A-Site Ordered Double Perovskite CaMnTi2O6 as a Multifunctional

Sep 11, 2017 - Using symmetry principles and first-principles calculations, we examine the structural origin of ferroelectricity in A-site ordered CaM...
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A‑Site Ordered Double Perovskite CaMnTi2O6 as a Multifunctional Piezoelectric and Ferroelectric−Photovoltaic Material Gaoyang Gou,*,† Nenian Charles,‡ Jing Shi,§ and James M. Rondinelli*,∥,⊥ †

Frontier Institute of Science and Technology and State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’ an 710049, People’s Republic of China ‡ Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States § MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Xi’ an 710049, People’s Republic of China ∥ Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208-3108, United States ⊥ Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States S Supporting Information *

ABSTRACT: The double perovskite CaMnTi2O6, is a rare Asite ordered perovskite oxide that exhibits a sizable ferroelectric polarization and relatively high Curie temperature. Using first-principles calculations combined with detailed symmetry analyses, we identify the origin of the ferroelectricity in CaMnTi2O6. We further explore the material properties of CaMnTi2O6, including its ferroelectric polarization, dielectric and piezoelectric responses, magnetic order, electronic structure, and optical absorption coefficient. It is found that CaMnTi2O6 exhibits room-temperature-stable ferroelectricity and moderate piezoelectric responses. Moreover, CaMnTi2O6 is predicted to have a semiconducting energy band gap similar to that of BiFeO3, and its band gap can further be tuned via distortions of the planar Mn−O bond lengths. CaMnTi2O6 exemplifies a new class of single-phase semiconducting ferroelectric perovskites for potential applications in ferroelectric photovoltaic solar cells.

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INTRODUCTION

In comparison with B-site ordering, A-site cation ordering is less common in perovskite oxides. As a general rule, A-site cation ordering requires alloying of two cations with large differences in ionic radii and oxidation states. In addition, A-site ordering is often found in combination with some specific octahedral rotation patterns (i.e., a+a+a+ and a+a+c− rotations in Glazer notation11) or anion/A-site cation vacancies.4 The appearance of either large octahedral rotations or anion/cation vacancies in perovskite oxides, however, is unfavorable for ferroelectricity. Therefore, bulk ferroelectric A-site ordered double perovskite oxides (A,A′)BO3 have rarely been reported. Nonetheless, A-site ordered perovskite (CaMn)Ti2O6 has recently been synthesized using a high-pressure technique.12 It crystallizes in a polar P42mc tetragonal symmetry and exhibits a sizable ferroelectric polarization. CaMnTi2O6 is a rare example where A-site cation order and ferroelectricity coexist. A better understanding of the interplay among cation ordering, ferroelectricity, and other structural distortions (i.e., octahedral rotations) in CaMnTi2O6 will enable the functional design of other cation ordered ferroelectric perovskites. Moreover, owing

Perovskite oxides are of great scientific and technological importance, as they exhibit various important material properties, including large ferroelectricity and piezoelectricity, ferromagnetism, superconductivity, and colossal magnetoresistance.1,2 Most perovskite oxides adopt the simple ABO3 chemical formula, where corner-sharing BO6 octahedra form a three-dimensional network and large A-site cations are located at the 12-coordinated cuboctahedral cavities. Owing to the structural and compositional flexibility of ABO3 perovskites, both A and B sites can accommodate a wide variety of atomic combinations.3,4 As a result, in those double perovskite (AA′)(BB′)O3 compounds, where either the A or B site contains multiple elements, cation ordering can play an important role in determining the properties.5,6 For example, A-site ordered CaCu3Ti4O12 exhibits a nearly temperature independent colossal dielectric constant.7,8 Magnetism in CaCu3Fe2Nb2O12 is highly sensitive to B-site Fe/Nb ordering.9 Various B-site order arrangements can also effectively tune the band gap of double perovskite Bi2FeCrO6 such that it becomes a novel semiconducting material suitable for solar energy conversion.10 © XXXX American Chemical Society

