Communication pubs.acs.org/JACS
Electric-Magneto-Optical Kerr Effect in a Hybrid Organic−Inorganic Perovskite Feng-Ren Fan,† Hua Wu,*,†,‡ Dmitrii Nabok,¶ Shunbo Hu,§ Wei Ren,§ Claudia Draxl,¶ and Alessandro Stroppa*,∥,§ †
Laboratory for Computational Physical Sciences (MOE), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China ‡ Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China ¶ Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Groβen Windkanal 6, D-12489 Berlin, Germany § Department of Physics, and International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China ∥ CNR-SPIN, Via Vetoio, L’Aquila 67100, Italy S Supporting Information *
predicted5,16 and experimentally shown in ABX3 MOFs.17 Interestingly, using density-functional calculations and symmetry analysis, some of us predicted that a novel Cr based perovskite MOF (hereafter called Cr-MOF) should be multiferroic and magnetoelectric.5 Cr-MOF is A-type antiferromagnetic (AFM) in the paraelectric phase, i.e., ferromagnetic (FM) spins within planes that are AFM coupled along the c-axis. In the polar phase, the spins tilt, and a canted magnetic moment of about 1 μB/Cr appears, which is further coupled to ferroelectricity. This would imply that the switching of the ferroelectric polarization P leads to the reversal of magnetization M and vice versa.5 In this work, we further explore, using computational experiments, the multifunctional properties by studying the coupling of P and M with magneto-optical excitations, i.e., the electric-magneto-optical Kerr effect (EMOKE). MOKE describes the change of a light polarization (the socalled Kerr rotation θK) when reflected from the surface of a magnetic material,18 see an illustrative picture in Figure S1 in the Supporting Information (SI). The Kerr rotation can be exploited, e.g., to read suitably stored magnetic information by optical means in modern high-density data storage technology,19−22 to probe the magnetic behavior of two-dimensional systems,23 and to detect the time-reversal symmetry breaking in unconventional superconductors.24−27 By symmetry analysis, it is possible to show that, when the system is invariant under the combination of time reversal operation (; ) and inversion symmetry (0 ), the material is not magneto-optically active, and therefore, there is no MOKE.28 This means that a magnetic compound may become magnetooptically active when the combined ;0 symmetry is broken, thus giving rise to a Kerr signal. Most of previous works on MOKE have been performed on FM systems, which usually retain the 0 symmetry but break the ; symmetry due to the magnetic order.29 Only very recently, this research has been extended to noncollinear30 or collinear28 antiferromagnets
ABSTRACT: Hybrid organic−inorganic compounds attract a lot of interest for their flexible structures and multifunctional properties. For example, they can have coexisting magnetism and ferroelectricity whose possible coupling gives rise to magnetoelectricity. Here using firstprinciples computations, we show that, in a perovskite metal−organic framework (MOF), the magnetic and electric orders are further coupled to optical excitations, leading to an Electric tuning of the Magneto-Optical Kerr effect (EMOKE). Moreover, the Kerr angle can be switched by reversal of both ferroelectric and magnetic polarization only. The interplay between the Kerr angle and the organic−inorganic components of MOFs offers surprising unprecedented tools for engineering MOKE in complex compounds. Note that this work may be relevant to acentric magnetic systems in general, e.g., multiferroics.
