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Unusual Multiferroic Phase Transitions in PbTiO3 Nanowires Takahiro Shimada, Tao Xu, Yoshitaka Uratani, Jie Wang, and Takayuki Kitamura Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b02370 • Publication Date (Web): 13 Oct 2016 Downloaded from http://pubs.acs.org on October 15, 2016

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Unusual Multiferroic Phase Transitions in PbTiO3 Nanowires Takahiro Shimada,1,* Tao Xu,1,** Yoshitaka Uratani,1 Jie Wang,2 and Takayuki Kitamura1 1

Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan

2

Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China

Abstract Unconventional phases and their transitions in nanoscale systems are recognized as an intriguing avenue for both unique physical properties and novel technological paradigms. Although the multiferroic phase has attracted considerable attention due to the coexistence and cross-coupling of electric and magnetic order parameters, mutually exclusive mechanism between ferroelectricity and ferromagnetism leaves conventional ferroelectrics such as PbTiO3 simply nonmagnetic. Here, we demonstrate from first principles that ultrathin PbTiO3 nanowires exhibit unconventional

multiferroic

phases

with

emerging

ferromagnetism

and

coexisting

ferroelectric/ferrotoroidic ordering. Nanometer-scale and nonstoichiometric effects intrinsic to the nanowires bring about nonzero and nontrivial magnetic moments that coexist with the host ferroelectricity. The multiferroic order is susceptible to surface termination and nanowire morphology. Furthermore, calculations suggest that the nanowires undergo size-dependent ferroelectric-multiferroic-ferromagnetic phase transitions. This work therefore provides a route to multiferroic transitions in conventional nonmagnetic ferroelectric oxides.

T.Shimada* and T.Xu** contributed equally to this work. * E-mail: [email protected]

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Keywords multiferroic phase transition, nanowires, ferroelectrics, nonstoichiometry, size effects

Table-of-Contents Graphic

Main Text The discovery of unconventional phases and associated transitions in condensed matter is of central scientific interest as a playground of nontrivial physical phenomena and novel technological paradigms.1-3 Of significant current interest are the phase transitions in ferroic systems, owing to their multiple functionalities and prospective technological applications.4-6 Multiferroic phases,

in which different

ferroic orders

such

as

ferroelectricity and

(anti-)ferromagnetism coexist and interact,7,8 have attracted significant attention since their discovery due to the multiple ferroic degrees of freedom and cross-coupling between different order parameters, such as the colossal magnetoelectric effect.9 These phenomena offer a plethora 2 ACS Paragon Plus Environment

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of opportunities for technological innovations that might potentially lead to novel functional device paradigms, such as new information storage devices made of multiferroic memory cells that can be written to electrically and read magnetically.10 However, there are very few materials that exhibit a multiferroic phase because of the mutually exclusive mechanisms for ferroelectricity and ferromagnetism:11 For ferroelectricity in conventional ferroelectrics such as PbTiO3 and BaTiO3, a formal d0 empty electron configuration of the transition metal (Ti4+) is essential for cation off-centering to form an electric dipole, whereas a partially occupied d state is necessary for ferromagnetism. Although numerous experimental and theoretical efforts have been made to seek multiferroic phases in perovskites and complex oxides,12-16 the current understanding of multiferroic phases and their transitions remains limited. As nanoscale systems have been recognized as an intriguing avenue for unconventional or novel phases and their transitions,17,18 the quest for unconventional phases and transitions in ferroelectrics has been driven toward low-dimensional nanostructures, both for industrial community and for fundamental purposes. As the size of ferroelectrics approaches the nanometer scale, the structure, phase stability, and properties are significantly different from those of the host bulk counterparts owing to size and surface effects. Numerous investigations have revealed unique structural stabilities and phase transition sequences intrinsic to the nanometer scale, including antiferrodistortion,19,20 unusual low-symmetry phase structures21, and more recently, striking topological phases such as electric vortices,22,23 which differ profoundly from the classical polarization order in the bulk crystal. Therefore, phase transitions, especially nanoscale transitions, offer fertile ground for emergent phenomena and novel technological paradigms in ferroelectrics. Here, we demonstrate via hybrid Hartree-Fock density functional theory that ultrathin 3 ACS Paragon Plus Environment

