We present an ab initio study of the [C(NH2)3][Cu(HCOO)3] compound. It belongs to a new class of multifunctional materials, namely multiferroic metal-organic frameworks. We show that this compound is multiferroic, with coexistence

of ferroelectricity and magnetism. Furthermore, it is also magnetoelectric. Our study suggests that multiferroic metal-organic frameworks are a very promising class of materials

Stroppa, Alessandro

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DOI 10.1393/ncc/i2012-11310-xCommunications: SIF Congress 2011IL NUOVO CIMENTO Vol. 35 C, N. 5 Settembre-Ottobre 2012Multiferroic and magnetoelectric metal-organic frameworksA. Stroppa(∗)CNR-SPIN - L’Aquila (AQ), Italyricevuto il 24 Gennaio 2012; approvato l’ 1 Febbraio 2012Summary. — We present an ab initio study of the [C(NH2)3][Cu(HCOO)3] com-pound. It belongs to a new class of multifunctional materials, namely multiferroicmetal-organic frameworks. We show that this compound is multiferroic, with coex-istence of ferroelectricity and magnetism. Furthermore, it is also magnetoelectric.Our study suggests that multiferroic metal-organic frameworks are a very promisingclass of materials.PACS 75.85.+t – Magnetoelectric effects, multiferroics.PACS 77.55.Nv – Multiferroic/magnetoelectric films.PACS 33.15.Fm – Bond strengths, dissociation energies.PACS 75.30.Kz – Magnetic phase boundaries (including magnetic transitions,metamagnetism, etc.1. – IntroductionMultiferroics are materials which show at least two coexisting ferroic orders in asingle phase [1] like for instance, ferroelectric and magnetic orders. They are potentialapplications in future magnetic data storage and spintronic devices [2-8] provided a simpleand fast way can be found to turn their electric and magnetic properties on and off.They can be applied as high-sensitivity ac magnetic field sensors and electrically tunablemicrowave devices such as filters, oscillators and phase shifters [9]. A special case iswhen both orders are coupled, thus allowing a cross-coupling where one can tune theferroelectric response by a magnetic field, and vice versa, one can tune the magneticresponse by an applied electric field [9].There is a great interest in the literature about multiferroic and magnetoelectric ma-terials. By a simple search in ISI WEB of Science, using keywords such as “multiferroic*OR magnetoelectric*” as topic, one gets a list of almost 1000 papers published in 2011giving an overall h-index of 97 cumulated over the years. However, most of these studies(∗) E-mail: alessandro.stroppa@aquila.infn.itc© Societa` Italiana di Fisica 5960 A. STROPPAFig. 1. – Crystal structure of the Cu-MOF. One can see the octahedra linked by HCOO groups,and the A-site of the perovskite network occupied by C(NH2)3 groups. For more details, werefer to ref. [25] The spin configuration is represented by arrows at Cu sites.deal with inorganic compounds, mainly complex oxides derived from the perovskite-typefamily. Only very recently, new directions started to emerge, shifting the focus towardsorganic or hybrid organic-inorganic materials [10]. A pioneering paper along this line isthe work by Jain et al. [11-14], where they show multiferroic behavior associated with anorder-disorder hydrogen bonding transition in metal-organic frameworks (MOFs) withperovskite ABX3 architecture. The search of multiferroicity in MOFs is a very attractiveemerging route already showing promising potential results [15,16].MOFs are crystalline hybrid materials containing both inorganic and organic compo-nents. They are very attractive materials for gas storage, drug delivery, catalysis, opticsand magnetism [17-19]. Essentially, the MOF structure is made up of a framework ofmetal ions coordinated by organic ligands and forming a porous framework, whose cavi-ties can be filled by molecular ions. An interesting class of MOF has recently attractedgreat attention. It has a ABX3 perovskite topology, where A is an organic cation, Bis a transition metal, X is an organic ligand. These compounds provide access to moreoxide-like properties, like for instance, multiferroicity [20-24].2. – Cu-MOFIn this framework, we have