Received: July 20, 2017

A

DOI: 10.1021/acs.inorgchem.7b01854 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry to the magnetic interactions between Mn2+ ions, CaMnTi2O6 exhibits an antiferromagnetic spin ordering with a Néel temperature TN = 10 K.12 The coexistence of ferroelectricity and magnetic order at low temperature suggest that it is a potential multiferroic. Many multiferroic materials, such as BiFeO3,13−16 Bi2FeCrO6,10,17 and hexagonal TbMnO3,18 have been extensively studied for ferroelectric photovoltaic applications, as they have (i) semiconducting band gaps (Eg < 3.0 eV) suitable for absorption of visible light10,13,18 and (ii) internal electric fields from polar ionic displacements that allow effective separation of photoexcited electron−hole pairs.15,19 Therefore, an assessment of the electronic structure and optical absorption properties of CaMnTi2O6 is required to determine its potential as a ferroelectric−photovoltaic material. In this work, we use first-principles calculations to examine the structural and ferroelectric properties of CaMnTi2O6. We show that the ferroelectric instability, corresponding to polar Mn and Ti cation displacements, is responsible for the electric polarization and ferroelectric to paraelectric phase transition in CaMnTi2O6. We also simulate the dielectric and piezoelectric responses for single-phase CaMnTi2O6 and propose that alloying with other ferroelectric end members can improve the acentric properties. We further investigate the magnetic properties of CaMnTi2O6 by calculating the spin exchange interactions among Mn ions. We find that there are overall weak magnetic interactions in the crystal that lead to the low ordering temperature. Finally, we examine the electronic structure of ferroelectric CaMnTi2O6 using a hybrid functional and demonstrate a feasible route to optimize the band gap of CaMnTi2O6 for photovoltaic applications.

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Figure 1. Crystal structure of ferroelectric CaMnTi2O6 with P42mc tetragonal symmetry. FM, A-AFM, C-AFM, and G-AFM collinear spin configurations were considered in our calculations, where the first-, second-, and third-nearest-neighbor magnetic coupling coefficients between Mn ions are represented by parameters J1, J2, and J3, respectively. Crystallographic a, b, and c axes are along pseudocubic [100], [010], and [001] directions, respectively.

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RESULTS AND DISCUSSION Structural and Ferroelectric Properties. Ground-State Structures and the Origin of Ferroelectricity. We start our investigation by studying the ground-state structures of the Asite ordered double perovskite CaMnTi2O6. In experiment, CaMnTi2O6 crystallizes in a tetragonal P42mc phase at room temperature, where Ca and Mn cations are arranged into columns along the c axis,12 forming “columnar” type A-site cation ordering along the crystallographic (110) plane (Figure 1). In such a columnar arrangement, Ca cations exhibit a 10coordinate polyhedral environment and Mn cations display alternating tetrahedral and square-planar MnO4 coordination. Moreover, A-site Mn2+ ions with high-spin states (3d5) should exhibit long-range magnetic order in CaMnTi2O6. After performing structural optimizations of the P42mc CaMnTi2O6 phase with different collinear spin structures between Mn ions, we determined C-type AFM ordering as the ground-state magnetic configuration. In such a magnetic configuration, Mn2+ ions (with high-spin moment of 4.39 μB) from the same column are ferromagentically coupled and each Mn−Mn column is antiferromagentically aligned to the nearest neighboring columns. Consistent with the experimental results (Table 1 and Table S1 of the Supporting Information), our optimized CaMnTi2O6

COMPUTATIONAL METHODS

Double perovskite CaMnTi2O6 was simulated using spin-polarized density functional theory calculations implemented in the QUANTUM ESPRESSO code (QE)20 and Vienna Ab initio Simulation Package (VASP).21,22 QE Computational Details. Nonlocal optimized norm-conserving pseudopotentials23,24 and a 60 Ry plane-wave energy cutoff were used for plane-wave calculations within QE. We used a 6 × 6 × 6 Monkhorst−Pack k grid,25 and the crystal structures of CaMnTi2O6 were fully optimized until the Hellmann−Feynman forces for each atom were less than 1 meV/Å and the stresses were less than 0.1 kbar. Partial core corrections26 were included in the Mn pseudopotential. The PBEsol exchange-correlation functional,27 which was successfully applied to manganite pervoskites,28,29 was used. To simulate the magnetic exchange interactions between Mn ions, ferromagnetic (FM) and A-type, C-type, and G-type antiferromagnetic (A-AFM, C-AFM, and G-AFM, respectively) collinear spin configurations within a 40-atom cell (see Figure 1) were considered for CaMnTi2O6. Phonon frequencies and eigenvectors were calculated on the basis of density functional perturbation theory (DFPT).30,31 The electronic contribution to the polarization was calculated following the Berry phase formalism.32 VESTA software33 was used to draw the crystal structure of CaMnTi2O6. VASP Computational Details. We treated the core and valence electrons using the projector augmented wave method34 with the valence electron configurations 3s23p64s2 (Ca), 3p63d64s1 (Mn), 3s23p63d24s2 (Ti), and 2s22p4 (O) and a 400 eV plane wave cutoff. Electronic structures for both QE optimized and experimentally measured CaMnTi2O6 structures were then examined using the HSE06 (25% of exact exchange and screening μ = 0.207) hybrid functional35,36 implemented in VASP.

