Letter pubs.acs.org/NanoLett
Multiferroic Domain Walls in Ferroelectric PbTiO3 with Oxygen Deficiency Tao Xu,† Takahiro Shimada,*,† Yasumitsu Araki,† Jie Wang,‡ and Takayuki Kitamura† †
Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
‡
S Supporting Information *
ABSTRACT: Atomically thin multiferroics with the coexistence and cross-coupling of ferroelectric and (anti)ferromagnetic order parameters are promising for novel magnetoelectric nanodevices. However, such ferroic order disappears at a critical thickness in nanoscale. Here, we show a potential path toward ultrathin multiferroics by engineering an unusual domain wall (DW)-oxygen vacancy interaction in nonmagnetic ferroelectric PbTiO3. We demonstrate from firstprinciples that oxygen vacancies formed at the DW unexpectedly bring about magnetism with a localized spin moment around the vacancy. This magnetism originates from the orbital symmetry breaking of the defect electronic state due to local crystal symmetry breaking at the DW. Moreover, the energetics of defects shows the self-organization feature of oxygen vacancies at the DW, resulting in a planar-arrayed concentration of magnetic oxygen vacancies, which consequently changes the deficient DWs into multiferroic atomic layers. This DW-vacancy engineering opens up a new possibility for novel ultrathin multiferroic. KEYWORDS: Dilute ferromagnetism, multiferroic monolayer, defects, domain walls, ferroelectrics, self-assembly
M
Conventional ferroelectrics with perovskite structure, such as PbTiO3 and BaTiO3, are prototypical electroceramics that possess not only large spontaneous polarization but also a variety of related properties including piezoelectric and dielectric properties.12−14 However, these are essentially nonmagnetic materials due to the mutually exclusive mechanisms for ferroelectricity and ferromagnetism: A formal d0 (empty) electron configuration of the transition-metal cations Ti4+ drives their positions off-center in classical ferroelectrics, while a partially filled d state is required for magnetism.15 This competition has prevented the realization of intrinsic multiferroic materials for a long time and is thus the reason why there are still only few single-phase multiferroics. On the other hand, oxygen vacancies, which are the most common and abundant defect in oxide materials and often induce a rich variety of intriguing phenomena,16−18 were very recently reported to be a source of unexpected room-temperature ferromagnetism in various nonmagnetic transition-metal oxides, such as TiO2, HfO2, In2O3, ZnO, and Al2O3,19−22 due to the local nonstoichiometry. This suggests a possible route to the discovery of new multiferroic materials by defect-driven ferromagnetism coexistent with the ferroelectricity in the host oxides. However, it has been shown that an isolated oxygen vacancy still remains nonmagnetic in ferroelectric oxides.23,24
ultiferroic materials with the coexistence of two different ferroic orders, such as (anti)ferromagnetism and ferroelectricity, have recently attracted significant attention in the fields of materials science and engineering due to scientific interest in the intriguing cross-coupling of these ferroic orders and promising technological applications with novel device paradigms such as multiple-state memory, logic devices, and magnetoelectric sensors.1−4 In particular, both fundamental scientific curiosity in unusual ferroic order states at the nanoscale and the ever-growing demand for the miniaturization of devices have spurred researchers to investigate lowdimensional multiferroic materials with nanometer dimensions such as ultrathin films.5 However, the ferroic orders are radically restricted by the critical thickness, below which one or both of the ferroic orders inevitably disappear. The critical size has been intensively investigated both experimentally and theoretically, especially for the ferroelectric order,6−8 which arises from a complicated balance between long-range Coulomb and short-range interactions.9 The surface effects and depolarization field due to accumulated charges at surfaces and interfaces suppress and even destabilize the ferroelectric order as the size of the material approaches nanoscale dimensions. The critical thickness for ferroelectricity has been revealed to be approximately 2 nm,6,10,11 thus fundamentally hampering and limiting their practical application for ultrahighdensity integration in multiferroic devices. Therefore, a new alternative concept or strategy is required for the realization of ultimately thin multiferroics. © XXXX American Chemical Society
Received: October 9, 2015 Revised: December 3, 2015
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DOI: 10.1021/acs.nanolett.5b04113 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. (a) Atomic structure of a 90° DW system. The corresponding unit cell in the domain and DW are shown in the top panel. The red arrow p indicates the direction of spontaneous polarization. (b) Polarization distribution in the perfect PbTiO3 DW system. (c) Oxygen vacancy formation energy across the 90° DW. (d) Magnetic spin moments of oxygen vacancies at the DW and inside the domain of ferroelectric PbTiO3.
