Recent Progress of Multiferroicity and Magnetoelectric Effects in ABX3‐Type Perovskite Metal–Organic Frameworks

Multiferroics have been investigated extensively in the last decades due to their wide range of applications in high‐density multistate storage, spintronics, and novel multifunctional magnetic–electric devices. One peculiar subgroup of multiferroic materials comprises 3D perovskite metal–organic frameworks (MOFs) with the general formula ABX3 (A = monovalent organic cation (such as an alkali metal or protonated amine), B = divalent metal cation, X = organic anion), for their coexistence of multiple orders (electric, magnetic, and elastic, et al.). The purpose of this review is to give a representative overview of the recent progress in the field of ABX3‐type multiferroic MOFs, containing 3d magnetic metal ions at B‐site. First, the perovskite multiferroic MOFs in which X‐site is occupied by formate, is examined and summarized. In particular, magnetoelectric coupling effects, such as electric‐field tuning of magnetic properties and magnetic field control of electric polarization, and pressure control of structural/magnetic/electric properties, are described and discussed. Then, it is focused on the structural phase transitions and ferroic orders by analyzing several representative multiferroic MOFs compounds with none‐formate. To motivate the researchers in this area, some promising topics that have not yet been fully explored in perovskite multiferroic MOFs are finally proposed.


Introduction
Metal-organic frameworks (MOFs) are a prototype of organicinorganic hybrid materials with porous structure. Among them, the ABX 3 -type perovskite MOFs, where A is the organic cation DOI: 10.1002/admi.202300123 located in the cavities of the framework, B is the metal ion and X is the anionic ligand, have attracted enormous interest for their intriguing physical properties and wide practical applications. As early as 1926, V. M. Goldschmidt put forward the concept of tolerance factor and successfully described the influence of ion size on the stability of perovskite oxide, which played an important guiding role in the synthesis of new perovskite-structured MOFs. [1] Perovskite MOFs have presented magnetic, ferroelectric, ferroelastic, multiferroic, and photovoltaic capabilities, [2][3][4][5][6][7][8] with prospective applications in sensors, gas storage, catalysts, photoluminescence, magnets, photovoltaics, and so on, as shown in Figure 1. For instance, the modest stereo effect of HCOO − is clearly advantageous for the development of coordination frameworks, and the short HCOO − bridge with a three-atom connection, appears to be promising for magnetic coupling between magnetic metal ion sites. [9] Furthermore, the H atom of amino group readily forms hydrogen bonds with the oxygen atom of formate ligand. Therefore, ammonium groups and formate ligands are generally chosen to form a more stable framework structure with metal ions in the synthesis of MOFs, which is known as ammonium metal formate frameworks (AMFF). [10] According to recent research, perovskite MOFs have many outstanding multiproperties and are a family of promising multifunctional material. In particular, the variable A and B components of ABX 3 perovskite allow for much flexibility in altering the magnetic and electric properties in a simple crystalline structure. In general, as shown in Figure 2, the A-site cations include methylammonium (MA + ), dimethylammonium (DMA + ), NH 4 + , HONH 3 + , methylhydrazinium (MHy + ), guanidinium (Gua + ), formamidinium (Fmd + ), imidazolium (Him + ), hydrazinium (Hyz + ), while B-site anions include SCN − , N(CN) 2 − , HCOO − , Au(CN) 2 − , ClO 4 − , BH 4 − , and so on. [11] It is worth mentioning that HCOO − has been widely demonstrated in creating coordinating polymers and magnets to a molecule with intriguing magnetic characteristics in recent decades. [11] Perovskite-like MOFs constructed by selecting organic groups containing formate ligands and divalent transition metal ions have been shown to exhibit interesting multiferroic and , have even become templates for studying multiferroic MOFs. [12][13][14][15][16][17][18][19][20][21][22][23][24] When temperature, strain, pressure, and magnetic/electric field change, MOFs can modify their physical properties accompanied by phase transitions. As an example, the charged components deviate from their initial position result in electric polarization due to the structure changes, while the magnetic properties caused by magnetic metal ions in the system. [25] Obviously, the B-site metal ions play a crucial role in magnetic characteristics for MOFs. For example, [Fmd][M(HCOO) 3 ] (M = Mn, Fe, Co, Cu), all compounds are ferromagnetic-like materials. [26][27][28] From our point of view, the MOFs containing Fmd + should present the ferroelectric properties in addition to ferromagnetic behaviors, which has not been confirmed experimentally. Ferroelectric characteristics have been reported in other MOFs with similar structures. Moreover, part of perovskite MOFs also show magnetoelectric coupling behaviors, which providing a new platform for physics study and designing novel electronic devices.
It is worth mentioning that the lanthanide organic frameworks system, in which the aforementioned transition metals ions are replaced by lanthanide ions, further expanding the application in the areas of sensors, catalysts, magnetism, and photoluminescence for MOFs. [29][30][31] Therefore, the potential of such a range of combinations opens many challenges for the series of MOFs. In addition, since the discovery of perovskite solar cells in the 2009, it has become a sort of disruptive photovoltaic technology. [32] However, its commercial application remains challenging due to the toxicity of lead and unstable structure. The AMFF system is a new kind of perovskite materials that can be used as a potential solar cell material and has impressive performance in multiferroicity. [33] Furthermore, a new member of the ferroic family named ferrovalley, with the perovskite structure that are promising multiferroic materials for information storage, has received tremendous research attention over the past few years. [34] Here we briefly summarize the recent research progress about multiferroic MOFs with ABX 3 perovskite-like structure, in particular those containing formate at X-site. Table 1 summarizes the structural phase transitions, magnetic and/or electric orders for ABX 3 -type MOFs with formate reported so far. It should be noted that those MOFs have been investigated by experimentally. This review aims to offer fresh insights to comprehend the role of multiferroic properties and magnetoelectric effect in the 3D perovskite MOFs with ABX 3 formula. Besides, some promising topics that have not yet fully discovered in multiferroic MOFs are proposed. Based on mechanistic understanding, we believe that this review will help to attract more attention and inspire more research efforts in the fast-evolving joint fields of multifunctional MOFs materials.

