Indirect but Efficient: Laser-Excited Electrons Can Drive Ultrafast

Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 3402−3407

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Indirect but Efficient: Laser-Excited Electrons Can Drive Ultrafast Polarization Switching in Ferroelectric Materials Chao Lian, Zulfikhar A. Ali, Hyuna Kwon, and Bryan M. Wong*

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Department of Chemical & Environmental Engineering, Materials Science & Engineering Program, and Department of Physics & Astronomy, University of CaliforniaRiverside, Riverside, California 92521, United States ABSTRACT: To enhance the efficiency of next-generation ferroelectric (FE) electronic devices, new techniques for controlling ferroelectric polarization switching are required. While most prior studies have attempted to induce polarization switching via the excitation of phonons, these experimental techniques required intricate and expensive terahertz sources and have not been completely successful. Here, we propose a new mechanism for rapidly and efficiently switching the FE polarization via laser-tuning of the underlying dynamical potential energy surface. Using time-dependent density functional calculations, we observe an ultrafast switching of the FE polarization in BaTiO3 within 200 fs. A laser pulse can induce a charge density redistribution that reduces the original FE charge order. This excitation results in both desirable and highly directional ionic forces that are always opposite to the original FE displacements. Our new mechanism enables the reversible switching of the FE polarization with optical pulses that can be produced from existing 800 nm experimental laser sources.

F

but observed only a temporary and partial polarization switching. While other researchers have reported related phenomena such as ultrafast domain wall movements,33−37 photoinduced depolarization,38−41 and coherent ionic movement,42−44 ultrafast polarization switching in these FE materials has not been completely successful. Ideally, one would like a more efficient mechanism, such as that shown in Figure 1a,d, in which a readily available laser source could be utilized to switch the polarization with one pulse and reversibly switched back with a second identical pulse. In this Letter, we propose a new mechanism that enables this efficient switching of the polarization in FE materials. By accounting for the detailed interactions between the electrons, nuclei, and electromagnetic field, our real-time time-dependent density functional theory (RT-TDDFT) simulations show that the ultrafast FE polarization switching in BaTiO3 occurs within 200 fs, after the material is excited by an 800 nm laser pulse. We find that this polarization switching commences when the laser pulse pumps electrons from 2p orbitals in oxygen to the 3d orbitals in titanium. This dynamic excitation process yields desirable and highly directional forces on the Ti and O atoms that are (1) always opposite to the original FE displacements and (2) can be harnessed to consistently switch the polarization of the material. By laser-tuning the dynamical potential energy surface, we show that this new mechanism can switch the FE polarization in both directions using identical pulses from experimentally available laser sources. We use our in-house time-dependent ab initio package, TDAP,45−47 for our RT-TDDFT calculations,48−50 where the

erroelectric (FE) materials are characterized by an intrinsic spontaneous electric polarization that can be further harnessed for next-generation electronic and energyharvesting materials. For example, tuning the FE polarization can vary the tunneling resistance over several orders of magnitude,1 enabling technological advancements such as nonvolatile memory in digital electronic devices,2 memristors,3 and integrated neuromorphic networks.4,5 In addition, by enabling a steady-state photocurrent, FE polarization effects can substantially increase light-harvesting efficiency, particularly in hybrid organic−inorganic halide perovskite solar cells.6−17 Finally, the variation in FE polarization on surfaces can also dramatically change the adsorption energetics in catalytic systems and could be further harnessed to enable other polarization-dependent surface mechanisms.18,19 All of these applications are intrinsically associated with FE polarization and can, therefore, be further enhanced by tuning and controlling this intrinsic material property. Polarization switching is typically accomplished through a static electric field; however, the switching time is relatively sluggish (on the order of nanoseconds) because of the slow recrystallization time of most materials (typically hundreds of picoseconds).20,21 To accelerate this switching process, significant research has focused on enabling ultrafast polarization switching via optical processes.22,23 Terahertz (THz) sources provide ultrafast pulsed electric fields that are expected to reverse the polarization via the same mechanism as a static electric field. However, even with state-of-the-art THz sources, a single THz pulse does not possess enough strength to switch this polarization.24−30 To circumvent the use of THz sources, Subedi recently proposed that activating an infrared-active phonon mode can also induce polarization-switching effects.31 Later, Mankowsky et al.32 conducted experiments on LiNbO3 © 2019 American Chemical Society