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nanowires of nonmagnetic ferroelectrics PbTiO3 exhibit multiferroic phases with emerging magnetism and unique ferroelectric/ferrotoroidic ordering. Nonstoichiometric and nanometer-scale effects intrinsic to the nanowires bring about magnetism coexisted with electric polarization, which can be tuned by the surface morphology of the nanowires. Furthermore, we investigate the diameter dependence of these multiferroic properties and predict the existence of unusual ferroelectric-multiferroic-ferromagnetic (FE-MF-FM) multiferroic phase transitions, beyond those previously known in PbTiO3. These results thus provide fundamental knowledge of multiferroic phase transitions in nanostructure ferroelectrics and suggest a new avenue for the realization of low-dimensional multiferroics in nonmagnetic ferroelectric nanowires. We simulated ferroelectric PbTiO3 nanowires via first-principles calculations with the hybrid Hartree-Fock density functional theory (referred to as the HSE06 functional)24,25 using the projector augmented wave (PAW) method26, as implemented in the VASP code27,28. The hybrid HSE06 functional can describe the atomic structures and electronic properties of wide band-gap oxides such as PbTiO3 with defects or nonstoichiometry29-31 more accurately than density-functional theory with the local density approximation or generalized gradient approximation, which often fail to reproduce the electronic and magnetic properties of nonstoichiometric systems due to incorrect delocalization of excess electrons/holes.32-35 PbTiO3 nanowires were modeled using a supercell set-up (Supplementary Figure S1). The nanowire surfaces were terminated by (100) and (010) surfaces, and were therefore oriented along the axial [001] direction. To study the effect of surface terminations, we considered both PbO and TiO2 termination of the nanowire surfaces as thermodynamically favorable configurations.36,37 For the cross-sectional morphology of the nanowires, sharp corner (NW-S) and round corner (NW-R) 4 ACS Paragon Plus Environment

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configurations were considered due to experimental observations and theoretical implications.37-39 The nanowire sizes were determined by the number of unit cells arranged along [100] and [010]. In this study, we focused on cross sections ranging from 4 × 4 to 1× 1 unit cells, paying particular attention to the 4 × 4 nanowires. More details relevant to the computational theory and models are available in the Supplementary Information. The ferroelectric properties of the nanowires were investigated by introducing site-by-site local polarization (pi) in each unit cell (see Supplementary Information). The polarization distribution of NWs-S is depicted in Figure 1, in which the polarization vectors curl in the cross-sectional plane and form a vortex ground state for the TiO2-terminated wire (Figure 1a), while nonzero dipole moments distribute along the axial direction in the PbO-terminated wire (Figure 1b). To characterize these two distinct polarization behaviors, we define a toroidal moment G about the wire axis and average axial polarization P, described as G = 1 N

1 N

N

∑ r × p and P = i =1

i

i

N

∑ p , respectively, where ri denotes a position vector from the nanowire center and N runs i =1

i

over all the unit cells in the nanowire. The exact values of G and P in both TiO2- and PbO-terminated NWs-S can be found in Table 1. Turning to NWs-R, on the other hand, the TiO2-terminated case similarly adopts a toroidal moment state and bears no spontaneous axial polarization at equilibrium, as visualized from the local polarization distribution shown in Figure 2a. Surprisingly, the local polarization configuration in PbO-terminated NW-R (Figure 2b) features a mixture of nonzero axial polarization components and a vortex pattern, i.e., spiral polarization. These concurrent order parameters were previously considered to be mutually exclusive.40 Thus, the PbTiO3 nanowires exhibit intriguing electric dipole orderings, including polar, toroidal and 5 ACS Paragon Plus Environment