ABX 3 -Type Perovskite MOFs with Formate
Perovskite is a class of ceramic oxides with the general formula ABO 3 , and CaTiO 3 was the first such compound discovered. [62] More kinds of anions can replace the O part of the general formula, so the general formula is changed from ABO 3 to ABX 3 . Perovskite materials are fundamentally and technologically essential for a variety applications, such as sensors, spintronic devices, solar cells.
In 1978, organic-inorganic hybrid perovskite compounds was first report by Weber, who opened up the new areas of perovskitelike MOFs research. [62] Subsequently, other materials in this family no longer rigidly adhere to the structure of traditional perovskite with formula ABX 3 but introduce new components at various sites, where A-site is usually occupied by alkali metals, alkaline earth, or rare-earth ions, transition metal ions occupy the B-site, and oxygen atoms or halogen elements usually occupy the X-site. However, with the introduction of organic components, the selection of the three sites becomes more flexible, and organic cations and anions can also be filled into the A-and X-sites, which brings more possibilities and variations to perovskite multiferroic MOFs compounds.  3 ] at a rate of 10 K min −1 . In this figure, the first heating and cooling cycle is labeled as "heating 1" and "cooling 1, while "heating 2" corresponds to the second heating cycle. Reproduced with permission. [40] [35,36,38,39] It is certain that these compounds undergo phase transitions, which can be confirmed by their differential scanning calorimetry (DSC) measurements shown in Figure 3a. [36] However, the details of the Ni member are not well-known because its large single crystal has not been successfully obtained. Nonetheless, we can reasonably speculate that it should have the similar structural phase transition compared with other isomorphisms. Interestingly, the phase transition temperature of [NH 4 ][M(HCOO) 3 ] (M = Mn, Fe, Co, Ni, Zn) members are positively related to their metal ion radius, that is, the higher the phase transition temperature corresponding to the larger the metal ion radius. [40] Gómez-Aguirre et al. selected Cd 2+ ion and synthesized a new compound of [NH 4 ][Cd(HCOO) 3 ], [40] which may have a higher phase transition temperature based on the large radius of the Cd 2+ ion. The properties of [NH 4 ][Cd(HCOO) 3 ] are pretty different from those of other isomers. It is an orthorhombic system with the Pna2 1 space group at room temperature. Furthermore, thermal analysis results indicate that it does not undergo structural phase transformations. It begins to decompose above ≈373 K, (Figure 3b), which may be related to its relatively abnormal structure. In most members of the family, the coordination environment for metal ions is octahedral, and the coordination mode between metal ions is anti-anti mode, while for Cd member the metal ions is syn-anti conformation. Kieslich et al. found that the tolerance factor of perovskite-like structure is conducive to structural stability when it is greater than 0.81. [63] However, in [NH 4 ][Cd(HCOO) 3 ], components is not well matched, which directly leads to the value of its tolerance factor being lower than 0.81. That is, the structure of [NH 4 ][Cd(HCOO) 3 ] should be unstable but it retains a noncentrosymmetric structure even at room temperature. Therefore, the coordination mode between metal ions should be responsible for the stability of the structure of [NH 4 ][Cd(HCOO) 3 ].
As mentioned above, the family of perovskite [NH 4 ][M(HCOO) 3 ] exhibits ferroelectric properties caused by the noncentrosymmetric structure. In special, the Cu member has the transition from simple antiferroelectric (AFE) to helical AFE at 353 K, while the Cd member maintains an asymmetry structure at high temperatures. [10] For Cu member, the phase transition process is completely different from that of other  [41] copyright 2016, Royal Society of Chemistry. d) Magnetization of chiral Hyz-Mn versus temperature. Inset: Field dependence of M measured upon increasing and decreasing the field (open and closed symbols, respectively). Reproduced with permission. [41] Copyright 2016, Royal Society of Chemistry. members, with a much higher phase transition temperature due to the Jahn-Teller (JT) effect of Cu 2+ . [64] Accordingly, Cu member is more stable than other isomorphisms, since the JT effect breaks the degeneracy and stabilizes the crystal structure.
The thermal analysis results of Cd member show that no phase transformation takes place until its thermal decomposition. Figure 3c shows that an apparent endothermic peak appears on "heating 1" in the DSC measurement, but it is caused by the moisture. When its moisture is completely removed, the DSC curve becomes "heating 2." Obviously, it has no phase transition characteristics. The temperature has no apparent influence on the structure of Cd member, except for pressure. According to the Raman spectra, we can conclude that pressure forces NH 4 + to produce displacement relative to the anionic framework, which will directly impact its ferroelectric properties. [10] In addition, in terms of the composition of the Cd member, we can start from the coordination mode of bridge ligand to enhance the stability of the structure, when the size of components in MOF is not very matched.
As can be seen from the Figure 3d, [NH 4 ][M(HCOO) 3 ] (M = Mn, Fe, Co, Ni) exhibits antiferromagnetism with ferromagnetic characteristics at low temperatures due to the net magnetic moment generated by spin-canting. Except for the magnetic compounds mentioned above, [NH 4 ][Cd(HCOO) 3 ] should also show magnetic properties, but the current research in this area is not in-depth. In addition, density functional theory (DFT) calculations also show that the organic cation of the Cd member has an eccentric displacement, resulting in the polarization strength. Therefore, the Cd member is a potential multiferroic material and can exhibit ferroelectric properties at high temperatures.

[Hyz][M(HCOO) 3 ]
[Hyz][M(HCOO) 3 ] (Hyz = hydrazinium, M = Mn, Fe, Zn) series have two crystal types, namely chiral perovskite phase I and perovskite phase II. [41] This family can exist in such an extraordinary situation because the size of the organic cation is between ammonium cation (or hydroxylammonium cation) and methylammonium cation, the former has a chiral structure, and the latter has a stable perovskite structure. Interestingly, we learned that different synthetic methods can significantly influence the structure it forms. [41] At present, Mn, Fe, Co, Zn, and Mg members have been successfully synthesized for this series. [41][42][43] Although not all of the two phases of these members have been synthesized, we can expect that each member has two phases.
The chiral Mn, Fe, Zn, Co, and Mg members undergo phase transitions at 296, 336, 367, 380, and 348 K, respectively (Figure 4a-c), and their space group changes from lowtemperature phase P2 1 2 1 2 1 to high-temperature phase P6 3 , showing the changes from low temperature antiferroelectric to high temperature ferroelectric. [41][42][43] This change is accompanied by low-temperature nonpolar structure to high-temperature polar structure. Their electrical properties are mainly provided by the  [41] Copyright 2016, Royal Society of Chemistry. Magnetism of 1Mn and 3Co (1Mn = Hyz-Mn, 3Co = Hyz-Co). c) Plots of T versus T under 100 Oe and 10 kOe fields, (inset) the ZFC/FC plots of the 1Mn and 3Co under 10 Oe field. Reproduced under terms of the CC-BY license. [42] Copyright 2014, The Authors, published by Royal Society of Chemistry. d) Isothermal magnetization plots of Hyz-Mn and Hyz-Co at 2 K, (top-left inset) the dM/dH plots, (bottom-right inset) hysteresis loop for 3Co. Reproduced under terms of the CC-BY license. [42] Copyright 2014, The Authors, published by Royal Society of Chemistry.
organic cations in the cavities of the framework. Due to the antiparallel arrangement of the organic cations at low temperatures, antiferroelectric phase appears in the low-temperature range. At high temperatures, the organic cations are in the same direction, resulting in the electric polarization of the structure. Their ability to maintain ferroelectric properties at room temperature make them potentially useful. However, their chiral structure is unstable, and they will gradually transform into perovskite structures. This transformation is probably caused by the mechanism of dissolution-recrystallisation of water-mediated on the sample surface. [43] The Hyz series perovskite members Mn and Zn undergo a phase transition at about 350 K (Figure 4b), and the Fe member undergo a phase transition at 347 K ( Figure 4c). Its space group changes from low-temperature phase Pna2 1 to high-temperature phase Pnma, and its structure changes from low-temperature polar phase to high-temperature nonpolar phase. In addition, there are also strong dielectric anomalies and anisotropic thermal expansion, furthermore, [(CH 2 ) 3 NH 2 ][M(HCOO) 3 ] (M = Zn, Mn, Cu) show more excellent dielectric properties and can be used as promising dielectric materials. [65,66] It is worth mentioning that the thermal motion of NH 3 NH 2 + causes both anisotropic thermal expansion and negative thermal expansion in these materials, the movement of organic cations forces the metal formate framework to change accordingly. The coupling between them may provide a new mechanism for negative thermal expansion of MOFs. In general, negative thermal expansion is inhibited by the presence of guest molecules or cations.
The chiral members Mn, Fe, and Co exhibit antiferromagnetic order below 12.5, 13.9, and 9 K, respectively (Figures 5 and 4d), while the perovskite members Fe and Mn exhibit antiferromagnetic phase transition temperatures below 12.5 and 7.9 K, respectively ( Figure 5). [41] They have ferroelectric and ferromagnetic properties that can be multiferroic materials. But now, their synthesis is still a challenge, and we currently do not have the right way to synthesize the remaining members for this family. It is worth mentioning that this series of compounds with chiral and perovskite structures are very special for AMFF compounds, they are in understanding the intrinsic mechanism of chiral structure has certain help, as well as providing insightful guidance on the origin of transforming perovskite structure into chiral ones.