Table 1. Calculated and Experimental Structural Parameters, Magnetic Moments, and Ferroelectric Polarization for the Ground-State P42mc CaMnTi2O6 Phasea PBEsol exptl a

a (Å)

c (Å)

c/a

V (Å3)

μMn (μB)

P (C/m2)

7.47 7.54

7.59 7.60

1.02 1.01

423.59 431.81

4.39 (4.57) 4.92

0.30 ∼ 0.24

μMn obtained from HSE calculations is given in parentheses.

structure with C-AFM ordering crystallizes in a polar P42mc symmetry, exhibiting an a+a+c− TiO6 octahedral rotation pattern in Glazer notation11 and a spontaneous polarization along the c axis. The a+a+c− rotation pattern is reported to be crucial to stabilize A-site cation ordering,4 as it can remove the crystallographic equivalence for A-site cations (CaO10 polyhedron vs tetrahedral and square-planar MnO4). We next use a symmetry-adapted mode decomposition37,38 to analyze the B

DOI: 10.1021/acs.inorgchem.7b01854 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 2. Three major crystallographic modes relating the ferroelectric P42mc CaMnTi2O6 phase to the high-symmetry P4/mmm reference structure: in-phase rotation (described by irrep A+4 ) and out-of-phase rotation (Z−2 ) of octahedral TiO6 and polar displacements along the crystallographic c axis (Γ−3 ). Oxygen anions are omitted for clarity. The crystallographic relations from the high-symmetry P4/mmm to low-symmetry P42mc CaMnTi2O6 phase are also presented.

structural modes in CaMnTi2O6. As shown in Figure 2, the ground-state P42mc phase is related to the high-symmetry P4/mmm reference (the distortion-free CaMnTi2O6 structure) via three primary crystallographic modes: in-phase a+a+c0 TiO6 octahedral rotation (described by the irreducible representation (irrep) A+4 ), out-of-phase a0a0c− rotation (Z−2 ), and polar displacements of Mn and Ti cations (Γ−3 ). Owing to the small tolerance factor, (τ = (rA + rO)/√2(rTi + rO) = 0.75, where rA is the average ionic radii of the A-site cations) of CaMnTi2O6, A+4 and Z−2 octahedral rotation modes have larger normalized mode amplitudes in comparison to the Γ−3 polar mode (0.80 and 0.53 vs 0.12). On the basis of crystallographic symmetry analysis, Figure 2 also summarizes the phase-transition sequences connecting the high-symmetry P4/mmm and ferroelectric P42mc phases. The combination of the A+4 and Z−2 modes yields the a+a+c− rotation pattern and reduces the symmetry to the centrosymmetric tetragonal P42/nmc phase. Further symmetry reduction from P42/nmc to P42mc phases occurs by involving the Γ−3 polar mode. We next determine the crystal structure of the P42/nmc phase (see Figure 2) by computing the phonon modes of the high-symmetry P4/mmm phase. The unstable phonon modes associated with the a+a+c0, a0a0c− octahedral rotations exhibit imaginary frequencies ω = 240.0i and 250.4i cm−1. The a0a0c+ polar displacement is also considerably unstable (ω = 185.6i cm−1). After imposing both the a+a+c0 and a0a0c− modes into the P4/mmm phase, followed by DFT structural relaxation, we obtain the nonpolar P42/nmc phase with a+a+c− rotations. Among the three phases, the ground-state ferroelectric P42mc phase is lowest in energy, followed by P42/nmc. The large energy difference between P42/nmc and P4/mmm phases (ΔE = 2.73 eV/f.u.) indicates the A+4 and Z−2 octahedral rotation modes are the major driving force in stabilizing the CaMnTi2O6 structure (see also Figure S1 of the Supporting Information). The P42/nmc space group (No. 137) is a minimal supergroup of P42mc (No. 105), and we find that the Γ−3 polar mode is the only (primary) order parameter across the P42/nmc → P42mc phase transition. We next assess the ferroelectric mechanism in CaMnTi2O6 by examining the atomic polar displacements and energy profile connecting the paraelectric P42/nmc and ferroelectric P42mc structures. Figure 3a shows the cation displacements in the ferroelectric P42mc phase with respect to the P42/nmc paraelectric reference: Ti and planar coordinated Mn cations displace along the c axis (opposite to O displacements), leading to broken inversion symmetry and a net polarization along the c axis. In addition, Ca cations from the neighboring Ca−Ca columns are displaced oppositely (also see Table S3 of the Supporting Information). We next use a

