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Strain Tuning of Ferroelectric Polarization in Hybrid Organic Inorganic Perovskite Compounds Saurabh Ghosh, Domenico Di Sante, and Alessandro Stroppa J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b01806 • Publication Date (Web): 29 Oct 2015 Downloaded from http://pubs.acs.org on November 3, 2015

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The Journal of Physical Chemistry Letters

Strain Tuning of Ferroelectric Polarization in Hybrid Organic Inorganic Perovskite Compounds Saurabh Ghosh,∗,† Domenico Di Sante,∗,‡,¶ and Alessandro Stroppa¶ †School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14850, USA ‡University of L’Aquila, Department of Physical and Chemical Sciences, Via Vetoio, L’Aquila ¶CNR-SPIN, Via Vetoio, L’Aquila, Italy E-mail: [email protected]; [email protected] Abstract Metal-organic frameworks (MOFs) are hybrid crystalline compounds comprised of an extended ordered network made up of organic molecules, organic linkers and metal cations. In particular, MOFs with the same topology as inorganic perovskites have been shown to possess interesting properties, e.g. coexistence of ferroelectric and magnetic ordering. Using first-principles density-functional theory, we have investigated the effect of strain on the compounds C(N H2 )3 Cr(HCOO)3 and (CH3 CH2 N H3 )M n(HCOO)3 . Here, we show that compressive strain can substantially increase the ferroelectric polarization by more than 300%, and we discuss the mechanism involved in the strain enhancement of polarization. Our study highlights the complex interplay between strain and organic cations’ dipoles and put forward the possibility of tuning of ferroelectric polarization through appropriate thin film growing.

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pling between two primary unstable non-polar modes with a secondary stable polar mode. Such a new mechanism has been called as “hybrid improper“ ferroelectricity and it was first shown in the case of inorganic perovskite materials. 12–16 This mechanism holds the promise for high-temperature magnetoelectric coupling 17,18 and it has been recently demonstrated experimentally. 19,20 Di Sante et. al. 10 studied another multiferroic MOF such as (CH3 CH2 N H3 )M n(HCOO)3 (hereafter called Mn-MOF) where the microscopic mechanism is different from the ”hybrid improper” ferroelectricity. In this case, A+ cation is the ethylammonium. Here, a peculiar canted ordering of the organic cation dipole moments gives rise to a ferroelectric polarization of ∼ −1.6 µC/cm2 along the c-axis. More interestingly, it has been shown that by choosing different organic cations, it is possible to increase the polarization up to ∼ 6 µC/cm2 . 10 The possibility of tuning the ferroelectric properties by considering different organic cations and modifications of them open new routes for engineering ferroelectric polarization in the class of hybrid organic-inorganic compounds. 10,21,22 However, there exists yet another way to modify the electric order which is largely unexplored so far, i.e. the use of the strain field by choosing the substrate on which the MOF films are grown. This should provide extra degrees of freedom to properly change their physical properties. 23–25 Indeed, strain can increase transition temperatures, can induce phase changes and modify the symmetry of the films. The symmetry changes usually bring important consequences in the functional properties (polarization, dielectric permittivity, piezoelectric response, etc), which are highly anisotropic. Recently, Li et al. reported the possibility of mechanical tunability via hydrogen bonding 26,27 by accommodating a large lattice strain (∼5%) through an orthorhombic to monoclinic transition in the ferroelastic MOFs. 26,27 These experimental results further highlight the potential of these flexible MOF perovskites to undergo large structural changes in response to an external stimulus. 28,29 The application of strain in thin films of inorganic perovskites is at a mature stage. 30–35 The emergence of a multiferroic state under biaxial tension requires even lower strains, thereby

