaneously both the cell shape and the atomic positions in AFM order. Both IL- and LN-type NiTiO3 are rhombohedral with ten atoms in the unit cell. To describe their geometry, we use the primitive (rhombohedral) unit cell in this work. Atomic fractional positions are also given in rhombohedral coordinates. The calculated equilibrium structural parameters are given in Table 1, where bulk modulus B0 and its pressure derivative B’0 are determined by fitting the curve of E–V (total energy versus volume) to Murnaghan’s equation of state [26]. Fig. 2 shows E (V) for U = 4.5eV, J = 0.9 eV. The value of the bulk modulus, B0, and its pressure derivative B’0, were found to be 196GPa and 5.6 for LN-type NITiO3, and to be 195GPa and 4.8 for IL-type. The computed pressure dependence of the enthalpies, relative to IL and LN phase are also shown in the inset of Fig.2. The IL phase is more stable than the LN phase, because the energy of LN phase is slightly higher (0.05eV per formula unit) than that of IL phase, which is in close agreement with the experimental results [27].The calculated volume agrees well with the experimental one. Since experimental atomic positions of LN-type NiTiO3 are not known, it was impossible to compare theoretical lattice parameters with corresponding experimental ones. For LN-type NiTiO3, the lattice parameter is underestimated by only 0.3%. The calculated lattice parameter combining with smaller calculated angle leads to a 0.6% underestimation along [111]. The negligible deviation between theoretical and experimental values indicates that GGA (PBE for solid) is

6

satisfactory as a computational method to describe the structures of NiTiO3. For the non-spin-polarization (paramagnetic) phase of NiTiO3, the calculated DOS is shown in Fig. 3(a). Both paramagnetic and ferromagnetic phase are unstable experimentally, but they provide a bridge to understand thoroughly the spin-polarized antiferromagnetic electronic structure. The spin-polarized calculation showed that antiferromagnetic ordering is the most stable phase in the rhombohedral structure. The AFM phase is 13meV lower in energy than that of ferromagnetic state. Fig. 3(b) shows the total DOS of NiTiO3 with ferromagnetic orderings in the rhombohedral phase. The large density of states at the Fermi level indicates that paramagnetic phase is metallic and unstable according to the usual Stoner argument [28] and a low-energy structure could be achieved by allowing spin polarization and structural distortion. The ferromagnetic (FM) ordering shows the insulated property with ~1.6eV band gap. Fig. 4 shows the total density of states and the electronic band structure along the high symmetry directions of LN-type NiTiO3 within the GGA+U calculated. The Fermi energy was fixed at 0 eV. Due to the antiferromagnetic nature, all the up spin in the total DOS are almost equal to those of the down spin. The electrons in G-AFM phase display more localization compared with FM phase. Such phenomenon indicates that G-AFM is more stable and is in consistent with the calculations of the total energy. Our calculations yielded a direct band gap of ~2.35eV. Both the top of the valence band and the bottom of the conduction band locate at the Gamma point. The DOS and the energy band of LN-type NiTiO3 in Fig.4 depict that the band structure spreads over three major energy regions. The uppermost part of the conduction band spreads over 2.35 to 4eV (shown partially). Below the Fermi level, the valence bands are divided into two parts: the first part is in the energy range

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from -16.59 to -0.78 eV, whereas the second part is in the energy range from -0.51 to 0 eV. The band gap of 0.75eV is increased compared with FM phase. The top of the valence bands (TVB) and the bottom of the conduction bands (BCB) are very flat. The angular momentum character of the bands spreading over different energy regions show it is the Ni-3d and Ti-3d states that are very localized in the TVB and BCB, respectively (see the partial density of states (PDOS) of the ions in Fig.5(b) and (c). The calculated local magnetic moment of Ni ion is 1.61µ B. As we discussed in the above paragraph, the GGA+U method can improve the agreement between the theoretical and the experimental values for magnetic moment. For the optimized G-AFM LN-type NiTiO3 , the bond length between Ti and O are 2.12 and 1.86 Å meanwhile those of Ni-O are 2.02 and 2.06Å. To understand the behavior of spin polarization of NiTiO3 in the rhombohedral phase, we present the partial DOS of O-2p, Ni and Ti-3d in the AFM ordering in Fig. 5. The energy region near Fermi level is dominant by the contributions of Ni-3d electronic states. The overlap between the energy regions of Ni-3d and O-2p states indicates that there is hybridization between O-2p and Ni-3d orbitals. The orbital-resolved DOS of Ni and Ti-3d states in the AFM ordering by the GGA+U calculation are shown in Fig. 5(b) and (c). The spin-up and spin-down Ni 3d orbitals are almost occupied. However, both the spin-up and spin-down Ti-3d are empty. Since the hybridization of Ti–O is stronger than Ni–O, the Ti ion in the B site in d0 state will dominate the polar behavior, at the same time, the Ni ion in the A site with the partially filled 3d8 orbitals is responsible for antiferromagnetic ground state. This should be the reason why LN-type A (Ni, Fe) TiO3 can be a potential material as multiferroic.