Received: April 12, 2019 Accepted: May 11, 2019 Published: June 7, 2019 3402

DOI: 10.1021/acs.jpclett.9b01046 J. Phys. Chem. Lett. 2019, 10, 3402−3407

Letter

The Journal of Physical Chemistry Letters

originate from the slight distortion of the Ti−O octahedron: the Ti atom deviates from the body-centered position along the z direction, and the O atoms deviate from the facecentered positions along the −z direction. These FE motions are characterized by their displacements from the symmetric FE positions ΔαI = αFE − αsym and αsym are the I I , where αI I positions of atom I (I = Ti, Ba, O⊥, and O∥) along the α = x, y, and z direction in the FE and symmetric phase, respectively. We calculate the FE polarization accordingly as P0 = 1 ∑I μI*ΔzI = 2.01 e/Å2 = 0.50 C/m2, where V = a × a × c V = 68.8 Å3 is the volume, ΔzI the ionic FE displacement, and μ*I the Born effective charge, as shown in Figure 1b and Table 1. Consistent with previous studies, semilocal exchange− correlation functionals slightly overestimate the c/a ratio and the static polarization, as discussed in refs 59 and 60. We apply laser pulses having a wavelength of λ = 800 nm, a polarization perpendicular to the FE polarization direction, and a duration lasting from t0 = 0 fs to tf = 100 fs. We characterize and monitor the laser-induced dynamics by calculating the dynamical polarization 1 P(t ) = ∑ μI*ΔzI(t ) V I (1)

Figure 1. (a) Schematic diagram of an FE array. The bright and dark blocks denote the (b) up-polarized (c) and down-polarized structures of BaTiO3, respectively. (d) Diagram of ultrafast optical polarization switching as a function of time. The red lines denote two sequential identical laser pulses. (e) Diagram of laser-induced modification of the dynamical potential energy surface (PES). The gray and black lines represent the ground- and excited-state PES, respectively.

wave functions and charge densities are obtained from the Quantum Espresso51,52 software package. We used the projector augmented-waves method (PAW) 53 and the Perdew−Burke−Ernzerhof (PBE) exchange−correlation (XC) functional54 in both our DFT and RT-TDDFT calculations. Pseudopotentials were generated using the pslibrary55 software package. The plane-wave energy cutoff was set to 55 Ry, and the Brillouin zone was sampled using a Monkhorst−Pack scheme with an 8 × 8 × 8 k-point mesh for the unit cell and a 2 × 2 × 2 mesh for a 3 × 3 × 3 supercell. To reproduce the experimental band gap, a scissor correction of 1.65 eV was added to both the ground-state and timedependent calculations. The electronic time step, δt, was set to 1.94 × 10−4 fs, and the ionic time step, Δt, was 0.194 fs. The Gaussian-type laser pulse utilized in our study is given by E(t) ÅÄÅ (t − t )2 ÑÉÑ = E0 cos(ωt )expÅÅÅÅ− 2σ 20 ÑÑÑÑ where |E0| is the electric field ÅÇ ÑÖ amplitude, ω = 1.55 eV the laser frequency, and t0 = 50 fs the temporal location of the electric field peak. The laser pulse is linearly polarized along the x direction, perpendicular to the ferroelectric polarization. The crystal orbital Hamilton population (COHP) analysis was calculated with the Lobster56−58 software package. We first optimized the structure of BaTiO3, which is shown in Figure 1b and Table 1. The lattice is tetragonal with a = b = 4.00 Å and c/a = 1.075. The ferroelectric properties of BaTiO3

Figure 2a shows the results under various laser fluences F = 21.94, 76.78, and 87.75 MW/cm2. We identify three types of

Figure 2. (a) FE polarization (P) and (b) effective temperature (T̃ ) as a function of time. FE displacements as a function of time for (c) α = z and (d) α = x. Solid lines denote the FE displacements calculated in the 1 × 1 × 1 cell, and dashed lines denote the average FE displacements in the 3 × 3 × 3 cell.