Figure 3. (a) Major cation displacements (indicated by black arrows) in the ferroelectric P42mc CaMnTi2O6 structure relative to the nonpolar P42/nmc phase. Ca cations from the neighboring columns displace in an opposite direction and are not shown for clarity. O anions displace oppositely to the Mn and Ti cations. (b) Energy evolution as a function of ferroelectric polarization connecting the ferroelectric P42mc and paraelectric P42/nmc phases (polarization of zero) of CaMnTi2O6. Symbols are first-principles results, and lines are fits to the data based on a Landau model. The ferroelectric double well energy profile is a signature of the second-order ferroelectric− paraelectric phase transition in CaMnTi2O6.

dynamic charge model, whereby the polarization contributed by 1 each cation is given as p ⃗ = Ω ∑i uiZi*, where Ω is the cell i volume and ui and Z* are the cation displacement and Born effective charges of the corresponding cations, resepctively, to calculate the polarization from the Ti and Mn cations as 0.18 and 0.06 C/m2, respectively. We find a negligible contribution (0.02 C/m2) from the Ca displacements. The overall good agreement between the Berry phase result (the total polarization P = 0.30 C/m2) and the dynamic charge model (P = 0.26 C/m2) indicates that the ferroelectricity in CaMnTi2O6 mainly originates from the aforementioned cation displacements. Figure 3b summarizes the energetics across the paraelectricto-ferroelectric phase transition in CaMnTi2O6. The doublewell P−E curve is obtained by recording the variation of the electric polarizations and total energy of CaMnTi2O6 with respect to the amplitude of the Γ−3 mode connecting the paraelectric and polar phases. Such a potential curve is well described using a second-order (continuous) Landau phase transition model: - (P) = α/2·(T − TC)P2 + β/4·P4, where TC is the Curie temperature of CaMnTi2O6. TC can be estimated by the Abrahams relation TC = (2.0 × 104)(Δz)2 K, where Δz is the largest cation displacement along the polarization direction, after a shift of origin to make ∑Δz = 0.39,40 For CaMnTi2O6, Δz = 0.16, −0.08, and −0.08 Å for the Ti, Ca, and Mn ions, respectively, and the estimated TC value is 542 K, which is close to the experimental value (630 K).12 Therefore, C

DOI: 10.1021/acs.inorgchem.7b01854 Inorg. Chem. XXXX, XXX, XXX−XXX

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are obtained. As shown in Table 3, Mn ions are in high-spin states for all magnetic CaMnTi2O6 configurations. Moreover,

CaMnTi2O6 undergoes a second-order (continuous) ferroelectric phase transition. Moreover, the symmetric energy curve [- (−P) = - (P)] indicates that CaMnTi2O6 is a proper ferroelectric similar to BaTiO3, rather than a rotation-induced hybrid improper ferroelectric as found in some A-site ordered double perovskites.41−44 Dielectric and Piezoelectric Responses. Our calculations indicate that the ground-state structure of CaMnTi2O6 is ferroelectric with sizable electric polarization and relatively high Curie temperature TC. Therefore, CaMnTi2O6 should exhibit stable ferroelectricity at room temperature and functional dielectric and piezoelectric responses (Table 2).