[NH 3 OH]M(HCOO) 3
The [NH 3 OH]M(HCOO) 3 (M = Mn, Co, Ni, Zn, and Mg) series were reported by Wang et al. in 2012. [44] The size of NH 3 OH + cation is similar to the aforementioned NH 4 + cation, but it has two nonhydrogen atoms. These compounds are isomorphic to each other and have a nonpolar chiral orthogonal space group Reprpduced with permission ,. [44] Copyright 2012, American Chemical Society. c) Plots of ′ versus T at 10 Hz. Inset: ″ versus T. Reproduced with permission. [44] Copyright 2012, American Chemical Society. d) Data for 2Co at 10, 100, and 1000 Hz. Reproduced with permission. [44] Copyright 2012, American Chemical Society. P2 1 2 1 2 1 . Unlike previous perovskite compounds, this family does not exhibit phase transition behavior until decomposition, and it has not ferroelectric characteristic due to nonpolar structure.
Although the electrical properties are mediocre in this perovskite formate family, it is worth noting that A-site monoammonium cations contain two nonhydrogen atoms, such as MA + , Fmd + , DMA + , and Gua + , etc., with a 4 1 2 6 3 topology. However, NH 3 OH + here forms a 4 9 6 6 topology, which is relatively rare. This is due to the small size of the NH 3 OH + cation and strong hydrogen bonds with the anionic framework. The study of NH 3 OH + series reveals that the relative size of the void space between cation and framework is critical for a phase transition. [44] Since the void space size are almost equal between NH 3 OH + cation and framework, it shows no phase transition behavior. Meanwhile, the size of NH 4 + is smaller than the void space of the framework, giving rise to phase transition behavior in the family of perovskite [NH 4 ][M(HCOO) 3 ]. [10,[35][36][37][38][39][40] Interestingly, PXRD (powder X-ray diffraction) measurements were carried out on the pressed tablet sample of the Mg member which showed a different pattern from the as-prepared sample, suggesting the phase transformation behavior triggered by pressure, which needs further study. 3 ], [41,42] and A[M(HCOO) 3 ] [67] (A = alkalimetal ions) series provide examples of chiral properties produced by achiral components in solids, which offers a good opportunity to examine the magnetic optics.

The compounds of [NH 4 ][M(HCOO) 3 ], [NH 3 OH]M[(HCOO) 3 ], [Hyz][M(HCOO)
From the magnetic measurements of Mn, Co, and Ni members, the T and ZFC/FC curves (Figure 6a,b) results show that the three are antiferromagnetic and exhibit weak ferromagnetic at low temperature due to spin-canting. However, the measure-ment of their complex magnetization (Figure 6c,d) shows a special result: there is no abnormal situation in the complex magnetization for Mn and Ni members, but Co member presents a relaxation behavior. As shown in Figure 6d, the reason for the wide peak appears in ″ of Co, which corresponds to the relaxation, should be due to the movement of domain walls [68] or chiralityrelated ac responses as observed in some chiral molecular-based magnets. [69,70] This reveals that Co member is a chiral soft weak ferromagnets with large spontaneous magnetization.

[DMA]M(HCOO) 3
Some members of DMA family were first reported by Gao et al. [22] There are several examples of perovskites containing three nonhydrogen monoammonium, among which the DMA family is the earliest and most comprehensive one studied. This formate family has been successfully synthesized, including Mn, Zn, Mg, and Cd members. [18] In recent years, IR (infrared spectroscopy), Raman spectrum, NMR (nuclear magnetic resonance), EPR (electron paramagnetic resonance), SHG (second harmonic generation), dielectric, and magnetic measurements have been performed to explore the structure and multiferroic properties of the perovskites DMA series. Apart from Mg, Fe, Cu, Zn, and Cd members, the space group for other members is transformed from low-temperature phase Cc to high-temperature phase R_3c. Experiments have not confirmed the structural details for Mg and Cd members. The structural transformation of Cu member cannot occur due to the serious distortion of its framework caused by the JT effect. [23] In addition, there have been many controversies over the phase transition mechanism for Zn member. Previous studies revealed that it should have the same structural phase transition as Mn member, but later studies overturned this view, which will be elaborated on in detail below. In addition to structural information, the multiferroic properties of the DMA series have attracted great attention from the scientific community. The magnetic properties of the DMA series are similar to perovskites discussed above, but there are different opinions on their ferroelectric properties.
First, we discuss the magnetic properties for this series-all members containing magnetic ions exhibit antiferromagnetism. [13,15,17,[20][21][22][23] The magnetic phase transition temperatures of Mn, Fe, Co, Ni, and Cu members are 7.6, [22] 15.8, [17] 14.9, [22] 35.6, [22] and 5.2 K, [23] respectively. Due to the DM effect, the antiparallel magnetic moment is slightly tilted, resulting in a net magnetic moment. Thus, these compounds, although antiferromagnetic, exhibit weak ferromagnetism. It is noteworthy that the Cu member exhibits quasi-1D magnetic properties, due to the Cu 2+ JT effect. [23] The EPR measurement on DMA-Cu show the favorable evidence for the one-dimensional spin system (Figure 7a). Further, the magnetic susceptibility was well fitted by the Bonner-Fisher formula (Figure 7b), which fully proves the quasi-1D magnetic behavior in the perovskite DMA-Cu.
Second, the study on the ferroelectric properties of DMA family was started by Jain et al. [16] They predicted that Zn member shows similar dielectric behavior as antiferroelectric NH 4 H 2 PO 4 (ADP), [71] but it have not been experimentally verified so far. By a variety of experimental methods, most of DMA members show apparent phase transition behavior, with the phase transition temperatures 185, 160, 165, 180, and 156 K for Mn, Fe, Co, Ni, and Zn, respectively. [16,17,21] As shown in Figure 8a-c, the SHG measurement shows significant signal strength below T C , which fully demonstrates noncentrosymmetric structure for this formate family. [8] According to the noncentrosymmetric structure, some scholars suggested that the DMA series exhibit ferroelectric phase transition rather than the antiferroelectric one, which is still in discussion. Recently, Peksa et al. conducted a further study on the ferroelectric properties of Zn member. [46] By measuring the structure of Zn deuteride members, they found that this compound is P1 symmetric at lower temperatures. Because [(CH 3 ) 2 NH 2 ][Zn(HCOO) 3 ] (DMA-Zn) and [(CH 3 ) 2 NH 2 ][Zn(DCOO) 3 ] (DMA-ZnD) are isomorphic, the low-temperature phase space group of DMA-Zn should also be P1, which is different from that for mostly DMA series compounds with the space group Cc. [46] In addition, Maçzka et al. performed the permittivity measurement at low frequencies for DMA-Zn [72] and found that the Curie-Weiss fitting at low frequencies shows surprising results, as shown in Figure 8d,e. Although linear dependence can be observed, the line extension to zero value does not pass through the phase transition temperature point even in the high-temperature region. So, the proper ferroelectric properties of this compound were seriously questioned. Indeed, the electrical properties of DMA-Zn are neither ferroelectric nor antiferroelectric, that is, an improper ferroelectric. [73] Even more important to note, they also pointed out that the origin of the DMA-Zn phase transition may not be caused by DMA + ordered arrangement but by the deformation of its framework. Because the dielectric permittivity at low frequencies no longer follows the Curie-Weiss law, the point where the fitted epitaxial line intersects the temperature axis is also much lower than the phase transition temperature, which indicates that DMA + may be an independent paraelectric system, and the completely ordered temperature is much lower than the phase transition temperature of DMA-Zn. This indicates that the structure phase transition in DMA-Zn is probably caused by the deformation of the framework. This phenomenon is an interesting finding and may contribute significantly to the origin of the structural phase transition of such perovskite multiferroic MOFs, although the underlying mechanism of the electrical properties has not been fully explored. Except for Zn member, the electrical properties of other members have not been studied intensely, and the present experimental evidence is not enough to explain the origin of ferroelectric properties in DMA family.
The perovskite formate family in the aforementioned research shows ferromagnetic and ferroelectric properties simultaneously, as well as magnetoelectric coupling effects. For instance, DMA-Mn [21,74] and DMA-Fe [20,74,75] members show magnetoelectric coupling behaviors confirmed by various physical  [72] Copyright 2023, Royal Society of Chemistry. Figure 9a, the electric polarization becomes larger by applying a higher magnetic field, i.e., ferroelectricity is improved in DMA-Mn. [21,74] Meanwhile, its magnetic susceptibility deviates from the Curie-Weiss law just at T c . For DMA-Fe, a cross coupling between magnetic and electric orders is clearly revealed by the magnetodielectric effect in the multiferroic phase, and the electric field control of magnetism is obtained below T c = 19 K, as shown in Figure 9b. [20] Besides, the dielectric permittivity exhibits sharp peak due to the magnetoelectric coupling, associated with the quantum tunneling of magnetiza-tion (Figure 9c), yields a novel resonant quantum magnetoelectric effect. [74,75] The appearance of magnetoelectric coupling in perovskite MOFs is beneficial to the practical application, such as dynamic random access memory, data storage media, telecommunication systems, electromagnetic sensors, and so on.

