Hybrid Improper Ferroelectricity in a Multiferroic and Magnetoelectric Metal‐Organic Framework

Abstract

Metal-organic frameworks (MOFs) are hybrid crystalline compounds comprised of extended ordered networks made up of organic linkers and metal cations, often forming porous materials at the interface between molecular coordination chemistry and materials science. They show unique properties arising from organic-inorganic duality [ 1 ] which has already resulted in an unprecedented variety of physical properties in a single class of materials and applications, such as gas storage, exchange or separation, catalysis, drug delivery, optics, and magnetism. [ 2 , 3 ] An additional feature is the possibility of creating ideally infinite new MOFs by varying inorganic/organic components, molecular topologies, organic linkers, etc. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] All these degrees of freedom can be exploited for a rational design of new materials with enhanced functionalities.MOFs with ABX 3 perovskite structure or closely related superstructures of this chemical chameleon have attracted much attention since they show promising properties in areas that have traditionally been dominated by inorganic materials, for example magnetism and ferroelectricity. [24][25][26][27][28] Combination of spontaneous magnetic and ferroelectric order in a single material, i.e., multiferroicity (MF), is of great technological and fundamental importance, in particular when both orders are coupled through a sizeable magneto-electric (ME) coupling. Despite the large activity devoted to multiferroics, [ 29 ] most of the past and current studies have been focused on inorganic compounds, though mainly in the family of perovskite-like oxides. Among these, a strong ME coupling is expected in magnetically driven improper ferroelectrics, such as rare-earth manganites or delafossite oxides, where the magnetic ordering is responsible for spontaneous electric polarization. [ 30 ] Unfortunately, the symmetry-breaking is usually associated with frustrated magnetism displaying complex antiferromagnetic or spiral order, and both measured electric polarization and critical temperatures are usually too small for any device applications. [ 30 ] The large ferroelectric polarization of proper multiferroics such as BiFeO 3 , on the other hand, originates from a polar lattice instability that is generally not coupled to any magnetic instability leading to a net magnetization. [ 31 ] Very recently, a third class of magnetoelectric multiferroics has been suggested, where a lattice instability is responsible for both ferroelectricity and the appearance of a weak-ferromagnetic (WFM) ordering, thus allowing for a potentially large ME coupling. The key ingredient is a trilinear coupling between a (stable) polar mode and two nonpolar instabilities, usually octahedron tilting and rotations in layered or double perovskites, as recently found in some inorganic compounds, where cation ordering leads to the required symmetry breaking. [32][33][34][35][36][37][38] The mechanism has been called "hybrid improper ferroelectricity", implying t...

Electric Field Control of Jahn-Teller Distortions in Bulk Perovskites

“…Acting directly on the amplitude of the JT distortion might, alternatively, allow one to control the magnetic state with an electric field, as recently proposed independently in superlattices [14] and metal organic frameworks [16], or to control metal-insulator phase transitions.…”

“…This concept is related to an unusual coupling of lattice modes, giving rise in the free energy expansion to a trilinear term −λPR 1 R 2 linking the polar motion P to two independent nonpolar distortions R 1 and R 2 . Such a coupling was identified in various layered perovskites [8,9,[12][13][14][15], metal-organic framework [16,17], and can even appear in bulk ABO 3 perovskites [18,19]. Interestingly, in Ruddlesden-Popper compounds [9,20] and ABO 3 =A 0 BO 3 superlattices [21], this trilinear coupling appeared as a practical way to achieve electric control of nonpolar antiferrodistortive (AFD) motions associated with the rotation of the oxygen octahedra (i.e., monitoring P with an electric field will directly and sizeably tune the nonpolar modes R 1 and/or R 2 ).…”

Novel magneto-electric multiferroics from first-principles calculations

“…A similar type of hybrid improper ferroelectricity has recently been reported in alternative magnetic systems such as NaLaMnWO 6 [113] or RLaMnNiO 6 [119] double perovskites, BiFeO 3 /LaFeO 3 superlattices [118] and even in metalorganic frameworks [115].…”

“…Further investigations have been since performed on PbTiO 3 /SrTiO 3 superlattices, clarifying the role of the strain on the relevant AFD motions and the polarization [112]. Alternative trilinear couplings have been obtained [113,111,114,115]. Guiding rules to identify alternative hybrid improper ferroelectrics have been proposed [114] and the emergence of ferroelectricity in rotation-driven ferroelectrics was discussed [116].…”

Designing new ferroelectrics with a general strategy

“…The HIF was also found in the double-layered Ruddlesden-Popper (RP) perovskite A 3 B 2 O 7 (A=Ca, Sr; B=Mn,Ti), [17][18][19] the 1:1 A-cation ordering perovskite-type superlattice, [20][21][22][23] A-cation ordering RP NaRTiO 4 (R = Y, La, Nd, Sm-Ho), 24 the 2:2 B-cation ordered superlattice, 25 and metal-organic perovskite material. 26 In the above-mentioned theoretically designed FEs, one usually starts from a high-symmetry structure (e.g., cubic perovskite structure), then the effect of atomic substitution and soft phonon modulations are examined to see whether the ferroelectricity can be induced or not. Finally, the trilinear coupling mechanism is discussed to understand the origin of improper ferroelectricity.…”