was modeled by the common periodic supercell approach.33 Further details on the theory and model are provided in the Supporting Information. We first relaxed the DW structure without vacancies, as shown in Figure 1a. The spontaneous polarizations P of the left-side and right-side domains are aligned along [1̅00] and [001], respectively. The local polarization profile across the DW was calculated using the Born effective charges34 and is shown at the bottom of Figure 1a. Here, ϕ is the direction angle of local polarization from the x axis. The profile shows that the 90° DW in PbTiO3 is 1.3 nm thick, which is in excellent agreement with previous studies33 and experimental observations.35,36 In this DW region, the crystal structure is locally broken into a monoclinic-like symmetry due to the rapid rotation of polarization. An oxygen vacancy, Vα (α = Oc and Oa), is thereafter considered by the removal of one corresponding atom from the supercell. Here, Oc and Oa are the oxygen atoms located in the polar c-axis and the nonpolar a-axis, relative to the Ti atom, respectively. The site dependence of the vacancy formation energy24 Evf (Vα) is calculated to determine the energetically favorable configuration of oxygen vacancies around DWs, as shown in Figure 1b. In the domain region, it is slightly more favorable for the vacancies to reside at the Oc site than at the Oa site. However, in the DW region the formation energy decreases from that in the domains and shows a minimum at the DW center (see the VOc2 site in Figure 1). The trap energy of an oxygen vacancy at the DW is given as Etrap = Evf(Vdomain ) Oc DW − Evf(VOc ) = 0.32 eV, which is consistent with previous study.37 This indicates that the oxygen vacancies are more likely
Therefore, the simple introduction of oxygen vacancies is insufficient to develop extra ferromagnetism in ferroelectric oxides, although the concept of defect engineering should be promising, as demonstrated in nonferroelectric oxides.19,25 Here, we demonstrate that extra magnetism with a localized spin moment can be developed by engineering oxygen vacancydomain wall (DW) interactions in conventional nonmagnetic PbTiO3 ferroelectrics by employing the recent hybrid Hartree− Fock density functional theories. Detailed electronic structure analysis determines that the origin of the unexpected magnetic moment is the spin-polarized defect states arising from orbital symmetry breaking of the defect state at the DW. The selfassembling nature of oxygen vacancies toward the DW and the emerging magnetism thus turns the DW into an atomically thin multiferroics beyond the critical thickness of intrinsic multiferroics, which provides a possibility for novel ultrathin multiferroic devices. First-principles calculations were performed on the basis of (generalized) Kohn−Sham theory using the projector augmented wave (PAW) method26 as implemented in the VASP code.27,28 The screened hybrid Hartree−Fock density functional theories (referred to as HSE06) were employed to accurately describe the atomic and electronic defect structures in wide band gap oxides including PbTiO3,23,29 whereas the commonly used local density approximation (LDA) or generalized gradient approximation (GGA) based densityfunctional theory usually fail to predict the electronic properties of vacancies.30−32 Here, we focus on the interaction between oxygen vacancies and 90° DWs in tetragonal PbTiO3, which B
DOI: 10.1021/acs.nanolett.5b04113 Nano Lett. XXXX, XXX, XXX−XXX
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To provide an electronic-level insight into the emerged magnetic moment of the oxygen vacancies at the DW, the electronic density of states (DOS) were analyzed, and the results are shown in Figure 3. We start to mention a typical electronic structure of nonmagnetic VOc in the domain (see Figure 3a). A single in-gap state is located at 1.61 eV above the valence band maximum (VBM), which is absent in perfect PbTiO3, that is, the defect state of VOc. This defect state is fully occupied by a majority and minority electron, and the domain is thus spin unpolarized. The defect state is highly localized around the vacancy site and neighboring Ti atom, and the shape of the wave function indicates dz2 character. Given that the dz2 orbital hybrids with the pz orbital of the O atom forming a pdσ bond in the defect-free PbTiO3, the dz2-dominated defect state at the Ti atom may originate from the ruptured pdσ bond due to the formation of VOc. In contrast, VOc1 at the DW has two distinct in-gap states, (i) and (ii), located at 1.65 and 1.48 eV above the VBM, respectively (see Figure 3c). Each defect state is now partially occupied by an up-spin electron. Therefore, these spin-polarized defect states contribute to the magnetic spin moment of 2.0 μB. The high-level defect state (i) is the same dz2 orbital localized at the adjacent Ti atom, whereas the lower defect state (ii) is mainly dominated by a new distinctive dzx orbital (see Figure 3d). The split of the fully occupied dz2 orbital and the resulting appearance of the dzxdominated defect state is the origin of the spin-polarization. Such orbital symmetry breaking may be due to crystal symmetry breaking at the DW. In the domain interior, PbTiO3 is in the tetragonal P4mm structure with spontaneous polarization nearly along [1̅00] for the left-side domain; the polar axis continuously rotates toward [1̅00] and subsequently toward [001] for the unit cells that cross the DW. As a result, the symmetry is broken in the x- and z-directions, and the original tetragonal crystal structure is reduced to a monocliniclike crystal for the unit cell in the DW center, which results in two nonequivalent Ti atoms next to the vacancy. This symmetry reduction further breaks the dz2-dominant defect state and induces the additional dzx orbital state. To further verify the emergence of this additional dzx orbital state, we compare the energy difference between dz2 and dzx orbital in tetragonal cell with that in the monoclinic cell (see Supporting Information Figure S3). The difference is smaller in the monoclinic cell. This indicates that the occupation of dzx orbital state is favorable at the DW. Furthermore, the total energy difference between magnetism and NM configurations for the DW system is calculated to be −0.29 eV, suggesting that the two electrons tend to occupy the dz2 and dzx orbitals rather than symmetrically on the same orbital. Similarly, orbital symmetry breaking and the appearance of a new defect state were observed for the magnetized VOc2 at the DW. On the basis of these above results, here we discuss the possibility of an oxygen-deficient DW as atomically thin multiferroics. Magnetic moments emerge where oxygen vacancies form at the DW. Note also that oxygen vacancies are easily trapped and accumulate at the DW center due to their large trap energy, which results in a high concentration of magnetized vacancies at the DW. Experimental observations have also shown a high concentration of oxygen vacancies at the DW.40,41 As a result, a considerable fraction of a ferroelectric DW is possible to be magnetized. This selfassembling nature of oxygen vacancies and the localized character of emerging spin moments thus turn the DW into a multiferroic atomic layer due to the atomically thin geometry.
to be trapped at DWs, which results in a high oxygen vacancy concentration at the DW center, as has also been extensively investigated previously.38,39 Experimental observations have also shown a high accumulation of oxygen vacancies near DWs and approximately 90% of total oxygen vacancies can be absorbed by 90° DWs.40,41 Note that the introduction of the oxygen vacancies usually influence the ferroelectric property of the host material.23,42 In the case of DW oxygen vacancy, the induced ferroelectric disturbance is nonlinear and complicated due to its low symmetry (see Supporting Information Figure S2). However, such effect is small (within 3% of bulk value) and only confined around the vacancy site, which will not considerably affect the polarization property of the DW. The magnetic spin moments of oxygen vacancies around the DW were then investigated, and the results are shown in Figure 1c. No spin moment is observed in the domains and the oxygen vacancies still remain nonmagnetic, which is consistent with previous hybrid functional studies on oxygen vacancies in bulk ferroelectric oxides.24 However, a nontrivial magnetic moment of 2.0 μB appears in the oxygen vacancies VOc1 and VOc2 at the DW, which are the favorable oxygen vacancy configurations. This indicates that the DW activates the magnetism of oxygen vacancies in PbTiO3. For VOc1, the emerged magnetic spin moment is highly localized around the VOc1 site and the upperleft nearest-neighbor Ti1 atom, as shown in Figure 2a. The
Figure 2. Spatial magnetic spin-density distribution around the oxygen vacancies at the DW, (a) VOc1 and (b) VOc2. The yellow region is the isosurface of the spin-densities of +0.01 μB/Å3. The red arrows indicate the directions of ferroelectric polarization, P.