Table 3. Optimized Structural Parameters, Magnetic Moments, Ferroelectric Polarizations, and Energy Differences (ΔE in meV/f.u., f.u. Corresponds to a 10-Atom Cell) for CaMnTi2O6 Structures with C-AFM, G-AFM, AAFM, and FM Spin Configurationsa c (Å)

c/a

μMn (μB)

P (C/m2)

ΔE (meV/fu)

7.47 7.48 7.48 7.48

7.59 7.56 7.58 7.56

1.02 1.01 1.01 1.01

4.39 4.21 4.39 4.19

0.30 0.25 0.26 0.23

0.0 2.5 13.6 13.4

C-AFM G-AFM A-AFM FM

Table 2. Computed Non-Zero Dielectric Response (ϵ), Piezoelectric Stress Coefficients (eij), and Piezoelectric Strain Coefficients (dij) for Polar CaMnTi2O6a dielectric response

a (Å)

a

The lattice parameters and ferroelectric polarizations are almost independent of the spin configurations, indicating weak spin−lattice and spin−polarization coupling.

piezoelectric coeff

index

ϵ∞

ϵph

ϵ

index

eij (C/m2)

dij (pC/N)

11 33

5.7 5.2

116.8 79.2

122.5 84.4

11 15 33

−0.2 0.3 4.9

−5.9 3.2 21.4

both lattice parameters and ferroelectric polarizations are weakly affected by the different magnetic orderings, indicating negligible spin−lattice and spin−polarization couplings in CaMnTi2O6. The CaMnTi2O6 structure with the C-type AFM magnetic order is lowest in energy, followed by G-AFM ordering. Therefore, antiferromagnetic ordering is determined to be the magnetic ground state for CaMnTi2O6, which is in good agreement with experiment. The other collinear magnetic spin configurations are also found to be stable, with a small energy difference (∼13 meV/fu) relative to the C-AFM state. The overall small energy separation among the different magnetic configurations indicates that there may be weak magnetic exchange interactions within CaMnTi2O6. To quantify the magnetic exchange interactions of CaMnTi2O6, we estimate the magnetic exchange coupling coefficients by mapping the energies of CaMnTi2O6 onto a Heisenberg spin Hamiltonian:

a

The total dielectric response can be divided into an electronic (ϵ∞) and lattice contribution (ϵph) as ϵ = ϵ∞ + ϵph.

The total dielectric responses ε include the electronic and lattice phonon (ionic) contributions (ϵ∞ and ϵph).45,46 Similarly to most ferroelectric perovskite oxides, the dielectric responses of CaMnTi2O6 are dominated by the lattice vibration contribution, ϵph. As shown in Table 2, our calculated dielectric tensors ε are anisotropic, ranging from 84 to 123. The experimentally measured dielectric permittivity of CaMnTi2O6 (∼100 at room temperature) falls well within our calculated dielectric range. To investigate the piezoelectricity, both the piezoelectric stress coefficients (eij) and piezoelectric strain coefficients (dij) are simulated (computational details for calculation of eij and dij are given in ref 47). The piezoelectric response of CaMnTi2O6 is dominated by the coefficient d33 (e33), which measures the change of polarization to an external stress (strain) applied along the polar axis. On the basis of our calculations, CaMnTi2O6 displays a moderate piezoelectric response comparable to the piezoelectric coefficients of other singlephase ferroelectric perovskite oxides, such as BaTiO3 (e33 = 5.3 C/m2)48 and BiFeO3 (d33 ≅ 25 pC/N).49 Therefore, similarly to many tetragonal ferroelectric perovskite oxides, CaMnTi2O6 can be used as the end member compound to alloy with other ferroelectric oxides with rhombohedral symmetry. In this case, enhanced piezoelectricity should be achieved around the morphotropic phase boundary in CaMnTi2O6-based solid solutions.50,51 Magnetic Properties. As discussed previously, high-spin Mn2+ ions can lead to AFM-type magnetic ordering in CaMnTi2O6. The coexistence of magnetic order and ferroelectric polarization indicates that CaMnTi2O6 can potentially be a multiferroic material. To quantify the possible multiferroic effect, we next investigate the ferroelectric CaMnTi2O 6 structures with different magnetic orderings and explore the magnetic exchange interactions within CaMnTi2O6. After imposing different collinear spin arrangement for the Mn ions, followed by structural optimization, the ferroelectric P42mc CaMnTi2O6 structures with various magnetic orderings