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The DOS data in Fig. 5 can also shed light on the bonding behavior in NiTiO3, especially the partial covalency of cation–anion bonds, which can be further correlated with the intrinsic properties of NiTiO3. From Fig. 5, we find that Ni-3d and O-2p states are hybridized in the uppermost part of the valence band in NiTiO3. For a detailed analysis, we plotted the charge density distribution calculated using GGA+U on (111) principal plane of the unit cell as shown in Fig. 6(a). It is shown that although most of the charges are symmetrically distributed along the radius of the circles, indicating the largely ionic nature of bonding, a small amount of covalency is also shown by minor asymmetry of the charges around O ions connected to the Ti ions. However, the nature of bonding interaction as determined from the charge density distribution alone is not conclusive. Electron localization function (ELF) can provide a proof of the local influence of the Pauli repulsion on the behavior of the electrons, and allows the mapping of core, bonding and nonbonding regions of the crystal in real space. Thus the ELF can be used as a tool to differentiate the nature of different types of bonds [29]. A large value of the ELF indicates a region of small Pauli repulsion, in other words, a space with anti-parallel spin configuration while the position with the maximum ELF value has the signature of an electron pair. Fig. 6(b) shows the ELF distribution in (111) principal plane of NiTiO3, respectively, calculated by the GGA+U method. Fig. 6(b) also depicts the maximum ELF value at O sites and small values at Ni site indicating a charge transfer interaction from the Ni to the O sites. Comparing Fig. 6(a) and (b), we found that an almost complete charge transfer takes place between the Ni and O ions. Furthermore, a similar charge transfer, albeit to a lesser extent, is also observed between the Ti and O ions. Thus we can conclude that the Ni–O bonds in NiTiO3 are more ionic than Ti–O bonds. In contrast, polarization of the ELF

9

from O sites toward other O sites and the finite value of the ELF between O and Ti indicates some degree of ionic characteristics. Therefore, from the charge density and ELF plots, we can conclude that Ti–O bonds in NiTiO3 are mainly of covalent character. 3.2 Ferroelectric polarization and weak ferromagnetic The nature of bonding can be further correlated with the BECs (Z*). These charges are important quantities in elucidating the physical mechanism of piezoelectric and ferroelectric properties since they describe the coupling between lattice displacements and the electric field. BECs are also indicators of long range Coulomb interactions whose competition with the short range forces leads to the ferroelectric transition. Previous studies on many perovskite ferroelectrics show anomalously large Born charges [30], which are often explained as a manifestation of the strong covalent character of the bonds between the specific ions. On the other hand, from the structural data we find that the cation–oxygen octahedra are highly distorted. Since ferroelectric and piezoelectric responses are combined manifestations of the structural distortions and effective charges of the constituent ions, it is imperative to calculate the BECs of the constituent ions in NiTiO3. Such a calculation would help to elucidate the nature of cation–oxygen bonds and the origin of polarization in the materials. To calculate the BECs, we use density functional perturbation theory (DFPT) [32] of the linear response formalism. Table 2 summarizes the results of BECs for Ni, Ti, and three O atoms. The tensors are reported in Cartesian coordinates with the z-axis along the [111] primitive cell direction (x perpendicular to b axis, y along b axis and z along c axis in hexagonal cell). It shows that Z* of Ni and Ti is nearly isotropic and the value along z-axis is