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allowing thicker high-quality crystalline films. 35 It is clear that strain can simultaneously control multiple order parameters thus representing an interesting way for creating new multiferroics. 35,36 Stimulated by these findings, we consider the role of strain in tuning the polarization in ABX3 organic-inorganic hybrid compounds. Although the growth of strained thin MOF films is still at an embryonic stage, theoretical calculations may provide a guide for further experimental investigations. In this letter, using first-principles density functional theory (DFT) calculations, we investigate the effect of strain on ferroelectric properties on Cr-MOF (i.e., C(N H2 )3 Cr(HCOO)3 ) and Mn-MOF (i.e., (CH3 CH2 N H3 )M n(HCOO)3 ). We consider these two particular MOFs because they provide compositional flexibility both at A and B sites and they show different mechanisms for the ferroelectric order. In case of Cr-MOF, the “hybrid improper“ mechanism is at work, 9 while in Mn-MOF the microscopic polarization is given by the canting of the Acation dipole moment driven by a Γ-point mode. 10 Despite this, we show that in both cases, the electrical order can be largely tuned, in particular under compressive strain. This represents an interesting message for material scientists attempting to growth thin films MOFs on substrates: whenever one wants to enhance the ferroelectric polarization, an appropriate substrate favoring compressive strain should be preferred. It may be interesting to discuss how the appropriate strain could be included during the growth of MOFs. Currently, among the thin film growth of MOFs, a special method is emerging called SURFMOFs (surface-attached metal-organic framework multilayers). 37 The method allows the growth of samples exhibiting one monolayer of functional groups at the external thin-film surface. These films consist of ultrathin (in the nanometer range) MOF multilayers that are perfectly oriented (at least in one direction of the growth). They are very smooth, the roughness of their surface is of the order of a few elementary cells, and they are often quasi-epitaxially grown on the substrate so that the thickness of the film and the crystalline domain size can be precisely controlled. The ideal SURMOF would be also characterized by large crystalline domains in the plane of the growth. SURMOFs also offer

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the possibility to transfer concepts known from inorganic condensed-matter single-crystal chemistry and physics to hybrid inorganic-organic materials, which, most importantly, includes the fabrication of heterostructures 38 (MOF on MOF, epitaxially grown) and chemical or structural modifications that are specific for the exposed external surface (top layer) of the films. 39 Using this method, appropriate strain field could be included. In this work, first-principles calculations have been carried out within the projector augmented wave (PAW) method, 40,41 and GGA exchange correlation functional, 42 as implemented in the Vienna ab initio simulation package (VASP). 43 The convergence in total energy and Hellman-Feynman forces were set to 1µeV and 0.5 meV/Å, respectively. All calculations have been performed with 400 eV energy cutoff and with 4 × 4 × 3 Monkhorst-Pack grid of k-points, convergence has been carefully tested with higher energy cutoff and finer k-mesh. The ferroelectric polarization was calculated using the Berry’s phase method, 44 as implemented in VASP. The symmetry analysis has been performed using the Bilbao Crystallographic Server, 45 and in particular using the symmetry softwares PSEUDOSYMMETRY 46 and AMPLIMODES. 47,48 We will first discuss the case of Cr-MOF and then we will focus on the Mn-MOF. Finally we will draw our conclusions. We briefly summarize previous studies on Cr-MOF. 9 The lowest energy, low symmetry structure of Cr-MOF belongs to the polar space group P na21 . Within collinear magnetism, it is an A-type anti-ferromagnet, i.e. ferromagnetic planes are coupled antiferromagnetically along the direction perpendicular to the planes. When the low symmetry P na21 structure is described with respect to the non-polar Imma structure, it turns out that the global distortion can be decomposed into three distinct atomic distortions: two zone boundary modes at the X point, transforming according to the irreducible representations X1− and X4+ , respectively, and a polar zone-center mode transforming according to Γ− 4 , as shown in Figure 1. These symmetry adapted distortion modes lower the symmetry to the isotropy subgroups P nna, P nma and Ima2, respectively, and notably, among them, only Ima2 is polar. However, the polar Γ− 4 mode turns out to be stable. The induced ferroelectricity in the lowest 5




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Table 1: Total and partial polarization of A-molecule and BX3 group for Cr-MOF. Relative changes with respect to the zero strained value for each column and for each strain has been calculated as, ∆P Relative = (Pf inal −Pinitial )/Pinitial ∗100 and they are reported in parenthesis, where Pinitial refer to zero strain value for each column. Strain

P (∆ PRelative ) T otal

PA (∆ PRelative ) A

% 4 3 2 1 0 −1 −2 −3 −4

µC/cm2 (%) −0.37 (68) −0.39 (77) −0.36 (63) −0.38 (72) −0.22 −0.44 (100) −0.52 (136) −0.69 (213) −0.92 (318)

µC/cm2 (%) −0.32 (45) −0.37 (68) −0.41(86) −0.43 (95) −0.22 −0.60 (172) −0.63 (186) −0.70 (218) −0.79 (259)

P (∆ PRelative ) PA+BX3 (∆ PRelative BX3 A+BX3 ) µC/cm2 (%) −0.05 (150) −0.02 (0) 0.05 (350) 0.04 (300) −0.02 0.16 (900) 0.11 (650) 0.01(150) −0.14 (600)