/=

∑ Jij Si ·Sj ij

where Si and Sj are the spins localized at the Mn sites i and j. Jij includes the exchange interactions from the first-, second-, and third-nearest-neighbor Mn ions (J1, J2, and J3 as shown in Figure 1). The normalized spin exchange energy (per f.u.) for various collinear magnetic CaMnTi2O6 states can be expressed as FM: E = E0 + 2J1S2 + 4J2 S2 + 8J3S2

A‐AFM: E = E0 − 2J1S2 + 4J2 S2 − 8J3S2

C‐AFM: E = E0 + 2J1S2 − 4J2 S2 − 8J3S2 G‐AFM: E = E0 − 2J1S2 − 4J2 S2 + 8J3S2

where E0 is a reference energy. S = 5/2, corresponding to the optimal high-spin Mn2+ (3d5) magnetic state. We calculate the magnetic exchange interactions in the experimental P42mc CaMnTi2O6 structure. Table 4 shows the magnetic energy difference for different CaMnTi2O6 magnetic configurations. Both PBEsol and HSE functionals predict the same energy trend, C-AFM < G-AFM < FM < A-AFM, except that in the PBEsol result the FM and A-AFM configurations are higher in energy relative to the C-AFM state. We then use the HSE energy results and obtain the following spin exchange D

DOI: 10.1021/acs.inorgchem.7b01854 Inorg. Chem. XXXX, XXX, XXX−XXX

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have lower band gaps suitable for absorption of visible light. CaMnTi2O6 also contains non-d0 Mn2+ (d5) ions. If it would exhibit a semiconducting band gap similar to those of BiFeO3 or Bi2FeCrO6, then CaMnTi2O6 could be used for solar energy conversion. Next, we use the HSE06 hybrid functional to calculate the electronic structures and optical properties of CaMnTi2O6. By including a fraction of exact exchange in the functional, the HSE-hybrid functional can predict band gaps for perovskite oxides more accurately than PBEsol.55 Both experimental and QE optimized CaMnTi2O6 structures are used in calculations, so that the effect of atomic structures on the electronic properties of CaMnTi2O6 can be examined. Figure 4 shows our calculated partial density of states (PDOS) for CaMnTi2O6 with C-type AFM ordering. The valence states of CaMnTi2O6 are mainly made of the hybridized Mn 3d and O 2p orbitals. The states at the valence band edge are separated into several narrow bands, corresponding to the crystal field splitting of Mn 3d orbitals under the planar Mn− O4 coordination.56,57 The majority of the conduction states consist of empty Ti 3d orbitals with minor contributions from the Mn 3d and O 2p states. An obvious difference is found in the PDOS for the two CaMnTi2O6 structures. In the QE-optimized CaMnTi2O6 structure, the highest valence band is separated from other valence bands by a larger energy range. Therefore, its energy gap between the top of the valence band and the bottom of the conduction bands is reduced. Indeed, the HSE calculations predict Eg ≈ 2.9 eV (Eg is almost independent of magnetic orderings) for the experimental CaMnTi2O6 structure and a smaller Eg value of 1.7 eV for the QE-optimized structure (Table 5).

Table 4. Calculated Energy Differences (ΔE in meV/f.u.) for the Experimental CaMnTi2O6 Structures with Different Spin Configurations, Obtained from PBEsol and HSE Calculations, Respectivelya ΔE PBEsol HSE