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spiral, which can be mediated by adjusting the cross-sectional terminations in the absence of an external electric field. The magnetic properties of the 4 × 4 nanowires are then investigated, and the results, manifested as the total magnetic spin moment and magnetic moment per unit volume, are listed in the right panel of Table 1. For TiO2-terminated NW-S, a nontrivial total magnetic moment of 2.0 μB (1.37 μB/nm3) appeared unexpectedly, i.e., the emergence of ferromagnetism, despite the fact that ferroelectric PbTiO3 is intrinsically nonmagnetic due to the well-known exclusive mechanisms of ferroelectricity and magnetism. The same magnitude of magnetic moment also emerged in PbO-terminated NW-S. Likewise, two kinds of NWs-R are also associated with magnetic spin moments: The TiO2-terminated one has a spin moment of 2.0 μB (1.40 μB/nm3), whereas a sudden increase in magnetization to 5.0 μB (3.50 μB/nm3) occurs in the PbO-terminated NW-R. All of these results indicate that ferroelectric PbTiO3 nanowires at the nanoscale have intrinsic magnetic moments, and thereby act as low-dimensional multiferroics regardless of the lateral surface terminations and edge characteristics. On the basis of the above results, we now discuss the multiferroic pattern of PbTiO3 nanowires. Figures 1 and 2 show the distributions of electric order and magnetic spin-density in 4×4 nanowires, classified according to the edge characters of the nanowires. For NWs-S, the ferroelectricity, in the form of either vortex polarization (TiO2-termination) or a polar state (PbO-termination), exists in all of the unit cells (see Figure 1), whereas the magnetization has a delocalized character and is confined to the Ti atoms in the inner regions of the nanowires. Consequently, the central region of NWs-S displays a multiferroic phase property, encompassed by the peripheral ferroelectrics. On the other hand, in NWs-R, electric dipoles also evenly spread over 6 ACS Paragon Plus Environment

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the entire cross sections of the TiO2- and PbO-terminated nanowires, displaying either a vortex or spiral polarization state, whereas the magnetism emerges preferentially around O atoms at the edge and outer shell for TiO2- and PbO-terminated nanowires, respectively (see Figure 2). NWs-R thus forms a nanocomposite consisting of a multiferroic shell/edge and a ferroelectric core, in a manner opposite to that of the sharp-edged nanowires. Therefore, nanoscale multiferroic phases with either a multiferroic core surrounded by a ferroelectric shell or a ferroelectric core combined with a multiferroic shell, as well as tunable dipole states, can be achieved in a pure PbTiO3 compound via termination engineering of the PbTiO3 nanowires. The stabilities of the nanowires have been further validated by ab initio molecular dynamics using the Nose−Hoover thermostat at 300 K. As shown in Figure S2 for the case of PbO-terminated NW-S, the structure skeleton remains nearly unchanged and the multiferroic phase is preserved after calculation. Similar results are also obtained in other kinds of nanowires, indicating the thermal stability of these new multiferroic phases. The important role of surface morphology in determining these multiferroic patterns of nanowires makes an important parallel with topological ferroelectrics, wherein the peculiar lattice topology also plays a crucial role. Similar surface morphology manipulations are also widely used in semiconducting nanowires to modify their dielectric and electronic properties.41-43 To provide electronic-level insights into the mechanism of the emerging magnetic moments and their particular structure-dependent patterns, we analyzed the electronic band structures of various nanowires (see Figure 3). The TiO2-terminated NW-S introduces two spin-polarized bands below the conduction band, with the low-lying level 0.5 eV below the Fermi level and the higher state near the bottom of the conduction band, both of which are absent in bulk PbTiO3. Interestingly, the lower band is fully occupied by majority-spin electrons and demonstrates 7 ACS Paragon Plus Environment