µC/cm2 (%) −0.37 (54) −0.39 (62) −0.36 (50) −0.39 (63) −0.24 −0.44 (83) −0.52 (116) −0.69 (187) −0.93 (287)

is found to be negligible, i.e. PBX3 = −0.02 µC/cm2 . Further decomposition of PBX3 into PB and PX3 gives 0.59 µC/cm2 and −0.51 µC/cm2 , respectively. Thus, despite the fact that relatively large contributions come from the B-cation and X-ligands, they compensate leaving mainly the contribution from the A-molecule. This is further supported by analyzing the distortion pattern of Γ− 4 mode (supplementary section B for more details). Functional mode decomposition analysis for the strained cases (see Table 1) shows the following: in the case of tensile strain, the contribution to the total polarization mainly comes from A-molecules, firstly increasing and then approaching a constant value; in the case of compressive strain, contribution from A-molecules increases with strain; at −4% strain, contribution from BX3 units starts adding to that from A-molecule, enhancing in this way the total polarization up to -0.92 µC/cm2 . Since the main contribution comes from the A-site, we investigate the microscopic origin of the polarization and its epitaxial strain dependence by performing structural distortion analysis on the A-molecule. Although the C-N bonds are polar, the isolated [C(N H2 )3 ]+ cation is non-polar by symmetry. However, in the crystalline field of the BX3 framework, 8


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consequence of a G-type and A-type antiferro-like arrangements of Da and Db components, respectively; but now a net Dc component is left which follows a ferro-like arrangement, and P leads to Dc 6= 0 (type, Aa Gb Fc in analogy with noncollinear spin structures 18,50 ). As a result, the effective polarization from A-molecule is due to this weak Dc component, which finally gives rise to the canting of dipoles and hence, to a weak ferroelectricity in the system, as shown in Figure 3(b).

Figure 4: Strain dependence of the canting angle Φ (in degree) of A-group [C(N H2 )3 ]+ molecular dipole effectively acting along C-N bond in C(N H2 )3 Cr(HCOO)3 (i.e., Cr-MOF) in polar P na21 space group.

In Figure 4, we show the dependence of Φ, i.e. the canting angle between D and Dc as a function of the applied strain. This dependence strongly correlates with the dependence of the polarization upon strain (as shown in Figure 2), therefore suggesting that dipole canting is the main driving force to enhance the ferroelectric polarization. We have found that the QX4+ mode becomes more pronounced as a function of the compressive strain which drives both the change in magnetic phase diagram and also modifies the weak N − H· · · ·O interactions, enhancing in turn the weak dipole Dc originating from 10


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A-molecule (see supplementary section A and C for more details). At −4% of strain the total polarization P is found to be −0.92 µC/cm2 , where the contributions coming from the Amolecule and BX3 units are PA = −0.79 µC/cm2 and PBX3 = −0.14 µC/cm2 , respectively. Thus, at ∼ −4% of strain, finite polarization from BX3 unit is effectively contributing to the one from the A-molecule further increasing the total polarization. We now focus our attention to the Mn-MOF (i.e., (CH3 CH2 N H3 )M n(HCOO)3 ). We briefly summarize a previous study for the experimental structure corresponding to the zero strain case. 10 Mn-MOF is qualitatively different from the previous Cr-MOF case because there is no JT distortion (d5 electronic configuration for M n2+ ions). More importantly, the isolated organic A cation has an intrinsic dipole moment which is further modified by the crystalline field. This gives rise to a larger ferroelectric polarization of ∼ −1.6 µC/cm2 along the c-axis due to a canted arrangement of CH3 CH2 N H3 dipole moments. By analyzing the atomic displacements of the ferroelectric phase (P na21 ) with respect to the reference centric structure (P nma), as reported in Figure 5 (a), we can see that the main contributions involve the organic A groups, while small distortions affect the framework. In the centric structure, the A group is forced to have the C-C-N bonds ferroelectrically coupled in the ab plane, while they are antiferroelectrically coupled with nearest planes along the c-axis. In the polar phase, molecules are tilted giving rise to a uncompensated weak ferroelectricity along the c axis. Symmetry-modes based analysis of the ferroelectric displacements shows that the distortion connecting the P nma to P na21 space groups belongs to the polar Γ− 4 irreducible representation. As previously done for Cr-MOF, it is possible to decompose the ferroelectric polarization according to the different A-cation and BX3 framework functional units: the largest contribution comes from the tilting of the organic molecules within the MOF’s cavities (PA ∼ −2.7 µC/cm2 ); on the other hand, the BX3 groups counterbalance with an opposite contribution (PBX3 ∼ 1.1 µC/cm2 ). In this work, we simulate the effect of the strain field on the Mn-MOF and we show that it can be a suitable way to engineer the ferroelectric properties. In Figure 5(b) and Table 2