C-AFM

G-AFM

A-AFM

FM

0.0 0.0

1.48 1.15

10.69 5.37

10.15 5.02

Mn cations maintain the high-spin magnetic states (μMn ≃ 4.4 μB from PBEsol and 4.6 μB from HSE calculations) in all configurations. a

parameters for CaMnTi2O6: J1 = −0.031, J2 = 0.092, and J3 = 0.004 meV. CaMnTi2O6 is dominated by the exchange interaction J2, corresponding to the in-plane antiferromagnetic coupling between neighboring Mn−Mn columns. In the CaMnTi2O6 structure, there is a large distance of 5.3 Å between the neighboring Mn−Mn columns. Moreover, without the direct Mn−O−Mn bond, antiferromagnetic couplings via superexchange of spin-antialigned Mn ions52 are quite weak. As a result, the intensity of J2 is about 1 order of magnitude smaller than the spin exchange coefficients in BiFeO3.53 On the basis of the mean field approximation,54 the Néel temperature of CaMnTi2O6 can be related to the spin exchange coefficients Ji as TN =

2S(S + 1) ·(2J1 + 4J2 + 8J3) 3kB

We predict TN = 22.9 K for CaMnTi2O6. Such a value is larger than the experimental result (10 K), as spin fluctuations are neglected in this mean field approximation; nonetheless, the predicted Néel temperature is far below room temperature. As a result, long-range magnetic order and ferroelectricity are unlikely to coexist at room temperature. Even below TN where magnetic order and ferroelectricity coexist, the weak dependence of polarization on magnetic ordering indicates a negligible spin−polarization coupling in CaMnTi2O6. Therefore, the low Néel temperature and the weak spin−polarization coupling make CaMnTi2O6 a weak multiferroic. Electronic Structures. Typical ferroelectric oxides, such as BaTiO3 and KNbO3, are wide-gap (Eg > 3.0 eV) insulators. On the other hand, multiferroic BiFeO3 (Eg = 2.7 eV)13 and Bi2FeCrO6 (Eg = 1.4−2.7 eV)10 containing Fe3+ (d5) cations

Table 5. HSE Predicted Energy Band Gaps (Eg in eV) for the Experimental CaMnTi2O6 Structure with Different Magnetic Ordersa Eg

C-AFM

G-AFM

A-AFM

FM

2.88 (1.70)

2.83

2.87

2.84

a

The QE-optimized band gap for CaMnTi2O6 with C-type AFM order is given in parentheses.

A change in band gap due to small atomic displacements will lead to different optical absorption properties for the two

Figure 4. Orbital/spin-resolved density of states and absorption coefficient (α(ω)) for the (a) experimental and the (b) QE optimized CaMnTi2O6 structures, calculated using the HSE functional. The Fermi level is set at 0 eV (broken vertical line). E

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Figure 5. Electronic band structures for experimental and QE-optimized CaMnTi2O6 structures calculated using the HSE functional. The wave function isosurfaces are also plotted for the highest valence band (VB) and lowest conduction band (CB) at the Γ point. The isosurface values are ±0.004 e/Å3 (red and blue surfaces). For clarity, Ca cations are not shown and only one square-planar coordinated Mn ion is plotted. The isosurface wave function plots illustrate that the highest valence band of CaMnTi2O6 is mainly composed of the hybridized Mn 3dx2−y2 and O 2px (2py) states, while the lowest conduction band mainly comes from the empty Ti 3d states.

CaMnTi2O6 structures. The optical absorption coefficient α(ω) is next simulated by calculating the frequency-dependent dielectric function (ε(ω)) based on the independent particle approximation (see computational details in ref 58). As shown in Figure 4, both CaMnTi2O6 structures show optical absorption in the visible-light energy range. Owing to the strong hybridization between the Mn 3d and O 2p states, optical transitions from the top edge of the valence band to the bottom edge of the conduction bands are allowed.57 Therefore, the optical absorption edges of CaMnTi2O6 occur at energies close to the band gap. However, CaMnTi2O6 exhibits an indirect band gap and its optical absorption coefficient near the band gap energy shows quadratic dependence on the photon energy (α ∝ (ℏν − Eg)2). Accordingly, the absorption coefficient α near the optical absorption edge of CaMnTi2O6 is small, leading to the relatively weak absorption of visible light. In comparison with the experimental CaMnTi2O6 structure, the optical absorption edge for the QE-optimized structure is shifted to lower energy owing to its smaller band gap. To reveal the origin of the band gap and optical absorption difference between the two CaMnTi2O6 structures, we calculate their electronic band structures and generate isosurface wave function plots for the corresponding valence and conduction bands. The band structure along the Γ−X−M direction for CaMnTi2O6 is shown in Figure 5. CaMnTi2O6 has an indirect band gap, with the valence band maximum (VBM) located at the M point and the conduction band minimum (CBM) located at Γ. The isosurface plots show that the highest valence band is primarily composed of 3dx2−y2 from the square-planar coordinated Mn ions and O 2p states. Moreover, there is a pronounced hybridization between the Mn 3dx2−y2 and O 2px (2py) states, as the lobes from Mn 3dx2−y2 are directed toward the four O anions. On the other hand, the lowest conduction band of CaMnTi2O6 mostly consists of isolated Ti 3d states, and the unoccupied Mn 3d state only accounts for a small portion of the conduction states, consistent with the PDOS. The band gap reduction upon comparing the experimental and QE-optimized CaMnTi2O6 structures arises from a shift of the highest valence band to higher energy. Owing to the 3d−2p hybridization, the energy level of the highest valence band substantially depends on the degree of orbital hybridization/ overlap between Mn 3d and O 2p. In our optimized CaMnTi2O6 structure, the planar Mn−O bond length is 2.04