measurements. As shown in
It is noteworthy that hydrogen bond can significantly contribute to the magnetoelectric coupling effects in the DMA series. Liu et al. studied the magnetoelectric effect of DMA-Mn and [(CH 3 ) 2 NH 2 ]Mn 0.5 Ni 0.5 (HCOO) 3 (DMA-Mn 0.5 Ni 0.5 ), respectively. [76] They revealed that the hydrogen bond strength Figure 9. a) The electric polarization as a function of temperature in 0, 7, and 13 T magnetic fields for DMA-Mn. Reproduced under terms of the CC-BY license. [21] Copyright 2013, The Authors, published by Springer Nature. b) Temperature dependence of the magnetization with and without electricfield poling in DMA-Fe. Reproduced under terms of the CC-BY license. [20] Copyright 2014, The Authors, published by Springer Nature. c) The dielectric permittivity as a function of magnetic field at 2 K in DMA-Fe. Reproduced with permission. [75] Copyright 2016, American Chemical Society.  [76] Copyright 2020, American Chemical Society. Temperature dependence of the linear thermal expansion along the [012] direction in several magnetic fields for c) the ferroelectric DMA-Co and d) the antiferroelectric DMA-Fe. Reproduced with permission. [45] Copyright 2019, Anerican Physical Society. e) The stair-shaped hysteresis loop obtained by subtracting the linear dependence is a sign of resonant quantum tunneling of magnetization. Reproduced with permission. [79] Copyright 2014, American Physical Society.
has a great impact on the polarization contributions from organic linkers and DMA + cations under external magnetic field, thus inducing tunability of the magnetoelectric effect in the paramagnetic state, respectively, as shown in Figure 10a,b. It was also found that hydrogen bond played a vital role in stabilizing the crystal structure of DMAM (M = Mn, Ni). [19] Additionally, Ma et al. found that the order-disorder phase transition of hydrogen bonds can be controlled by an external magnetic field in DMA-Co and DMA-Fe, respectively, as shown in Figure 10c,d. [45] Similarly, the ordering of hydrogen bonds plays a vital role in inducing the paraelectric to ferroelectric phase transition in multiferroic (NH 4 ) 2 [FeCl 5 (H 2 O)]. [77,78] Besides this, resonant quantum tunneling of magnetization which is well interpreted based on a selective long-distance super exchange model, has been observed in DMA-Fe (Figure 10e). This peculiar magnetic behavior is due to the exchange interaction between transition metal ions through an organic linker depends on the position of hydrogen bonds. [79] This work demonstrates that the magnetic structure strongly depend on the position of hydrogen bonds in multiferroic MOFs with the ABX 3 perovskite-like structure.
In addition to the DMA series, there is a class of B-site-doped DMA compounds that also exhibit interesting physical properties. For example, doping Cr 3+ in DMA-Mn can enhance the magnetism, provide an effective way for adjusting the magnetic properties of MOFs series through doping. [80,81] However, with the increase in the Cr 3+ doping level, the hydrogen bond network in this family will weaken and decrease the flexibility of the framework, which leads to a lower ferroelectric phase transition temperature, as well as phase transition diffusion. It is worth noting that this class of compounds can show optical characteristics by doping some specific elements, such as Cr and Eu. This feature gives rise to a series of potential modern device applications such as sensors, solid-state lightning devices, nonlinear optical devices, etc. In addition, EPR measurement results show that Cu 2+ is distributed unevenly in Cu-doped DMA-Zn. [82] Due to the JT effect of Cu 2+ , the framework structure near Cu 2+ is distorted, making the rotation of organic cations easier. This leads to a decrease in the temperature of structural phase transition. Based on the dielectric measurements, the doped samples are found that their cluster sizes are not uniform.
There are also some mixed-  6 ], [83] possessing the niccolite type structure, other than a perovskite one. Nevertheless, they also show interesting magnetic and luminescent properties. In addition, an interesting mixed valence compound [(DMA) 3 12 ], in which part of DMA + is replaced by a neutral molecule such as H 2 O, showing the modified multiferroic properties through removing the neutral molecule in the framework. [84] In addition, large pressure is an alternative way to modify multiferroic properties when chemical doping has reached its GPa. E = 700 kV m −1 was persistently applied to the sample in the poling process from above the ferroelectric transition temperature T c to low temperature. Reproduced with permission. [85] Copyright 2020, American Chemical Society.
tuning ceiling for MOFs. Yu et al. have investigated the pressure effect on the order-disorder ferroelectric transition in a hydrogen bonded DMA-Co. [85] The pressure suppressed the electric polarization accompanied by a transition temperature shift to a lower temperature before ferroelectricity disappeared at about 1.6 GPa, which is associated with the large distortion of the anionic framework (Figure 11). Subsequently, Zhou et al. found the multiferroic phase diagram of DMA-Ni under different pressures. [86] The change of multiferroicity was due to the pressure-modified magnetic superexchange interactions and long-range ferroelectric orderings (Figure 12a-c). Interestingly, due to the pressureenhanced spin-phonon coupling effect, the multiferroic phase region expanded to higher temperature in DMA-Ni (Figure 12d). This work provided an effective way to modify multiferroic properties when chemical doping has reached its tuning ceiling for perovskite-like MOFs.