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slightly different from that along x- and y-axis. For the O, the BECs tensor exhibits strong anisotropic character with the presence of finite off-diagonal elements as well. It is known that the formal valence of Ni, Ti and O in NiTiO3 are +2, +4 and -2, respectively. Since Z* can reflect the covalency of the bonding environment of each atom with respect to their formal valence, comparing these values with Z* in these two structures, we find that the Z* of Ti and O atoms are significantly anomalously large. The maximum change can be expressed as: ∆ max = ( Z * − Z ) / nv , where Z represents the nominal ionic charge and nv represents the number of valence. The maximum changes for Ti and O are 54% and 76% compared with the nominal charge expected in a purely ionic crystal, revealing that a large dynamic contribution superimposed to the static charge, that is, a strong covalence effect. As an important feature, this anomalism was also commonly found in other ferroelectric compounds [33]. The maximum change for Ni is only 7% compared with the static charge, indicating a relative smaller covalence effect than Ti. This is consistent with our conclusion deduced from ELF and charge density calculated above. By comparing analysis of the Z* of Ti and O in the two different structures, it can be seen that the absolute value of Z* in R-3c phase is larger than that in R3c phase whereas the value change of Ni is slight. The intrinsic electric polarization in this compound is calculated to be 97µC/cm2 by using the Berry phase method, two orders of magnitude larger than that in other perovskite compounds [34]. The direction of Ps is along the [111]-axis. According Fennie’s strategy, for NiTiO3, the weak ferromagnetism arises as a small perturbation—caused by the spin orbit interaction to a predominately collinear magnetic state, i.e., J >> D , where D and J are Dzyaloshinskii-Moriya and Heisenberg exchange,

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respectively. We also calculated the self-consistent spin-density (see Fig. 6c) in the presence of the spin-orbit interaction for the R3c structure. The spins were initialized in a collinear configuration, e.g., L0 = (2 g µ B S , 0, 0), M 0 = (0,0, 0) , and then allowed to relax without any symmetry constraints imposed. We obtain the values of spin moment and orbital moment listed in Table Ⅲ. The orbital moment of the Ni2+ ion is nonzero, which indicates that the JT distortion is not strong enough to completely quench the orbital angular momentum of Ni2+. For NiTiO3 the induced moment was very strong, M = (0, 0.31,0) µ B / f .u. , it’s agree well with Fennie’s results M = (0, 0.25, 0)µ B / f .u. , where spin-orbit effects are larger than that in FeTiO3 [11]. 4. CONCLUSIONS We have presented a theoretical study of the structure-property relationship in NiTiO3. The calculations support a rhombohedral structure with R3c symmetry and antiferromagnetic spin configuration in the LN-type phase. The electronic density of states shows hybridization among Ni-3d, and O-2p states. The calculations of electronic charge density demonstrate that symmetrical charge almost distribution on most of the major planes indicating an ionic nature of Ni-O bonds. The calculation of the electron localization function further supported a strong ionic character of Ni-O bonds and a finite degree of hybridization among Ti, O ions. Moreover, in comparing with the nominal ionic charges, the Born effective charges emphasize the covalent character of the Ti-O bonds. Our calculations also show a spontaneous polarization of 97µC/cm2 along the [111]-direction. In NiTiO3, the spin-orbital coupling effect is large, and due to the DM interaction, the spin-cant will be happened so that can lead to weak ferromagnetic.

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ACKNOWLEDGMENTS This work is supported financially by National Natural Science Foundation of China (grant No.10904024), Program for Innovation Research of Science in Harbin Institute of Technology (PIRS of HIT A201413), Funded Project of China Postdoctoral Science Foundation (grant No.20090460890), Project of Heilongjiang Postdoctoral Financial assistance (LBH-Z08158), Development Program for Outstanding Young Teachers in Harbin Institute of Technology (HIT) (HITQNJS. 2009. 071), and the Fundamental Research Founds for the Central Universities (HIT. NSRIF. 2012040). We thank the High Performance Computing Center of HIT for calculation resource.