Å, shorter than the experimental value (2.18 Å). The shorter planar Mn−O bond arises from the increased TiO6 octahedral rotation angles in the DFT calculations and results in larger orbital overlap and stronger Mn−O interactions. These effects simultaneously lead to the upshift of the highest valence band. On the basis of our calculation, a 0.14 Å reduction in the planar Mn−O bond length decreases the band gap of CaMnTi2O6 by more than 1 eV. The strong dependence of the band gap on the Mn−O bond length offers a feasible way to engineer the band gap of CaMnTi2O6. In experiment, reducing the planar Mn−O bond length to achieve lower Eg can be realized by either using compressive epitaxial strain or chemical substitution with cations of smaller radius (i.e., replacing Mn2+ with Fe2+). Accordingly, the ferroelectric CaMnTi2O6 with semiconducting and highly tunable band gap should be suitable for visible light absorption.

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SUMMARY AND CONCLUSIONS

We performed first-principles calculations to investigate the structural, ferroelectric, piezoelectric, magnetic, and optical properties of CaMnTi2O6, a novel ferroelectric A-site ordered double perovskite oxide prepared in experiment. Symmetry and structural mode analyses show that the polar displacement of planar coordinated Mn cations, together with B-site Ti displacements, induce ferroelectricity in CaMnTi2O6. Our calculations reveal that single-phase CaMnTi2O6 exhibits room-temperature-stable ferroelectricity and shows moderate piezoelectric responses. The presence of Ti disrupts the Mn− O−Mn bond network and results in weak magnetic interactions between Mn2+ ions and therefore poor multiferroic properties. Additionally, using HSE hybrid functional calculations, we predict that CaMnTi2O6 exhibits a semiconducting band gap similar to that of BiFeO3, suitable for absorption of visible light. Furthermore, the energy band gap of CaMnTi2O6 is found to be sensitive to the planar Mn−O4 bond network. Accordingly, it should be possible to tune the band gap of CaMnTi2O6 by altering planar Mn−O bonds using experimentally feasible routes. We therefore propose that CaMnTi2O6 is a promising candidate for ferroelectric−photovoltaic applications on the basis of its room-temperature-stable ferroelectricity and highly tunable semiconducting energy band gap. F

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Inorganic Chemistry

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01854. Detailed crystal structures for ferroelectric and paraelectric CaMnTi2O6 phases, Born effective charge tensors and polar displacement of cations in CaMnTi2O6, and energy mode distortion amplitude plot for the highsymmetry P4/mmm CaMnTi2O6 phase (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail for G.G.: [email protected];. *E-mail for J.M.R.: [email protected]. ORCID

James M. Rondinelli: 0000-0003-0508-2175 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Work at XJTU was supported by funding from the National Science Foundation of China, under Contract No. 11574244 and National Supercomputer Center (NSCC) in Tianjin. N.C. and J.M.R. were supported by the National Science Foundation (NSF) under Grant No. DMR-1420620 and the U.S. DOE, Office of Basic Energy Sciences, Grant No. DE-AC0206CH11357. Portions of this work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF Grant No. ACI-1548562.

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DOI: 10.1021/acs.inorgchem.7b01854 Inorg. Chem. XXXX, XXX, XXX−XXX