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insulating characteristics, whereas the upper band is partially filled, intersects the Fermi level, and has a metallic nature. This indicates that NW-S exhibits half-metallic behavior. The excess electrons are derived from the nonstoichiometric composition of the n × n nanowires (n = 4 in this case): The TiO2-terminated NW-S is composed of n2 Pb, (n+1)2 Ti, and (3n + 1) × ( n + 1) O atoms, which does not correspond to an integral number of PbTiO3 unit cells. The whole valence of the nanowire was determined to be +2 on the basis of nominal ionic charge of Pb2+, Ti4+, and O2- in bulk PbTiO3. This indicates cations (Pb2+ and Ti4+) are more abundant than anions (O2-) in the nanowire, hence some cations will reduce to lower valence states as a mechanism of charge compensation and give rise to two excess electrons in the system (n-type). These two spin-polarized electrons give rise to a net magnetic moment of 2.0 μB in the nanowire. As visualized from the shape of the wave functions, the spin-polarized states have d orbital characteristics, which primarily originate from the central region of Ti atoms. In the same manner as in the TiO2-terminated nanowire, two excess electron states also appear just below the Fermi level in the PbO-terminated NW-S due to the nonstoichiometry (see the right panel of Figure 3a). These two excess electrons similarly go into Ti 3d-dominated orbitals in the spin-up states, giving rise to a total magnetic moment of 2.0 μB. It is worthwhile to note that these excess electrons are particularly confined within the narrow core region of NWs-S in both cases, which essentially determines the distribution of emerging magnetic moments and the resulting unique texture of the multiferroic/ferroelectric nanocomposite. On the other hand, the spin-resolved band structures of NWs-R are pictured in Figure 3b, and showed typical p-type characteristics. For the TiO2-termianted nanowire, two split unoccupied states appear just above the Fermi level. Through similar analysis of the composition (16 Pb, 21 Ti 8 ACS Paragon Plus Environment

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and 65 O atoms), the whole valence state in the nanowire was determined to be −6, indicating that cations are insufficient relative to anions. This charge imbalance hence introduces six holes into the system. Two of these holes are majority spin, and the other four are minority spin. These spin-polarized hole states contribute to a total magnetic moment of 2.0 μB in the nanowire. Visualization of the squared wave function indicates that the six bands accommodating the holes can be ascribed to s and p hybridized orbitals of the under-coordinated edge Pb and O atoms, respectively, in line with the position of the emerging magnetic moments. A similar charge imbalance and the associated six holes occupying the Pb-s and O-p bands were also observed in the PbO-terminated nanowire. Nevertheless, one half-hole resides in the spin-up band while the other five and one-half holes are in the minority states, resulting in a larger total magnetic moment of 5.0 μB. Therefore, it is the excess electrons and holes in the nanowires due to significant nanometer-sized nonstoichiometric effects that give rise to the emergence of unexpected magnetic moments. Finally, we characterized the above multiferroic behaviors with respect to the nanowire diameter and predict unusual multiferroic phase transitions in PbTiO3 through the investigation of smaller nanowires (n = 3 to 1). As summarized in Table 1 and Figure 4, the magnetic moment per unit volume increases monotonically for all kinds of nanowires with decreasing cross-section, due to the increase in the surface-to-volume ratio and associated nonstoichiometric effects. The electronic band structures of these nanowires are shown in Figure S3 and Figure S4. In contrast, the electric ordering, either an axial polarization or a toroidal moment, generally decreases gradually with decreasing dNW. In particular, the dipole order disappears in the TiO2-terminated NW-S once the diameter is narrower than four unit cells. As a result, the MF-FM phase transition 9 ACS Paragon Plus Environment