[Gua]M(HCOO) 3
Gua series was first synthesized by Hu et al. [47] At present, all members with B-site transition metal ions have been successfully synthesized. The space group for this family is nonpolar Pnna, except for the Cu member with a polar Pna2 1 . Although ferroelectric behavior has been preliminary experimentally verified in Cu member, there is still some controversy for the mechanism. [49] Furthermore, all of the compounds did not undergo a structural transformation [47] (Figure 13a,b), which was related to the large number of hydrogen bonds formed between Gua + cation and the framework, which significantly stabilized the structure. In addition, both of these compounds with magnetic ions exhibit antiferromagnetism and weak ferromagnetism because of spincanting. Among them, the Cu member shows low dimensional magnetism with a significant distorted structure, due to the JT effect. It is noteworthy that the magnetoelectric coupling effect were observed in multiferroic Cu member. [47] Hu et al. discussed the magnetic properties of the perovskite Gua series in 2009. [47] As shown in Figure 13c, Mn, Fe, Co, Ni, and Cu members exhibit weak ferromagnetism, and their critical temperatures are 8.8, 10.0, 14.2, 34.2, and 4.6 K, respectively. [47,87] Among them, the Co member has a large canting angle, thus more magnetic than the other members. Furthermore, Cu member exhibit not only low-dimensional magnetism but also exhibit magnetic relaxation behavior. The abnormal characteristics of Cu member have attracted many scholars to conduct in-depth studies on them.
The magnetoelectric coexistence, which is supported by theoretical calculations and experiments for Cu member, is highly probable,. [48,49] The mutual verification of experiment and calculation fully demonstrates the magnetoelectric coexistence and coupling in Cu member. Moreover, the ferroelectric behavior of Cu member at near room temperature makes the material promising for application (Figure 14a,b). According to the experimental results, Gua-Cu, as a polar structure compound with no structural phase transition, exhibits ferroelectric characteristics below ≈280 K. As is known to all, the polar structure will lead to ferroelectric properties. However, Gua-Cu maintains the polar structure until decomposition but only exhibits ferroelectric behavior below 280 K. It is very worthy of further study whether thermal motion leads to the disorder of organic cation or there are other reasons. In addition, the compound has paramagnetoelectric (PME) effect, which is generally caused by magnetostriction or piezoelectric effect (Figure 14c). [88] The dielectric measurements performed on Cu member showed an abnormal peak at ≈5 K, which can be attributed to magnetostriction. [49] Although the ferroelectric behavior has been found in Cu member, its origin is unrevealed, like the similar improper ferroelectric behavior occurred in DMA series.

[MA]M(HCOO) 3
Perovskite MA series of compounds are the first reported organic-inorganic hybrid perovskite compounds where magnetic ordering-induced multiferroic behavior. So far, Mg, Mn, Fe, Co, Cu, Zn, and Cd members have been successfully synthesized, but most of the research is focused on Mn, Co, and Cu members. [24,51,52,89] Unlike the perovskite MOFs discussed previously, the determination of the space group of this series of compounds presents a major challenge. The structures of all members were identified as orthorhombic Pnma, which is characterized by XRD with a broad temperature scanning range of 100-300 K. [51] Later, Mazzuca and co-workers were the first to explore a low-temperature structural phase transition in Co member. [54] The neutron diffraction measurement was performed for the structure of Co member, where a hightemperature and low-temperature phases exist between two incommensurate phases. [55] These phase transitions directly affect the distortion of the framework and the hydrogen bond network, thus having a corresponding impact on the physical properties of Co member. It provides a powerful help for understanding its internal mechanism. According to previous experience, there are not many hydrogen bonds between MA + cations Figure 12. a) Normalized ac magnetic susceptibility as a function of temperature under different pressures. Here, the peak of normalized ' denotes the PM−AFM phase transition. The inset is the schematic illustration of the high-pressure ac magnetic susceptibility setup by using a mutual induction method. Reproduced with permission. [86] Copyright 2022, American Chemical Society. b) Electric polarization versus temperature at different pressures and c) corresponding pyroelectric current with a poling electric field of 500 kV m −1 . The electric field was applied perpendicular to the (012) plane. Reproduced with permission. [86] Copyright 2022, American Chemical Society. d) Temperature-pressure phase diagram of multiferroic DMA-Ni. Reproduced with permission. [86] Copyright 2022, American Chemical society. and anionic frameworks as the Gua series. So, the structure of MA-MOFs should be similar to the DMA + , Hyz + , NH 4 + series of compounds. We think there is more to explore for the lowtemperature structure of the perovskite MA-MOFs.
[MA]M(HCOO) 3 (M = Mn, Co, Ni, Cu) have been experimentally confirmed the existence of antiferromagnetism, but no further magnetic studies have been carried out for Fe member. [52] It is worth noting that magnetic ordering-induced multiferroic behavior has been verified by experiments for the first time for Co member, which aroused scholars to search for multiferroic materials in organic-inorganic hybrid perovskite compounds. As shown in Figure 15a,b, the Co member exhibits field-induced electric polarization in the external magnetic field, [53] but the magnetoelectric coupling is not significant in the absence of an external magnetic field. [54] In addition, Co member also exhibits a memory effect (Figure 15b), and their electric polarization is related to the previous two magnetic field pulses, which is similar to copper dimethyl sulfoxide dichloride. [90] These unique  magnetoelectric properties are of great benefit to the practical application of Co member. In addition to magnetic materials, dilute magnetic materials can be obtained by doping nonmagnetic metals into AMFF compounds. [89] A dilute magnetic system can make us a better study of spin dynamics, random field effect, and critical behavior and also provides a typical model for percolation problems. [91][92][93] In addition, dilute magnetic semiconductor materials have both semiconductor properties and magnetic properties, which may play an essential role in spintronic devices. [94][95][96][97] In AMFF system, doping magnetic or nonmagnetic metal ions has been widespread. The excellent tunable properties of perovskite materials enable us to synthesize more dilute magnetic materials. Another interesting magnetic compound, [MA]Cu(HCOO) 3 (MA-Cu), shows a sizeable structural distortion characteristic due to the JT activity of Cu + . Interestingly, Wang et al. found that defects induced the ferromagnetism in such quasi-1D antiferromagnetic chains. [98] The structural distortion of Cu member leads to quasi-1D, similar to the Cu containing AMMF compound in the aforementioned research. This effect can transform the banal antiferromagnetism into ferromagnetism, providing more possibilities in the practical application and helping us understand some peculiar magnetic phenomena in quasi-1D magnetic materials.
Interestingly, only the Co member in this family has exhibited magnetoelectric coupling effect. The ferroelectric properties of the other members have not been testified experimentally, but first-principles calculations predict ferroelectric behavior in some members. [99] Indeed, Co member exhibits antiferroelectric properties at 103 K (Figure 15c,d) with nonpolar structures below this temperature. [54] However, the structural phase transition process is complex, and it remains to be investigated whether the phase transitions inducing the electrical properties. For other members, the X-ray diffraction measurements are needed at lower temperature ranges to verify the similar situations as the Co member.

[Fmd]M(HCOO) 3
The Fmd family has been successfully synthesized, including Mn, Fe, Co, Cu, Zn, and Mg members, but there are few studies on their magnetic and electric properties. The most early study on Mg member was to investigate its gas storage capacity. [58] Subsequently, Mączka et al. successfully prepared three compounds, Mn, Fe, and Co members, and discussed their structure, magnetic and dielectric properties. [27] It is worth noting that only the Mn member in the current study shows structural phase transition. Its phase transition temperature is quite high because the organic cation forms a large number of hydrogen bonds with the framework, which greatly enhances the structural stability. Compared with the previous several perovskite MOFs, the related studies on the mulitferroic and magnetoelectric properties for Fmd series are rare. Our research group is carrying out further measurements and analyses on this perovskite formate family.
For magnetic properties of this family, Fmd-Mn, Fmd-Fe, and Fmd-Co members show antiferromagnetic ordering with the transition temperatures (T N ) 8, 13, and 17 K, respectively. Due to the DM effect, all three compounds exhibit weak ferromagnetism caused by a tiny canting of the underlying antiferromagnetic lattice, and the extremely insignificant hysteresis loop proves their weak ferromagnetism. [26] However, the multiferroic properties of Cu member have not been clearly verified.  [101] measured for increasing H || [101] at different temperatures. Reproduced with permission. [53] Copyright 2016, American Chemical Society. b) Raw magnetoelectric current, I ME , along [10-1] at 3.2 K for a series of positive and negative magnetic field pulses applied along [101], and which almost overlap in the case of the blue and black line. Reproduced with permission. [53] Copyright 2016, American Chemical Society c) Relative permittivity as a function of temperature (black curve on cooling and red curve on warming). The measurement was done on a pellet sample at 10 kHz, using an amplitude of 1 V. Reproduced with permission. [54] Copyright 2018, John Wiley and Sons. d) Temperature dependence of the dielectric loss of [CH 3 NH 3 ][Co(COOH) 3 ] compound, at zero magnetic field. Reproduced with permission. [54] Copyright 2018, John Wiley and Sons.
It is worthy to note that Fmd-Mn and Fmd-Co members may show multiferroicity which has been experiments so far. [26,28] As shown in Figure 16a, DSC results show that Mn member undergoes a structural phase transition at 355 K, and the structure changes from R_3c symmetry at high temperature to C2/c symmetry at low temperature. Furthermore, dielectric measurements indicate that this compound should be antiferroelectric for Fmd-Mn and Fmd-Co (Figure 16b-e), but more experimental evidence is needed to prove this mechanism. Interestingly, the structure of other compounds in this family is mostly Pnna, while the Mn member has a completely different structure, which needs further study.