H
ybrid organic−inorganic perovskites are a recent class of perovskite materials (formula unit ABX3),1−7 where the A- and/or X-sites are replaced by organic cations and/or organic linkers, respectively.8,9 The organic components give additional functionalities and structural flexibility that cannot be achieved in purely inorganic compounds, therefore offering substantial new opportunities for tuning and modulating the chemio-physical properties.10,11 A promising class of hybrid compounds is the so-called dense (but not porous) metal− organic frameworks (MOFs), in which metal ions are linked together by organic bridging ligands, e.g., the carboxylate ligand (HCOO−). This framework hosts organic cations interacting through hydrogen bond with the framework itself. With different choices of metal atoms and organic units, these materials display abundant and interesting behaviors, such as electrical, magnetic, catalytic, and optical properties to name a few.12−14 Recently, a new series of ABX3 MOFs sharing the perovskite topology, named as [C(NH2)3]M[(HCOO)3], has been synthesized where A, B, and X are [C(NH 2 ) 3 ] + (guanidinium organic cation), M2+ (transition metal cations), and (HCOO)−, respectively.15 Multiferroicity was theoretically © 2017 American Chemical Society
Received: May 12, 2017 Published: August 30, 2017 12883
DOI: 10.1021/jacs.7b04911 J. Am. Chem. Soc. 2017, 139, 12883−12886
Communication
Journal of the American Chemical Society where, although the compounds are centrosymmetric, the 0 symmetry is broken by external electric field and ; is broken by the magnetic order. In this work, we focus on the MOKE properties of multiferroic and magnetoelectric Cr-MOF where both 0 and ; symmetries are broken due to ferroelectric and magnetic orders. Using first-principles calculations (see the Cr-MOF crystal structure and the computational details in SI), we demonstrate that the Kerr angle can be tuned by an external electric field acting on the electric polarization P and its reversal can be accompanied by a reversal of P. We also predict that changing the A-site organic cations can introduce additional flexibility in tuning the Kerr angle thus opening new routes to Kerr engineering in these multifunctional hybrid organic− inorganic materials (see SI for details). Most importantly, our computational experiments support the idea that while either P or magnetization M can be exploited to tune its magnitude, the switching of the Kerr angle can occur only by switching of both P and M altogether. The paraeletric and ferroelectric structures of Cr-MOF have Pn′n′a′ and Pn′a′21 magnetic space group, respectively. The total energy as a function of the normalized amplitude of atomic distortion (λ) shows the characteristic double well profile (Figure 1). The polarization increases with the polar
Figure 2. (a) Variation of the Kerr rotation as a function of the incident photon energy. (b) Some maxima and minimum are shown as a function of ferroelectric polarization. The sign of the Kerr rotation can be switched by the ferroelectric polarization.
of θK increases as λ increases. Note that in a nonmagnetic material (without the time-reversal symmetry breaking), the inversion symmetry breaking alone cannot produce EMOKE, see more test calculations about MOKE without time-reversal symmetry breaking in SI. However, in a polar AFM system, EMOKE is present when the ;0 symmetry breaking makes the two constituent FM sublattices inequivalent. Because the ferroelectric polarization P shows a smooth behavior as a function of λ, the above results suggest a smooth variation of the Kerr angle as a function of P. To highlight this point, we have studied the magnitude of the local peaks in the Kerr spectra as a function of the polarization (Figure 2b). We focus on the peaks at ∼2.75 and 3.20 eV. θm K changes continuously and monotonously as long as P increases, and it changes its sign when P is reversed. This clearly confirms the possibility of tuning the Kerr rotation by an external electric field coupled to the ferroelectric polarization. It is well-known that the Kerr angle can be switched by reversing M in standard FM materials which usually are metallic and thus they cannot sustain a ferroelectric polarization. This switching property has been used in magneto-optical disks. It is now interesting to investigate how the reversal of M affects the Kerr angle when considering the electric polarization state. We first treat M and P as two independent variables in the calculations, although in some cases they are coupled, e.g., in the magnetoelectric Cr-MOF. We use these artificial states to explore how the MOKE depends on P and M in Cr-MOF, (Figure 3a−c). Then we study the joint effects of M and P on the Kerr angle, see Figure 3d. Upon the treatment of M and P as two independent variables, our computations show that when Cr-MOF has a proper lattice distortion and thus the electric polarization (either +P or −P), a reversal of M does not switch θK but does change its magnitude (Figure 3a). The couple of states in the (P, M) space are shown in the inset with black and white circles connected by a red line that denotes that the Kerr angles for a fixed energy are not opposite to each other. This is unexpected and contrary to a common belief. Correspondingly, we consider the possibility of switching the polarization from +P to −P but fixing the magnetization at either +M or −M. The calculated
Figure 1. Variation of the total energy (orange triangles), the ferroelectric polarization (red circles) and Mz component (blue squares) both along the c-axis, as a function of normalized amplitude of the polar distortion λ.