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occurs for this type of NW-S at a critical size of approximately 1.5 nm. It is worthwhile to mention that the axial polarization in PbO-terminated NWs-S is comparable or even slightly larger than the corresponding bulk value of 1.08 C/m2 due to the charge transfer from the interior of nanowire to the surface as demonstrated previously.40 The charge transfer from the penultimate TiO2 layer to the outer PbO layer in the Pb-O terminated nanowires strengthens the Pb-O bonds hence increases tetragonality and leads to large polarization. By contrast, the same phenomenon decreases the interior Pb-O covalent bonds and dramatically reduces the tetragonality in TiO2-termianted nanowires, and thus axial polarization is entirely suppressed. Note also that the axial polarization in PbO-terminated NW-R systems is reduced by about 30% compared to the corresponding NW-S type, which is also ascribed to the weakened covalence of Pb-O bonds and reduced c parameter. On the other hand, the emerging magnetic moments are expected to decay gradually with increasing dNW, since the nonstoichiometric effects become more dilute with increasing nanowire volume. For an extremely large diameter, for which the number of atoms can be assumed to be infinite, the ferroelectric properties are favored, while the number of spin-polarized free carriers per unit volume is virtually negligible, so the resulting magnetism is suppressed, triggering an MF-FE phase transition. Therefore, PbTiO3 nanowires experience intriguing multiferroic phase transitions consisting of three phase states as the diameter is decreased. These are completely different from the conventional transitions in PbTiO3 and bear significant technological implications. Here, we briefly discuss a route to low-dimensional multiferroics by engineering the nanostructures of nonmagnetic ferroelectrics. Nanowires with a diameter of 3 nm have been manufactured owing to the advancements in fabrication techniques44,45, which provides the 10 ACS Paragon Plus Environment

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possibility for the realization of the proposed multiferroics in practice. The key element of nonstoichiometry is ubiquitous and intrinsic in such finite nanoscale systems.46-49 These nanometer-sized nonstoichiometric effects could be extended and applied to other finite dimension systems, such as nanorods and nanodots, to develop magnetism in addition to the existing host functionalities. Therefore, our results may inspire further interest in various low-dimensional functional oxides to explore novel physical phenomena and functionalities with emerging magnetism. In summary, we have demonstrated unusual multiferroic phases with emerging magnetism and unique ferroelectric ordering in ultrathin PbTiO3 nanowires through first-principles calculations. Nanometer-scale nonstoichiometric effects intrinsic to the nanowires provide magnetic moments that coexist with the host electric ordering, which can be mediated by engineering the surface morphology of the nanowires. These multiferroic properties were further investigated in terms of nanowire diameter, and unconventional FE-MF-FM phase transitions were predicted theoretically. These results provide the possibility of designing low-dimensional multiferroics with tailored ferroic order by engineering the nonstoichiometry of non-magnetic ferroelectric nanowires. This study thus provides a new route to multiferroic phase transitions in finite-dimensional systems, which may promote the further development of low-dimensional novel multifunctional devices.

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Acknowledgements The authors acknowledge financial support from SPS KAKENHI (25000012, 26289006, and 15K13831) and the National Natural Science Foundation of China (11321202 and 11472242).

Author Information Corresponding author. *E-mail: [email protected] Author Contributions. T.S. and T.X. conceived the project, designed and directed computational experiments, and wrote the entire manuscript. Y.U. performed the theoretical calculations and interpreted the data. J.W. supported the calculations and discussed the results. T.K. supervised the work and provided critical feedback on the manuscript. All authors read and commented on the manuscript. T.S. and T.X. contributed equally to this work. Notes The authors declare no competing financial interest. Associated Content Supporting Information. Hybrid Hartree-Fock density functional calculations; simulation models; definition of local polarization; phonon bands; Electronic band structures of small nanowires. This material is available free of charge via the Internet at htpp://pubs.acs.org.


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Table 1 Multiferroic properties, i.e., average axial polarization P (C/m2), toroidal moment G (10-10 C/m), magnetic moment M (μB), and magnetic moment per unit volume M/Ω (μB/nm3), in various NWs with different morphologies and diameters calculated from the HSE06 hybrid functional.