emerged magnetic moment of VOc2 also has a localized character, but is particularly concentrated around the lowerleft neighbor Ti2 atom with respect to the VOc2 site (see Figure 2b). The Ti1 (or Ti2) atom is bonded with the Oc1 (or Oc2) atom in a perfect DW by forming a pdσ bond through hybridization of the Ti 3d and Oc 2p orbitals.43 This suggests that a dangling bond due to the formation of oxygen vacancies may be responsible for the localized magnetism, as will be discussed below. C
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Figure 3. Defect electronic structures in the domain and DW of PbTiO3. (a,c) Electronic DOS for nonmagnetic VOc in the domain and ferromagnetic VOc1 at the DW, respectively. (b,d) Squared wave functions of defect states of nonmagnetic VOc in the domain and ferromagnetic VOc1 at the DW, respectively. The yellow area is the isosurface of the spin-densities of +0.01 μB/Å3. The red arrows indicate the directions of ferroelectric polarization, P.
energetically favorable for larger defect−defect distances, where the interaction gradually decays with an increase of the distance. Therefore, the coupling of the local magnetic moments will induce ferromagnetic or antiferromagnetic order, depending on the concentration of oxygen vacancies. In addition, this result suggests another possibility to realizing ultrahigh density integration of multiferroic layers. The concentration of DWs can theoretically increase as the device dimensions are decreased,44 and a considerably high concentration of DWs with just a few or even one lattice spacing has been reported in experiments.45,46 A large number density of DWs will therefore realize an ultrahigh concentration of spatially arranged multiferroic elements macroscopically. DWs are also well-known for their mobility and controllability, which provides apparent advantages over fixed interface structures, such as grain boundaries47 and heterointerfaces.48 Thus, it is also appealing to envision a new active multiferroic element with confined ferroic orders that can be tailored at will. The concept and mechanism proposed here could be extended and applied to other structural interfaces with local symmetry breaking to induce magnetization and other novel functionalities that deviate significantly from those in the bulk, which will be addressed in future work. In summary, we have demonstrated the emergence of magnetism in an oxygen-deficient ferroelectric DW in lead
To further investigate the magnetic ordering in the oxygendeficient DW, calculations were performed with a supercell containing two magnetized vacancies and the energies for the magnetic moments in the antiferromagnetic and ferromagnetic states were compared (see Figure 4). The ferromagnetic state has lower energy than the antiferromagnetic state for the defects in the nearest-neighbor and second nearest-neighbor positions, while the antiferromagnetic alignment becomes
Figure 4. Energy difference ΔEAFM‑FM (in eV) as a function of the magnetized vacancy−vacancy distance. D
DOI: 10.1021/acs.nanolett.5b04113 Nano Lett. XXXX, XXX, XXX−XXX
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titanate by employing the hybrid Hartree−Fock densityfunctional calculations. A DW oxygen vacancy could induce a magnetic spin moment localized at the neighboring Ti atom due to the orbital symmetry breaking of the defect state caused by the local structure symmetry breaking at the DW. The energetics of oxygen vacancies suggest that the vacancies are trapped at DWs, which results in considerably high vacancy concentrations. This self-concentration feature of oxygen vacancies in conjunction with the emerging magnetism changes the ferroelectric DW into an atomically thin multiferroics.
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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.nanolett.5b04113. Simulation methods and model; definition of local polarization; ferroelectric disturbance induced by oxygen vacancy; atom-resolved angular-momentum-projected density of states (DOS) for tetragonal and monoclinic cell. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
T.X. and T.S. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by JSPS KAKENHI Grants 25000012, 26289006 and 15K13831. REFERENCES
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