distortion, from zero at λ = 0 (centrosymmetric structure) to a value of 0.22 μC/cm 2 at λ = 1 (polar structure). 5 Correspondingly, the uncompensated FM moment (Mz) of the magnetoelectric Cr-MOF changes from 0 to 1.4 μB. It is clear that as long as λ is different from zero, both Mz and P become nonzero because both ; and 0 symmetries are broken. Therefore, Cr-MOF could have an electric-magnetooptically active Kerr effect. Then we have performed a series of calculations of the Kerr angle as a function of λ, i.e., we calculated the spectra θK (λ, E) where E is the energy of the incident photon. We show in Figure 2a that the Kerr rotation, θK, for the paraelectric phase and for the two ferroelectric phases as a function of energy. First of all, we note that for the paraelectric phase, θK is always zero because the system possesses ;0 symmetry. As λ increases toward ±1, i.e., approaching the two stable polar phases, the ;0 symmetry is broken and, consequently, a sizable Kerr angle appears. For different λ, the spectra changes smoothly but significantly: while the local maxima and minima are located almost at the same energy points, the absolute value 12884
DOI: 10.1021/jacs.7b04911 J. Am. Chem. Soc. 2017, 139, 12883−12886
Communication
Journal of the American Chemical Society
Figure 3. Variation of the Kerr rotation as a function of incident-light energy. Left column: nonswitchable states, only M (a) or P (b) is reversed. Right column: switchable states, (c) P (M) is reversed with M (P) equal to 0; (d) P and M are switched at the same time. Each couple of states considered in the panels a−d is shown in the (P, M) space as a couple of black and white circles. The green (red) connection line represents the switchability (nonswitchability) of the Kerr angle.
In principle, we could consider θK as a power expansion in terms of P and M keeping only linear terms, i.e., θK(P, M) = αP + βM where α = α(E) and β = β(E). To test the validity of our hypothesis, we extended our computational experiments by considering an appropriate grid of points in the (P, M) space and we have performed a multinear regression by considering the scalar function θK(P, M) = αP + βM for each fixed energy (see SI for more details). In Figure 4, we show θK(P, M; E =
spectra are shown in Figure 3b. Also in this case, θK cannot be switched. Therefore, we can conclude that θK cannot be switched by reversing only M (or P) when P (or M) is nonzero, which forms a new finding in this work. Then, a natural question arises: Is it possible to switch θK by reversing M (or P) when P (or M) is zero? To answer this question, we have performed computational experiments by considering the couple of states (+P, M = 0) and (−P, M = 0), and (P = 0, +M) and (P = 0, −M) as well. The results are shown in Figure 3c. Surprisingly, we can see that θK is switched when M = 0 and P is reversed or when P = 0 and M is reversed. The former case, i.e., (±P, M = 0) corresponds to an AFM polar system where the Kerr angle changes sign by reversing the electric polarization. This result supports the switchability of the Kerr angle by an external gate voltage.28 The latter case, i.e., (P = 0; ±M) simply restores the standard situation of a nonpolar FM material where the Kerr angle is switched by reversing the magnetization. Note that in the inset of Figure 3c, the couple of points in the (P, M) space are now connected by a green line to highlight the switchability of the Kerr angle. We now consider a general case where both P and M are nonzero, i.e., the couple of states (+P, +M) and (−P, −M), and (+P, −M) and (−P, +M). The results are shown in Figure 3d. The switching of the Kerr angle occurs when both P and M reverse simultaneously, and this is also highlighted in the inset by black and white circles connected by a green line. Graphically, switching of θK occurs when the couple of points are connected by a line passing through the center of the (P, M) space. It is now clear that θK not only depends on M but also on P, and only when P and M are reversed at the same time can θK be switched. Note that in standard FM materials MOKE is usually considered as a function of M, and moreover, they are usually metallic, which explains why the possibility of ferroelectric polarization has not been considered in the past. Our study highlights an important example of new crosscorrelation among electric-magneto-optical properties in multifunctional materials. Then, in general, the Kerr angle should be considered be as a function of P and M for a fixed energy E, i.e., θK(P, M; E).