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Figure Captions FIG. 1. (Color online) Crystal structures of the NiTiO3 in ilmenite and LiNbO3 phase. (including both rhombonedral and hexagonal representation). Grey octahedral represents NiTiO6, blue octahedral represents TiO6. FIG. 2. (Color online) Total energy versus volume for R3c and R-3 structures of NiTiO3 calculated at U = 4.6 eV, J = 0.9eV. The inset shows the relative enthalpy vs the pressure for LN and IL-type phase. FIG. 3. (Color online) Total (DOS) of the paramagnetic (a), ferromagnetic (b) structures of NiTiO3. The zero energy is set at Fermi level. FIG. 4. (Color online) Electronic structure of Rhombohedral (R3c) NiTiO3 calculated using the GGA+U method. The left panel shows a plot of the total density of states while the right panel shows the electronic band structure along high symmetry directions. FIG. 5. (Color online) Partial density of states plots of O-2p states (a); Orbital-resolved DOS of Ti-3d states (b); Ni-3d states (c), in the AFM ordering. FIG. 6. (Color online) Plots of (a) charge density along (111) principal plane of NiTiO3 unit cell, (b) ELF calculated using the GGA+U method along (111) principal plane of NiTiO3 unit cell, (c) the 3D spin density isosurface.

Table Captions TABLE 1. Optimized and experimental lattice parameters (a in Å, α in degree, and equibrium volume V0 in Å3) atomic positions and bulk modulus (B0 in GPa) of NiTiO3 phase.

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TABLE 2. Born effective charges tensor for antiferromagnetic NiTiO3 in the ferroelectric R3c and paraelectric R-3c phase. TABLE 3. Spin and orbital moments of the Ni2+ ions of NiTiO3 in the AFM state determined from GGA+U calculation.

Table 1 Phase

Unit cell parameters

Position

B(GPa)

a=5.4201;α=54.7595;

Ti(2a): 0.0005, 0.0005, 0.0005;

196.69

V0=98.85a

Ni(2a): 0.2945, 0.2945, 0.2945; O(6b): 0.0939, 0.3751, 0.7132

LN-type

a=5.4363;α=55.1136; V0=100.69b a=5.3844;α=55.1266; V0=97.87b a=5.3942;α=55.1147;

Ti(2a): 0.1431, 0.1431, 0.1431;

V0=98.91a

Ni(2a): 0.3492, 0.3492, 0.3492;

IL-type

O(6b): 0.5608, 0.9464, 0.2352 a=5.4385;α=55.1147;

Ti(2a): 0.1445, 0.1445, 0.1445;

V0=100.82c

Ni(2a): 0.3506, 0.3506, 0.3506; O(6b): 0.5607, 0.9481, 0.2277

a

Present work.

b

Ref. [11].

c

Ref. [9]

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195.34

Table 2

Ni

Ti

O1

O2

O3

1.86 -0.23 -0.00 6.14 -0.84 -0.00 -1.96 -0.63 -0.14 -3.52 -0.39 1.01 -2.53 0.85 -0.87

Ferroelectric phase 0.23 1.86 -0.00 0.84 6.14 -0.00 -0.52 -3.38 -1.08 -0.27 -1.82 0.42 0.96 -2.81 0.67

-0.00 -0.00 1.78 -0.00 0.01 4.97 -0.12 -1.23 -2.25 1.12 0.51 -2.25 -1.00 0.72 -2.25

3.21 -0.00 0.06 7.11 0.13 -0.01 -3.12 -0.49 -0.90 -4.04 0.00 1.88 -3.15 0.49 -0.91

Paraelectric phase 0.00 2.99 0.08 -0.16 7.08 -0.04 -0.53 -3.65 -1.36 -0.01 -2.85 0.02 0.53 -3.66 1.41

Table 3 Atoms Direction Spin moment Orbital momet

Ni1

Ni2

a

1.613

0.000

b

0.000

-0.155

c

0.000

0.000

a

-1.613

0.000

b

0.000

-0.155

c

0.000

0.000

18

-0.06 0.01 6.08 0.01 -0.06 8.18 -0.69 -1.34 -4.74 1.46 -0.00 -4.69 -0.71 1.34 -4.79

Figures:

FIG. 1

FIG. 2

19

FIG. 3

FIG. 4

20

FIG. 5

FIG. 6

21


We confirmed that NiTiO3 in the LiNbO3 structure is a metastable phase.
The electronic structure results show that the antiferromagnetic (AFM) phase of LiNbO3 (LN)-type NiTiO3 has a direct band gap of 2.16eV. The calculated local magnetic moment of Ni ion is 1.61µ B


The calculations also showed a spontaneous polarization of 97µC cm−2 along the

[111]-direction.
Furthermore, we show the polar lattice distortion can induce weak ferromagnetic.

22