Table 1. Symmetric Positions αsym (α = x, y, z), FE I Displacements ΔzI, and Born Effective Charge of the Ith Atoma atom I

xsym I

ysym I

zsym I

Δz (Å)

μ* (|e|)

Ba Ti O1⊥ O2⊥ O∥

0.0 0.5a 0.0 0.5a 0.5a

0.0 0.5a 0.5a 0.0 0.5a

0.0 0.5 0.5c 0.5c 0.0

0.00 0.08 −0.12 −0.12 0.21

2.73 7.17 −2.02 −2.02 −5.74

lattice dynamics: (1) At the lowest fluence of F = 21.94 MW/ cm2, P(t) slightly decreases and oscillates around P0. (2) When F increases to a critical fluence of 76.78 MW/cm2, P(t) substantially decreases to around 0 within 100 fs, while P(t) recovers to P0 in the following 100 fs. (3) When F further increases to 87.75 MW/cm2, we observe a switching of the polarization. P(t) continuously decreases past 0 until it reaches its maximum polarization in the opposite direction.

a

We categorize these three O atoms into two types: one O∥ atom that is parallel to the polarization and two O⊥ atoms that are perpendicular to the polarization. 3403

DOI: 10.1021/acs.jpclett.9b01046 J. Phys. Chem. Lett. 2019, 10, 3402−3407

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The Journal of Physical Chemistry Letters

ρFE(x, y, z) = ρtot(x, y, z) − ρsym(x, y, z). Obviously, 1 1 ρsym x , y , 2 c − z = ρsym x , y , 2 c + z is the centrosymmetric part of the total charge that characterizes the original symmetric order, whereas ρFE(x, y, z) is the asymmetric part that characterizes the FE order. Figure 3a−i depicts a two-dimensional contour of the charge density, ρi(x, z, t) (i = tot, sym, and FE), at the Ti−O surface

In contrast to other experimental strategies discussed previously, this laser-induced polarization change is a nonthermal process. To clearly demonstrate this, we plot the effective temperature T̃ (t) = Ekin(t)/kB as a function of time, where Ekin is the kinetic energy of the ions and kB is the Boltzmann constant. As shown in Figure 2b, T̃ (t) is much lower than room temperature throughout our entire dynamics simulations regardless of the laser fluence. In addition, T̃ (t) is different from the thermodynamic equilibrium temperature, which is produced by random ionic movement. Instead, in the laser-induced polarization switching process, the ionic movements are highly directional. As shown in Figure 2c, the laser radiation triggers a set of FE displacements, ΔzI(t), that are nearly antiparallel with the original values, ΔzI(t0). ΔzI(t) of the oxygen atoms O⊥ and O∥ changes sign from negative to positive, while the titanium atom moves in the opposite direction from positive to negative. Considering that the oxygen and titanium atoms have effective Born charges with opposite signs (Table 1), the movements of all the atoms contribute consistently to the polarization switching. Moreover, along the directions perpendicular to the polarization, the displacement, ΔxI(t), just slightly oscillates around the equilibrium position, as shown in Figure 2d. This leads to an abnormal fluence dependence of the effective temperature T̃ (t), which slightly decreases as the fluence increases. Although the laser pulse induces larger ionic forces at higher fluence, the system needs to overcome the small energy barrier to reverse the polarization, as shown in Figure 1e, which consumes the kinetic energy and decreases the effective temperature. In comparison, with a lower influence, the ions can not overcome the energy barrier, resulting in a higher effective temperature for the oscillation. Thus, the highly directional FE movements predominantly contribute to the relatively low effective temperature T̃ (t), indicating a unique laser-induced nonthermal mechanism. Coherence is another distinguishable feature of our polarization-switching mechanism in which the laser pulse drives the movement of the ions in a synchronized fashion. To verify that this coherence is not an artifact of size effects due to the use of a single unit cell, we carried out the TDDFT calculations using a 3 × 3 × 3 supercell for comparison. We analyzed the average laser-induced displacements as a function of time, ⟨ΔzI(t)⟩ = ∑s27= 1ΔzsI(t), where s denotes the index of the unit cell. As shown in Figure 2c,d, ⟨ΔzI(t)⟩ in the 3 × 3 × 3 supercell case is almost identical to ΔzI(t) in the 1 × 1 × 1 unit cell case, which indicates that the unified switching of the FE displacements occurs over all the laser-irradiated area. Consequently, no nucleation and growth of oppositely polarized domains are needed in this polarization switching mechanism, which accelerates this switching process to finish within 200 fs. We illustrate the atomistic mechanisms of the polarization switching by analyzing the carrier dynamics; that is, we monitor the differential charge density ρtot(x, y, z, t) = ρchg(x, y, z, t) − ρatom(x, y, z, t) as a function of time, where ρchg is the charge density and ρatom is the superposition of the atomic charge densities. Thus, ρtot(x, y, z, t) captures the spatial distribution of the bonding (+) and antibonding (−) densities. The FE polarization can be treated as the asymmetric disturbance of the symmetric phase, which is characterized by the centrosymmetric charge order. Thus, we divide the total charge ρtot(x, y, z, t) into two parts, ρsym(x, y, z) and ρFE(x, y, z), where ρsym(x, y, z) = [ρtot(x, y, c − z) + ρtot(x, y, z)]/2, and