Figure 4. Kerr rotation as a function of both the normalized P and M at E = 3.82 eV. (Pmax = 0.22 μC/cm2 and Mmax = 1.4 μB refer to the polar phase of the magnetoelectric Cr-MOF with λ = 1). The solid orange line represents the locus of points in the (P, M) space having zero Kerr angle. The solid black curve is the magnetoelectric curve.
3.82 eV) as color code in the (P, M) space, where each point corresponds to the calculated θK via the associated color. The real switching path is along the solid black curve. We can conclude that θK can be switched only when both P and M change their signs, that is θK(P, M; E) = −θK(−P, −M; E). Our results point out an important and new multifunctional property in perovskite hybrid framework compounds: the Kerr angle is tunable by both macroscopic variables P and M, and its switching property is strictly correlated to the reversal of both P and M. We postulate that this property is quite general 12885
DOI: 10.1021/jacs.7b04911 J. Am. Chem. Soc. 2017, 139, 12883−12886
Journal of the American Chemical Society
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and would apply to other ferroelectric and magnetic compounds. To summarize, we studied the interplay between magnetooptical properties and ferroelectric polarization in a perovskite metal−organic framework. We have found that the Kerr spectra significantly change when the ferroelectric polarization changes. This supports the possibility of electric tuning of the Kerr angle thus opening new directions in the electric-magneto-optical properties of multiferroic and/or magnetoelectric compounds. Most importantly, the switching of the Kerr angle is achieved by reversing both the electric polarization and magnetization altogether thus suggesting possibly new applications in electricoptical devices using ferroelectric antiferromagnetic compounds, where information is coded as “up” and “down” states depending on the orientation of the ferroeletric domain and read optically through Kerr rotation. We postulate that the interplay between magneto-optical properties and combined electric and/or magnetic ordering represents new interesting directions to explore in multifunctional acentric magnetic systems in general.
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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/jacs.7b04911. Illustrative MOKE picture, crystal structure of Cr-MOF, computational methods, test MOKE without timereversal symmetry breaking, MOKE calculated from antisymmetric part of the optical conductivity tensor, the role of the A-site and trilinear coupling, Cu-MOF, and the details of fitting (PDF)
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Communication
AUTHOR INFORMATION
Corresponding Authors
*
[email protected] *
[email protected] ORCID
Feng-Ren Fan: 0000-0002-3363-0573 Shunbo Hu: 0000-0003-0472-0999 Claudia Draxl: 0000-0003-3523-6657 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS All authors thank the anonymous reviewers for their deep reading of this manuscript and for their insightful comments. F.-R. F. and H.W. were supported by the National Natural Science Foundation of China (Grants No. 11474059 and 11674064) and by the National Key Research and Development Program of China (Grant No. 2016YFA0300700). D.N. and C.D. acknowledge partial funding from DFG. S.H. and W.R. are supported by the National Key Basic Research Program of China (Grant No. 2015CB921600), and the National Natural Science Foundation of China (Grant No. 51672171). A.S. is grateful to M. Perez-Mato for useful discussion (http://www.cryst.ehu.es), and thanks a visiting professorship at Fudan University in 2014−2015 when this project was initialized, and gratefully acknowledges the HighEnd Foreign Expert and Eastern Scholar Chair Program hosted by Shanghai Municipality via Shanghai University. 12886
DOI: 10.1021/jacs.7b04911 J. Am. Chem. Soc. 2017, 139, 12883−12886