[MHy]M(HCOO) 3
In the last 10 years, more and more metal-organic framework compounds have been reported. A series of metal-organic formate framework compounds linked to metal ions by formate ligands have been listed in the previous references, showing exciting multiferroic properties. More recently, the MHy series with metal formate framework compounds reported by Mączka et al. have also exhibited interesting multiferroic properties and structural phase transitions. This family has two structural phase transitions, which is quite rare among the compounds in question, like the previously reported azetidinium zinc formate. [66] The structure space groups of this series are respectively R_3c, R3c, and P1 in descending order with temperature, and these compounds exhibit ferroelectric behavior in intermediate and LT phases. In addition, Mn and Fe members exhibit magnetic ordering at 9 and 21 K, respectively.
The Mn and Fe members were successfully synthesized and exhibited ferromagnetism, which is also due to the spin-canting induced by the DM effect. [59] However, as shown in Figure 17a, the ZFC/FC curves of Fe member show an anomaly below the magnetic phase transition temperature, which is similar to the previously reported behavior in [DMA]Fe(HCOO) 3 (DMA-Fe). They may be caused by magnetron blocking of single-molecule magnets. [100,101] A stair-shaped hysteresis loop has been found in magnetization measurements of Fe member, which is one of the strong evidences for the hypothesis (Figure 17b-d). The magnetization of the Mn member at 2 K has a linear relationship with the strength of the external magnetic field, which fully demonstrates its weak ferromagnetism with almost no spin-canting angle.
All four compounds with M = Mg, Mn, Fe, and Zn, have exhibited two structural phase transitions. [85] DSC and change of  [26] Copyright 2014, The Authors, published by American Chemical Society. The real b) and imaginary c) part of the complex dielectric constant of Fmd-Mn at different frequencies. Inset shows the Arrhenius plot for the dielectric relaxation. Reproduced unter terms of the CC-BY license. [26] Copyrith 2014, The Authors, published by American Chemical Society. Temperature dependence of dielectric constant d), loss e) measured at different frequencies for Fmd-Co. Reproduced under terms of the CC-BY license. [28] Copyright 2017, the Authors, published by AIP Publishing. entropy measurements are consistent, and two abnormal peaks in DSC indicate that the compounds have two structural phase transitions, as presented in Figure 17e,g,h. With the decrease in temperature, the first phase transition temperature was 310-327 K, and the results of pyroelectric measurements showed the appearance of the ferroelectric phase ( Figure 17f). Simultaneously, the space group of compounds changed from R_3c to polar R3c. This change in structural symmetry is related to the degree of order of the MHy + cation, which is partially ordered in the R3c phase, resulting in electric polarization. When the temperature is further decreased, the motion of MHy + becomes sluggish with further ordering. Meanwhile, the framework is also affected and begins to deform. The space group of the low-temperature phase is identified as P1. It is worth noting that the experimentally measured entropy change is much smaller than expected, indicating the relaxor nature of the phase transition, so they can be regarded as relaxation ferroelectric. Moreover, the feature exhibiting ferroelectric properties at room temperature makes them potentially applicable. However, further studies of Zn member did not yield the desired electrical hysteresis loops. [60,61] Because a higher electric field would breakdown the sample, and the polarization could only be measured at a low electric field. However, the low electric field was insufficient for the sample to exhibit an electric hysteresis loop. [60] Although the absence of hysteresis loops does not deny the ferroelectric properties of Zn member, the vulnerability to electrical breakdown also limits its application.
In addition to a temperature-induced structural phase transition, a reversible structural phase transition caused by pressure was also confirmed in Mn member. High-pressure Raman scattering studies of Mn member show that a phase transition occurs between 4.8 and 5.5 GPa, with the change of the metal formate framework and MHy + structure. [59] It is worth mentioning that pressure has become an effective tool to tune the structure and subsequently magnetic and electric properties of perovskite MOFs. [102][103][104][105][106][107] In particular, ferroelectric properties are sensitive to external pressures, which provides a new idea for the application in novel electronic devices. [40] In addition, a kind of organo-inorganic hybrid perovskite compound with hypophosphate as a bridging ligand was reported. [108] Unlike formate, Hypophosphites can form different hydrogen bonds for the framework, which makes the structure of the compound more distorted and off-center of MHy + , which enable them as potential candidates for ferroelectrics.  and field-cooling (FC, closed symbols) regimes in various magnetic fields; for the sake of clarity, the experimental curves were multiplied by the factors indicated on the right side. Solid lines serve as guides for the eye, and the arrows mark the ordering temperature Tm and the blocking temperature Tb; Magnetization (M) of MHy-Fe as a function of H measured at various, b) 2 K, c) 10 K, and d) 25 K temperatures upon increasing and decreasing fields (open and closed symbols, respectively); thin solid lines and arrows serve as guides for the eye; thick solid lines display ΔM, which is the magnetization after subtraction of the linear component. e) DSC traces for the prepared samples in heating and cooling modes. f) Pyroelectric current as a function of temperature after poling [MHy]Mn(HCOO) 3 (MHy-Mn) from 350 to 150 K with ±2 kV cm −1 , during heating with the temperature rate of 1 K min −1 . The inset shows the estimated change of the spontaneous polarization of the polycrystalline sample as a function of temperature; Change in (g) C p and (h) S related to the phase transitions in the studied compounds. Reproduced with permission. [59] Copyright 2017, American Chemical Society.

[BTBA][M(dca) 3 ] and [BTEA][M(dca) 3 ]
The coordination polymer is affected by many factors. XRD measurements at room temperature showed that they were all isomorphic and orthorhombic (space group Pnma). It is worth noting that the -Po framework cannot be obtained if organic cations with smaller sizes are replaced. By using other cations (such as Ph 4 P + , Ph 4 As + , MePh 3 P + or [M(2,2'-bpy) 3 ] 2 + ), some other structures can be obtained. [110][111][112] This fully shows that the selection of organic cations plays a crucial role in forming the [M(dca) 3 ] − network. In addition, these compounds also exhibit antiferromagnetic order, and their ferroic properties are worthy of further study.

(SPh 3 )Mn(dca) 3
After these prior works, Schlueter et al. chose triphenylsulfonium (SPh 3 + , Ph = Phenyl) cation as a template to synthesize a new compound with a 3D [M(dca) 3 ] − structure, in order to further study the magnetic superexchange interactions of the [M(dca) 3 ] − Figure 18. a) Temperature dependence of T measured in a dc field of 1 kOe for a polycrystalline sample of (SPh 3 )Mn(dca) 3 . The solid line illustrates the fit of the data to a Heisenberg 3D AFM model. b) Real or in-phase ( ') and imaginary or out-of-phase ( "") components of the ac susceptibility of a polycrystalline sample of (SPh 3 )Mn(dca) 3 as a function of temperature, measured in an oscillating field of amplitude H ac = 2 Oe and frequency f = 125 Hz. Reproduced with permission. [113] Copyright 2004, American Chemical Society.
network. [113] This compound also has the -Po structure, but its space group is P2 1 /c at room temperature. In addition, it also exhibits antiferromagnetic order at temperatures below 2.5 K. As shown in Figure 18a, the value of T drops rapidly around 2 K, indicating a long-range antiferromagnetic phase transition in the compound. In Figure 18b, the real and imaginary parts of the ac susceptibility show a sharp peak at T = 2.5 K, indicating the noncollinear antiferromagnetism of the compound.