(

)

(

)

Figure 3. Two-dimensional contour plots of the charge densities at the plane y = a/2 for (a) ρtot(x, z, t0), (b) ρsym(x, z, t0), (c) ρFE(x, z, t0), (d) ρtot(x, z, tf), (e) ρsym(x, z, tf), (f) ρFE(x, z, tf), (g) Δρtot(x, z, tf), (h) Δρsym(x, z, tf), and (i) ΔρFE(x, z, tf), where t0 and tf are the start and end times of the laser pulse, respectively. Panels j and k depict the bonding and antibonding charge, respectively, as a function of time. For ease of comparison, the initial values of ρtot, ρsym, and ρFE in panel j are downshifted by 20.7 × 10−3, 20.0 × 10−3, and 5.70 × 10−3 a.u., respectively.

along the plane y = a/2. Comparing Figure 3a−c, we find that ρsym(x, z, t0) is the dominant component of ρtot(x, z, t0) even when FE effects are included, whereas ρFE(x, z, t0) is localized around the Ti positions. As such, these figures show that an electron transfers from a Ti 3d orbital to an O 2p orbital, which triggers a pseudo-Jahn−Teller effect (PJTE)61 and stabilizes the FE phase. By comparing the laser-induced charge density difference, Δρi(x, z, t) = ρi(x, z, t) − ρi(x, z, t0) (i = tot, sym, FE), with the ground-state charge density ρi(x, z, t0), we find that (1) the laser induces an electron transfer from a bonding to an antibonding area, where Δρtot(x, z, tf) (Figure 3g) is opposite to that of the ground-state bonding charge ρtot(x, z, t0) (Figure 3a). (2) The majority of the induced charge has a centrosymmetric periodicity; that is, Δρsym(x, z, tf) (Figure 3h) dominates the induced total charge Δρtot(x, z, tf) (Figure 3g). (3) The most important feature is that the 3404

DOI: 10.1021/acs.jpclett.9b01046 J. Phys. Chem. Lett. 2019, 10, 3402−3407

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The Journal of Physical Chemistry Letters

Figure 4. (a) Time-dependent band structures and snapshot of band structures at (b) t = 0 fs and (c) t = 150 fs. The circles in panel b denote the momentum-resolved projected density of states (PDOS) of the Ti 3d and O 2p orbitals. The circles in panel c denote the momentum-resolved distribution of photocarriers. Panel d depicts the crystal orbital Hamilton population (COHP) of Ti−O bonds and the photocarrier distribution fc as a function of energy. The COHP of Ti−O⊥ is multiplied by 5 for comparison. The negative (positive) region of the COHP denotes bonding (antibonding) states. The negative (positive) values of the photocarrier distribution denote the photoinduced electron (hole) density.

induced FE charge density ΔρFE(x, z, tf) (Figure 3i) is opposite to that of the original ρFE(x, z, t0) (Figure 3c), indicating a decrease in the FE order. We quantitatively evaluate the laserinduced change in the charge density by analyzing the integrated charges Qi(t) = ∫ |ρi(r, t)| dr and Ci(t) = ∫ |ρi(r, t) − ρi(r, t0)| dr = ∫ |Δρi(r, t)| dr, where i = tot, sym, and FE. The former characterizes the change in the bonding strength, and the latter denotes the weakening of bonds. As shown in Figure 3j, the values for the percentage decrease in the bond strength, [Qi(tf) − Qi(t0)]/Qi(t0), are 32.45%, 35.92%, and 10.77% for i = tot, sym, and FE, respectively. Accordingly, Ci(t) increases with a ratio of Ctot(tf):Csym(tf):CFE(tf) = 1:0.97:0.27, which is nearly the same as the ratio of the initial bonding charges Qtot(t0):Qsym(t0):QFE(t0) = 1:0.97:0.34. Thus, the laser-induced bonding−antibonding transfer is nearly homogeneous, lowering both the centrosymmetric and FE order proportionally. Because the decrease in Qsym affects all chemical bonds homogeneously, the overall effect of the decrease in Qtot is to lower the stability of the FE polarization. Thus, the laserinduced charge-density change, Δρtot(x, z, t), is always opposite to the original FE charge order and, therefore, weakens the original ionic bonding and PJTE, creating the unsymmetrical dynamical PES shown in Figure 1e. We now analyze the carrier dynamics in momentum space for the interorbital transition. As shown in Figure 4a, the timedependent band structures from our RT-TDDFT calculations show that the band gap increases from 3.38 to 4.17 eV while the band dispersions only slightly change. Because the initial and final states are degenerate at the ground state, the gap increase is attributed to the photocarrier generation. Upon comparison of panels b and c of Figure 4, the multiphoton excitation process produces carriers that are distributed from −4 to 6 eV, which indicates that the laser-induced electrons are mostly transferred from O 2p orbitals to Ti 3d orbitals. This transition is opposite to the electron flow induced by the PJTE, which introduces a highly selective bond weakening for Ti−O∥ over the Ti−O⊥ bond. We can quantitatively evaluate the weakening of Ti−O bonds as