Edge character

Ferroelectricity

Termination

Size

TiO2

4×4 3×3 2×2 1×1

0.00 0.00 0.00 0.00

4×4 3×3 2×2

NW-S PbO

TiO2

P (C/m )

G (10

Ferroic phase

M/Ω(μB/nm3)

1.34 0.00 0.00 0.00

2.0 2.0 2.0 2.0

1.37 2.15 3.82 8.59

MF FM FM FM

1.05 1.05 1.09

0.00 0.00 0.00

2.0 1.4 1.0

1.37 1.50 1.91

1×1

1.15

0.00

1.6

6.86

4×4

0.00

3.19

2.0

1.40

3×3

0.00

1.26

2.0

2.22

2×2

0.00

1.96

2.0

4.04

MF MF MF MF MF MF MF

4×4

0.79

1.12

5.0

3.50

3×3

0.75

0.69

6.0

6.65

2×2

0.35

0.41

2.0

4.04

-10

C/m)

Magnetism M (μB)

2

NW-R PbO


MF MF MF

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Nano Letters

Figure 1. Ferroelectric (FE) and ferromagnetic (FM) properties of (a) TiO2-terminated and (b) PbO-terminated NWs-S (sharp corner). The arrows indicate the local polarization. The contours indicate the angle between the polarization vector P and the x direction. The yellow areas indicate isosurfaces with magnetic spin densities of 0.02 μB/Å3.


Nano Letters

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Figure 2.

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Ferroelectric (FE) and ferromagnetic (FM) properties of (a) TiO2-terminated and (b)

PbO-terminated NWs-R (round corner). The arrows indicate the local polarization. The contours indicate the angle between the polarization vector P and the x direction. The yellow areas indicate isosurfaces with magnetic spin densities of 0.02 μB/Å3.


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Nano Letters

Figure 3. Electronic band structures of (a) NWs-S and (b) NWs-R. The green lines denote the Fermi level. The red and blue lines indicate the spin-up and spin-down orbitals, respectively. The squared wave functions of the in-gap states are shown on the right side of each band structure. The orange and light-blue colors indicate isosurfaces of spin-up and spin-down densities of 0.001Å-3, respectively. The predicted band gap of bulk PbTiO3 is 3.41 eV.


Nano Letters

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Figure 4. Diameter-dependent magnetic properties of PbTiO3 NWs. The solid lines are the values of the magnetic moment per volume in various NWs with cross sections ranging from 4 × 4 to

1× 1 unit cells.


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Nano Letters

Figure 1. Ferroelectric (FE) and ferromagnetic (FM) properties of (a) TiO2-terminated and (b) PbOterminated NW-E. The arrows indicate the local polarization. The contours indicate the angle between the polarization vector P and the x direction. The yellow areas indicate isosurfaces with magnetic spin densities of 0.02 µB/Å3. 272x211mm (300 x 300 DPI)


Nano Letters

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Figure 2. Ferroelectric (FE) and ferromagnetic (FM) properties of (a) TiO2-terminated and (b) PbOterminated NW-S. The arrows indicate the local polarization. The contours indicate the angle between the polarization vector P and the x direction. The yellow areas indicate isosurfaces with magnetic spin densities of 0.02 µB/Å3. 274x207mm (300 x 300 DPI)


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Nano Letters

Figure 3. Electronic band structures of (a) NWs-S and (b) NWs-R. The green lines denote the Fermi level. The red and blue lines indicate the spin-up and spin-down orbitals, respectively. The squared wave functions of the in-gap states are shown on the right side of each band structure. The orange and light-blue colors indicate isosurfaces of spin-up and spin-down densities of 0.001Å-3, respectively. 613x496mm (240 x 240 DPI)


Nano Letters

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Diameter-dependent magnetic properties of PbTiO3 NWs. The solid lines are the values of the magnetic moment per volume in various NWs with cross sections ranging from 4x4 to 1x1 unit cells. 263x208mm (300 x 300 DPI)


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Nano Letters

Table-of-content Graphic 269x176mm (300 x 300 DPI)


Unusual Multiferroic Phase Transitions in PbTiO3 ... - ACS Publications

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