[TPrA][M(dca) 3 ]
In general, in the previously studied organic-inorganic hybrid perovskite materials, magnetic coupling is generally provided by magnetic metal ions in octahedral, and the organic cations in frame cavities cause ferroelectric polarization. Interestingly, MOFs with [M(dca) 3 ] − networks have been studied extensively in the past few decades, with some interesting results reported by Bermúdez-García et al. [114] The most interesting is that the coexistence of ferroelectric and ferromagnetic properties were found in TPrA (TPrA = tetrapropylammonium, [(CH 3 CH 2 CH 2 ) 4 N] + ) series compounds.
First, it should be emphasized that the TPrA cation is nonpolar and cannot form hydrogen bonds with the framework, so the dielectric response mechanism, which is related to the off-shift of organic cations and the order-disorder process of dicyandiamide ligands, is entirely different from that in the aforementioned multiferroic MOFs. This provides a novel mechanism for the magnetoelectric properties for this family. Then, the phase transition process of Mn member [114] is significantly different from that of Fe, Co, and Ni members. [115] Only one phase transition (T C = 330 K) is observed for the Mn member, but three phase transitions occur in the temperature range of ≈210≈360 K for the other three members. Correspondingly, the permittivity also undergoes three transitions, as shown in Figure 19a-c. In contrast, the Cd member undergoes structural phase transition at 228, 241, 362, and 386 K, respectively, corresponding to the four anomaly peaks in Figure 19d, which indicates that the framework of [TPrA][Cd(dca) 3 ] (TPrA-Cd) has higher flexibility. [116] Meanwhile, its dielectric properties also appear four turns accordingly. It is worth noting that TPrA-Cd can maintain a 2D layered structure at room temperature and irreversibly transform into a 3D perovskite structure at ≈380 K, which is presented in Figure 19e. [117] In addition to the dielectric properties, this family exhibits multiple sensitivity to both temperature and pressure, [114] which makes them potentially useful in the field of temperature/pressure sensors.

Recently, He et al. synthesized a new 3D molecular perovskite
. [118] Unexpectedly, a noncentrosymmetric structure was obtained from two centrosymmetric structure materials. [119] The physical properties have been strengthened in many aspects for these mixed-phase materials, which provides a new route to design multifunctional molecular materials.
For [(EPCF) x (EPCCl) 1−x ][Mn(dca) 3 ], the chiral phase P2 1 2 1 2 1 is generated and has an SHG response when x = ≈0.170-0.405. [118] Notably, when x = 0.230, the spontaneous strain of the ferroelastic increased by 50% (0.021) and the Curie temperature increased from 2.4 to 4.0 K (Figure 20), compared to the parent material [EPCF][Mn(dca) 3 ]. [120] This work reflects the great application potential for this family. The solid solution method, which can modulate material properties, providing a novel way to synthesize noncentrosymmetric chiral compounds without the common synthesis method by using centrosymmetric compounds. This has laid a good foundation for ferroelectric properties, and we may be able to synthesize multifunctional materials with ferroelectric properties in this new route.
The dicyandiamide framework of these compounds shows the coexistence of polar and magnetic order. It should be noted that these compounds can dehydrate in the temperature range of Figure 19. Temperature dependence of the dielectric constant ( r') of the a) Fe, b) Co, and c) Ni compounds measured at different frequencies (105)(106). Reproduced under terms of the CC-BY license. [115] Copyright 2016, The Authors, published by Royal Society of Chemistry. d) Change in Cp related to the phase transitions in TPrA-Cd. Reproduced with permission. [116] Copyright 2019, Royal Society of Chemistry. e) TPrA-Cd transformation in the reconstructive phase transition from the layered to the perovskite-like crystal structure. Reproduced with permission. [117] Copyright 2018, Royal Society of Chemistry.
350-380 K. However, the SHG signal intensity of dehydrated and undehydrated compounds is significantly different, and the SHG response of anhydrous BeTriMe[Mn(dca) 3 ] (BeTriMe-Mn) is about four times smaller than that of hydrated analogs, as shown in Figure 21b. Anhydrous BeTriMe-Mn can absorb water in the air, thereby gradually increasing its SHG response to hydrate analogue levels. This process is irreversible and can remain stable for several days. This property can be used as a remote nonlinear optical marker to count whether the materials have ever reached the threshold temperature. In contrast to linear optics, this method is more difficult to fake.

[DMA][Cd(N 3 ) 3 ]
In ABX 3 -type MOFs materials, organic and inorganic hybrid perovskite materials are a large branch. Popularly, the Xsite anion could choose the halogen, CN − and HCOO − anions. The length of these anions is relatively small, and organic cations rather than frameworks usually induce the structural phase transition for such compounds. However, the length of N 3 − is longer, and it participates in structural phase transitions and makes the framework more flexible, similar to the dicyandiamide ligand. [122][123][124][125][126][127] There is also a longer  [120] Copyright 2019, John Wiley and Sons. c) The zero field cooling (ZFC)/field cooling (FC) susceptibilities for the composition (x = 0.230) under an applied field of 30 Oe. Reproduced with permission. [118] Copyright 2021, Royal Society of Chemistry. Figure 21. a) The crystal structure of BeTriMe-Mn is built of 2D Mn-dca layers; the coordinated water acts as a linker, joining neighboring sheets through HB interactions. The Mn center is octahedrally coordinated. The red dashed lines denote hydrogen bonds, and the black long dashed lines stand for water coordinate bonds. Reproduced with permission. [121] Copyright 2020, Royal Society of Chemistry. b) Plots of integral intensity of the SHG signal of BeTriMe-Mn for heating and cooling runs. Reproduced with permission. [121] Copyright 2020, Royal Society of Chemistry.  [128,129] The solvated Ag compound has the inclination of adjacent octahedral perpendicular to the rotation axis, which is not found in traditional perovskite compounds. This behavior indicates that the system has excellent framework flexibility, similar to the situation in the dicyanamide hybrid organic-inorganic perovskite compound. It makes sense that a longer bridge ligand would build a larger framework, but the larger framework would soften the structure, allowing the molecules inside to be freer.
[DMA][Cd(N 3 ) 3 ] is a hybrid perovskite compound synthesized by N 3 − ligand. It exhibits a reversible ferroelastic phase transition, which is caused by the deformation of the [Cd(N 3 ) 3 ] − framework. [130] Interestingly, dielectric relaxation was found in both the ferroelastic and paraelastic phases of the compound (Figure 22). Due to the deformation of the framework, the or-ganic cations have cooperative movement, which is the essential reason for the change in the dielectric properties. With the help of this system, we may further understand the dynamics of organic cations in confined space. Similarly, this mechanism has been found in [TMA][M(N 3 ) 3 ] (TMA = trimethylammonium, (CH 3 ) 3 NH + ), which may provide a new way to find controllable dielectric materials. [131]
respectively. [133] This result indicates that the desired multiferroic materials could be found in the system.
In recent years, azide ions have played an important role in coordination polymers and constructing a variety of 1D, [134][135][136][137][138] 2D, [139] and 3D [140] compounds, showing many interesting physical properties. As a bridging ligand, the ion has two bridging modes, end-to-end (EE) and end-to-on (EO). The coexistence of two modes was found in [TeMA][Cu(N 3 ) 3 ] (TeMA-Cu), making TeMA-Cu a 1D structure. [133] This is an infrequent phenomenon. On the other hand, as an isomorphism, [TeMA][Mn(N 3 ) 3 ] (TeMA-Mn) possesses a 3D structure, and the bridge between Mn + ions is in the EE mode. [133] It is worth mentioning that the bridging mode may affect the magnetic properties for this family, and antiferromagnetism and ferromagnetism are usually related to EE and EO bridging modes, respectively. [133] Both compounds exhibit antiferromagnetism, meanwhile TeMA-Mn also exhibits a structural phase transition at 310 K. [141] The nature of this transition is due to a variety of reasons, including rotation of the [MnN 6 ] octahedron and order-disorder transition of azide ions and organic cations, as well as the offcenter shift of organic cations. In addition, antiparallel dipoles in TeMA-Mn were also observed at low temperatures, according to DFT calculations. In the dielectric measurement, an anomaly occurred at ≈310 K, which may be caused by the transformation of the AFE phase into the PE phase. More interesting is that unusual anisotropic thermal expansion was found in TeMA-Mn, indicating that the compound is ferroelastic. [141] Moreover, the phase transition, which is accompanied by a significant entropy change (≈80 J K −1 kg −1 ), [142] indicating that it has giant barocaloric effects and can be used as an excellent cooling material. Taken together, combined with three ferroic properties simultaneously, this family is a fairly rare example and provides a good template for our search for perovskite multiferroic materials.
Another analogue, [TeMA][Cd(N 3 ) 3 ] (TeMA-Cd), also shows interesting ferroelasticity. [122] It undergoes three phase transitions, and abnormal peaks corresponding to the three-phase transitions can be clearly seen through DSC measurement results, as shown in Figure 23. These phase transitions are related to the dynamics of azide ions and organic cations. In the process of phase tran-sition, the symmetric element decreased from 48 to 4, which is judged to be a ferroelastic phase transition. However, other ferroic properties of this compound have not been studied. It is known that Mn member has the coexistence of three ferroic orders, which is possible found in Cd member because they possess the similar structure and phase transitions.