studied by ab initio calculations the[C(NH2)3][Cu(HCOO)3] MOF (hereafter called Cu-MOF), where the A group isthe guanidinium cation C(NH2)3+, B is Cu+2 and X is HCOO−. Details of thecomputational parameters can be found in ref. [25] In fig. 1 we show a side view of thecompound. It is easy to recognize the octahedra connected by carboxylic ligands andthe guanidinium cation which fill the A-site of the perovskite topology.MULTIFERROIC AND MAGNETOELECTRIC METAL-ORGANIC FRAMEWORKS 61Fig. 2. – Electronic degeneracy removed by Jahn-Teller distortions through the Q2 mode.An important feature in this compound is the presence of Jahn-Teller active Cu+2 ions,having a d9 electronic configuration. The degeneracy of this configuration is removedby an octahedra structural distortion, which, in turns, introduces long and short Cu-Obonds in the ab basal plane (Q2 Jahn-Teller mode). A schematic summary is presentedin fig. 2.The different orientations of the long Cu-O bonds on different Cu sites give rise to acharacteristic anti-ferrodistortive pattern: the long Cu-O bond on one Cu site is almostperpendicular to the long Cu-O bond on neighboring Cu site. One can introduce afunction through the definition of a parameter φ. This parameter is an effective anglewhich quantifies the “degree” of antiferro-distortion (AFD): for φ = 4π/3 or 2π/3, onehas a maximum distortion in our system, while for φ = π, one has that Cu-O longand short bonds are equal. It must be noted that AFD modes are usually non-polar instandard inorganic ABX3 compounds. We will come back to this point shortly.The ground state is antiferromagnetic, with Cu spins ferromagnetically coupled withinthe ab plane while antiferromagnetically coupled between parallel ab planes (see fig. 1).Note that, by introducing the spin-orbit coupling in the calculations, a weak ferromag-netic component appears, i.e. the spins are tilted. This will have important consequencesfor the magnetoelectric behavior in this compound (see ref. [25]). It is important to stressthat the Cu-MOF crystallizes in a polar space group, Pna21 [23]. Therefore, the magneticground state in a polar space group suggests a possible multiferroic behavior. In order toexplore this possibility we have introduced a virtual paraelectric (centric) structure byusing the PSEUDOSYMMETRY tool [26]. This virtual paraelectric structure has Pnanspace group. In this way, one can present the crystal structure as due to symmetry-lowering structural distortion from the high-symmetry centric group. It is useful tointroduce a parameter λ which is proportional to the amplitude of the polar distortionconnecting the centric to the polar structure: λ = 1 represents the compound in thePna21 space group, λ = 0 represents the Pnan centric space group. For each λ ∈ (0, 1),one can linearly interpolate between the two end-points, defining a continuous path as afunction of λ. Obviously, one can also consider the λ = −1: this state has again Pna21space group symmetry, but the polarization has been reversed with respect to λ = 1.62 A. STROPPAFig. 3. – Energy, polarization and AFD distortion along the path connecting the virtual para-electric structure and the polar ones. The insets show the orientations of the long Cu-O bondsof the two Cu sub-lattices.We found that at λ = ±1, the system has a finite polarization P = 0.37μC/cm2. Asexpected, at λ = 0, P = 0. It turns out that P = P (λ) is a monotonically increas-ing odd function of the polar distortion. The calculated energy profile as a function ofλ produces the expected double-well profile characteristic of a switchable ferroelectricsystem. Surprisingly, by monitoring the changes of φ along the path, we have found aclear correlation between P = P (λ) and φ(λ). In principle, one has φα,β(λ), where α, βdenotes the two Cu-sublattice in the ab plane. Each sublattice has the same orientationof the long Cu-O bonds, but the orientation “rotates” by 90 degrees in the neighboringCu site. One can see that P = P (λ) and φ(λ) have the same behavior as a function of λ,thus suggesting that AFD distortions can be the source of the ferroelectric polarization.In fig. 3 we show the energy E, the