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Table 2: Total and functional polarization of A-molecule and BX3 group for Mn-MOF. Same conventions as in Table 1 have been used. Strain

P (∆ PRelative ) T otal

PA (∆ PRelative ) A

% 4 3 2 1 0 −1 −2 −3 −4

µC/cm2 (%) −1.56 (-4.9) −1.60 (-2.4) −1.66 (1.2) −1.75 (6.7) −1.64 −2.22 (35) −2.51 (53) −2.72 (66) −3.34 (103)

µC/cm2 (%) −2.42 (-9.0) −2.47 (-7.1) −2.53 (-4.9) −2.58 (-3.0) −2.66 −2.71 (1.9) −2.75 (3.4) −2.82 (6.0) −2.93 (10)

P (∆ PRelative ) PA+BX3 (∆ PRelative BX3 A+BX3 ) µC/cm2 (%) 0.87 (-22) 0.92 (-17) 0.94 (-15) 0.95 (-14) 1.11 0.72 (-35) 0.62 (-44) 0.45 (-59) 0.03 (-97)

µC/cm2 (%) −1.55 (0) −1.55 (0) −1.59 (2.6) −1.63 (5.2) −1.55 −1.99 (28) −2.13 (37) −2.37 (53) −2.90 (87)

shows an intrinsic dipole moment as a consequence of a tilted arrangements of covalent C-C and C-N bonds. Such bonds are strong and rather insensitive to framework arrangements, resulting in a molecular charge redistribution not affected by the strain (differently from CrMOF where the polar tiltings of [C(N H2 )3 ]+ molecules are directly induced by the framework via the Jahn-Teller distortions). As for the dependence of magnetic properties on strain, the ground state of Mn-MOF does not change, resulting in a G-type AFM ordering of Mn magnetic moments at all studied strain values. In summary, we have investigated the strain dependence of polarization in Cr and Mn based MOFs. In the former case, A-molecule is found to be the most sensible to the applied compressive strain. In the latter case, the BX3 framework is more sensible to strain than the A groups. However, in both cases, compressive strain (up to 4% strain) increase the polarization by more than 300% for Cr-MOF and by more than 100% for Mn-MOF. Finally, we want to draw here an analogy with spin-ordered systems. The presence of strongly localized dipole moments embedded in the BX3 framework lead to the interpretation of net polarization arising from uncompensated dipole moments, i.e. tilting of the dipoles leaving out a "weak"-ferroelectric component (in case of Cr-MOF type, Aa Gb Fc ). This is in close 13



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analogy with the tilting of spin moments, giving rise to weak-ferromagnetic component. 50 However, while the theory of spin-canting is already at a mature stage and different mechanisms have been proposed, 51,52 the theory of dipole canting in a BX3 framework has not been developed yet, and it would also bring analogies to the theory of ferroelectric liquids. It goes without saying that these are topics to address in future theoretical investigations, since they hold a vital role for the ferroic properties.

Acknowledgement S.G acknowledges useful discussions with Dr. Hena Das (AEP, Cornell University). S.G. supported by the Army Research office under grant No. W911NF-10-1-0345. A.S. acknowledges support from CNR Short Term Mobility program prot. AMMCNT-CNR 0026336 and the kind hospitality of Prof. J. van den Brink (IFW Leibniz Institute, Dresden, Germany) where this work was partially done. D.D.S. and A.S. acknowledge the CARIPLO Foundation through the MAGISTER project Rif. 2013-0726. The authors acknowledge discussions with Craig J. Fennie (Cornell University), S. Picozzi (CNR-SPIN), P. Barone (CNR-SPIN), P. Jain (Los Alamos National Laboratory).

Supporting Information Available We have discussed in more details: the strain dependence of the magnetic state, the BX3 unit displacement of the polar (Γ4 −) mode and the dipole canting driven weak ferroelectricity in the case of C(N H2 )3 Cr(HCOO)3 compound (i.e., Cr-MOF). This material is available free of charge via the Internet at http://pubs.acs.org/.

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