population (COHP), and fc(ϵ) is the photocarrier distribution, as shown in Figure 4d. From this analysis, we find that Δη[Ti− O∥] = 1.57 is much larger than Δη[Ti−O⊥] = 0.01, which indicates that the weakening of Ti−O∥ is much more significant than the weakening of the Ti−O⊥ bond. Thus, the anisotropic Ti−O bonds in BaTiO3 result in a highly directional laser-induced polarization instability: the bonds parallel to the polarization are largely weakened while the bonds perpendicular to the polarization direction are barely affected. On the basis of our photocarrier dynamic analysis of BaTiO3, we have uncovered an electronically driven polarization switching mechanism that is different from the conventional ionic-driven mechanism used in existing THz experiments. As shown in Figure 1e, our mechanism is based on a laser-tuned dynamical potential energy surface, which can be generated with the time-dependent energy E(t) and the time-dependent polarization P(t) obtained in the TDDFT calculation as E[P(t)]. Because the dynamical PES is timedependent, the laser radiation transforms the ground-state PES into a dynamical PES by first exciting the material and automatically driving the ions to the opposite polarization. This PES-based mechanism encompasses three steps: (1) The laser pulse raises the PES of BaTiO3 by pumping electrons from the 2p orbitals of oxygen to the 3d orbitals of titanium, inducing an anti-FE charge order (Figure 3i). (2) This dynamic excitation process yields desirable and highly directional forces on the Ti and O atoms that are always opposite to the original FE displacements, transforming the lattice into a structure with an opposite FE polarization along the nonequilibrium TD-PES within 200 fs (Figure 2a). (3) The photoexcited system relaxes to the ground state in conjunction with the recombination of the photocarriers (which occurs beyond our simulation time). We speculate that this dynamical-PES-based polarization switching is ubiquitous in all the FE materials, and therefore, the same mechanism can be used to manipulate the polarization in other FE perovskite materials such as PbTiO3 and LiNbO3, multiferroic materials, and even recently discovered twodimensional SnTe-based FE materials.62 Most importantly, this new mechanism enables the switching of the FE polarization in both directions, with identical pulses that can be produced from experimentally available 800 nm laser sources. Taken

∞

Δη[bond] =

∫−∞ COHP[bond](ϵ) fc (ϵ)dϵ

(2)

where ϵ is the energy; “bond” represents either the Ti−O⊥ or Ti−O∥ bond; COHP(ϵ) denotes the crystal orbital Hamilton 3405

DOI: 10.1021/acs.jpclett.9b01046 J. Phys. Chem. Lett. 2019, 10, 3402−3407

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The Journal of Physical Chemistry Letters together, these findings provide a new mechanistic understanding of electronically driven FE dynamics via laser-tuning of the dynamical potential energy surface, which can accelerate the design of more efficient, ultrafast FE devices.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Chao Lian: 0000-0002-2583-9334 Bryan M. Wong: 0000-0002-3477-8043 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.L. and H.K. acknowledge support from the UC Riverside Collaborative Seed Grant. Z.A.A. and B.M.W. acknowledge financial support from the Office of Naval Research (Grant N00014-18-1-2740).

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Letter

The Journal of Physical Chemistry Letters

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DOI: 10.1021/acs.jpclett.9b01046 J. Phys. Chem. Lett. 2019, 10, 3402−3407