polarization P , and the “amplitude” of the AFDdistortions along the path.The microscopic explanation of the ferroelectric polarization and its relation to AFDmodes have been discussed in details in ref. [25] Here we remind the main ideas. The[C(NH2)3]+ molecular group interacts with the BX3 framework through hydrogen bond-ing N−H· · ·O, where the first H belong to NH2 of the [C(NH2)3]+ group, and the O isbond to Cu. Both the H atoms of the NH2 group feel the H bonding, but while at theλ = 0 state, the H bonding strength is the same, for λ larger than 0, i.e. towards theferroelectric state, the H bonding strength becomes asymmetric for the two H atoms,due to the crystalline environment [25]. Since the AFD mode basically controls the oxy-gen positions, the change of the AFD mode amplitude (changing φ along λ), inducesasymmetric distortions in the NH2 part of the A-group, i.e. there is an induced dipolemoment which then sums up to give a finite polarization. This explains the microscopicorigin of the ferroelectric polarization in this compound.3. – ConclusionWe have shown that the Cu-MOF, belonging to the metal-organic framework fam-ily with ABX3 topology, shows a rich and fascinating physics. Our study supports thefollowing picture: i) It is ferroelectric with an estimated polarization of 0.37μC/cm2.MULTIFERROIC AND MAGNETOELECTRIC METAL-ORGANIC FRAMEWORKS 63ii) The origin of the ferroelectricity is very intriguing: nonpolar distortions (i.e. antiferro-distortions) give rise to a loss of inversion symmetry, paving the way for the appear-ance of polarization; note that this mechanism is not found in classical ABX3 inorganiccompounds. iii) Hydrogen bonding plays a major role in coupling the nonpolar distor-tions acting in the BX3 framework with the organic cation. iv) A weak ferromagneticcomponent is allowed and it is coupled to the ferroelectricity: by using this very rareproperty, it would be possible to control the polarization by an applied magnetic field,and vice versa. This is called magnetoelectricity. This feature has not been discussedhere, but we refer to ref. [25] for more details.∗ ∗ ∗This research was funded by the European Research Council under the EuropeanCommunity, 7th Framework Programme (2007–2013)/ERC Grant Agreement no. 203523won by Dr. S. Picozzi. Computational support by CASPUR Supercomputing Centerin Rome through Standard HPC Grant 2010 is gratefully acknowledged. Figures wereplotted using the VESTA package [27].REFERENCES[1] Schmid H., Ferroelectrics, 162 (1994) 317.[2] Bibes M. et al., IEEE Trans. Electron Dev., 54 (2007) 1003.[3] Gajek M. et al., J. Appl. Phys., 97 (2005) 103909.[4] Gajek M. et al., Phys. Rev. B, 72 (2005) 020406(R).[5] Gajek M. et al., Nat. Mater., 6 (2007) 296.[6] Stroppa A. et al., Phys. Rev. B, 75 (2007) 195335.[7] Wu H. et al., Phys. Rev. Lett., 105 (2010) 267203.[8] Stroppa A. et al., Phys. Rev. B, 77 (2008) 035208.[9] Nan C. W. et al., J. App. Phys., 103 (2008) 031101.[10] Kagawa F. et al., Nature Phys., 6 (2010) 169.[11] Jain P. et al., J. Am. Chem. Soc., 130 (2008) 10450.[12] Jain P. et al., J. Am. Chem. Soc., 131 (2009) 13625.[13] Baker P. et al., Phys. Rev. B, 82 (2010) 012407.[14] Jain P. et al., Proc. Natl. Acad. Sci. USA, 108 (2011) 6828.[15] Ramesh R., Nature, 461 (2009) 1218.[16] Rogez G., Angew. Chem. Int. Ed., 49 (2010) 1821.[17] Yaghi O. M. et al., Nature, 423 (2003) 705.[18] Fe´rey G. et al., Science, 283 (1999) 1125.[19] Rao C. N. R. et al., J. Phys.: Condens. Matter, 20 (2008) 083202.[20] Cheetham A. K., Science, 318 (2007) 58.[21] Fe´rey G. et al., Chem. Soc. Rev., 37 (2008) 191.[22] Wang X. Y. et al., Inorg. Chem., 43 (2004) 4615.[23] Ke-Li H. et al., Chem. Eur. J., 15 (2009) 12050.[24] Clausen H. F. et al., J. Solid State Chem., 178 (2005) 3342.[25] Stroppa A. et al., Angew. Chem. Int. Ed., 50 (2011) 5847.[26] Capillas C. et al., Z. Krist., 226 (2011) 186.[27] Momma K. et al., J. Appl. Crystallogr., 41 (2008) 653.

Multiferroic and magnetoelectric metal-organic frameworks

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Multiferroic and magnetoelectric metal-organic frameworks

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