Halogen Perovskite Compounds Promising for Perovskite Solar Cells
After decades of development, the types of perovskite materials have been developed in a spurt. In addition to the perovskite compounds in the aforementioned research, halogen perovskite compounds also show many interesting physical properties and applications. In 2009, Kojima et al. applied MAPbI 3 as candidate for solar cells and achieved a photoelectric conversion efficiency of 3.8%. [32] Since then, the new star of perovskite solar cells has risen and triggered extensive research worldwide. MA series of perovskite compounds containing iodine is a direct bandgap semiconductor, in which the forbidden bandwidth is 1.55 eV. In fact, the forbidden bandwidth can be modified by the replacement of X-site using the halogen for this series of ABX 3 -type compounds. [143][144][145][146][147] Subsequently, it was found that doping of Cs + can also improve the stability and efficiency of perovskite solar cells. [148,149] Over time, more and more regulation methods are applied in this field to update the photoelectric conversion efficiency for perovskite solar cells constantly. In 2004, FmdPbI 3 was found to have higher absorption strength than MAPbI 3 outside the infrared light region, [150] which means that this material has potential application for solar cells, while it has trigonal and hexagonal crystal systems at room temperature, which is the defect of this material.

Conclusion and Outlook
Benefitting from the robust responses to magnetic, electric, mechanical, and optical fields, multifunctional perovskite MOFs materials have potential applications in manufacturing new functional devices, such as electrochemical energy storage. The multiferroicity and magnetoelectric effects in MOFs with the perovskite ABX 3 architecture has recently attracted much attention. Being the largest subclass of these multiferroic MOFs, the formate family has some important advantages: 1) Formic acid is relatively safe, and the pollution and danger caused by synthesis are low, which enable this system as potential Eco-friendly materials for many application; 2) As a polyatomic bridging ligand, formate ion has a longer molecular size than halogens and other mono-atomic ligands, resulting in a larger metallic formate framework, which can accommodate larger inlaid organic cations at the cavity; 3) Formate ion carries two oxygen atoms, which can form strong and considerable hydrogen bonds with A-site organic cations, making the physical properties of the framework even more interesting.
The mainly discussed compound of the formate family in this review, AMFF, wherein NH 4 + with the smallest size of organic cation, has a unique chiral perovskite structure. Interestingly, the NH 3 OH + family also exhibits similar structural features with the www.advancedsciencenews.com www.advmatinterfaces.de similar-sized NH 4 + , while organic cations with larger sizes in AMFF, such as DMA + , Gua + , etc., are all perovskite structures. Medium-sized Hyz series compounds show the feature of coexistence of the chiral phase and perovskite. These results reveal that the size of organic cation is related to the chiral properties of the perovskite structure. It is more likely to obtain the chiral perovskite structure when the intrinsic size of A-site group is smaller. In addition, the syn-anti mode was found in [NH 4 ]Cd family, which is very rare in AMFF. Cd 2+ has a large ionic radius, and the addition of Cd makes the tolerance factor of [NH 4 ]Cd smaller, indicating the structural instability of the compound. However, the experimental results show that it remains stable above room temperature. Therefore, the existence of the syn-anti mode promotes the structure to be more stable for this family. This enables people to synthesize stable multiferroic MOFs with perovskite structure by considering the bridging mode between metal ions.
On the other hand, most of AMFF compounds exhibit electrically related properties, and the ferroelectric polarization is directly related to the order of organic cations. It is worth noting that Maczka et al. proposed very different opinions on the electrical properties of DMA-Zn, and experimentally proved that it was an improper ferroelectric. This is the only case in AMFF that the origin of ferroelectric requires further investigation. Based on this, we can further to study the internal mechanism of this nonintrinsic ferroelectric behavior in this family.
In addition, we present the multiferroicity in nonformate metal perovskite MOFs. Among them, the nature of the perovskite formed by dicyandiamide and azide ions is striking. Due to the longer molecular lengths compared to that of formate, they have a more flexible framework. It should be noted that the ferroelectric properties of these compounds are directly related to the deformation of the framework, and the deformation of the framework and the movement of the cation are the main reasons for the structural phase transition. However, they also have some drawbacks, namely, the strength of coupling effects between magnetic ions are relatively weak, and their magnetic ordering temperatures are mostly only a few Kelvin. Surprisingly, three ferroic orders are found in TeMA-Mn, a rare example that provides a good template for the study of perovskite multiferroic materials.
The physics underpinning the aforementioned phenomena involves the intricate interplay of polarization with geometric coordination, electron correlation, and spin state under either static or dynamic conditions. Towards building a clearer structureproperty relationship and maximizing performance of multiferroic MOFs with the ABX 3 perovskite-like structure, several potential topics for carrying out multiferroicity research are generalized as follows.
1) Improve the structural stability and enhance the magnetic ordering temperatures. From the perspective of physical significance and device application, the structural stability and higher magnetic phase transition temperature in perovskite multiferroic MOFs is needed to be fully explored. The template effect of organic cations and tolerance factors are the key factors for designing new crystal structures of MOFs. On the other hand, for most reported multiferroic MOFs materials, low magnetic ordering temperatures have been cen-tral obstacles in deep research of magnetism. It is essential to address this issue by discovering more perovskite magnetic members. In comparison with the extensively studied MOFs magnets with 3d electrons, the rare-earth system with 4f electrons may provide much stronger spin-orbit coupling and much larger local magnetic moment, which may supply more possibilities for enhancing magnetism and dealing with the above problem. In addition to that, when chemical doping has reached its tuning ceiling, high pressure is an alternative route to manipulate the magnetic superexchange interaction between magnetic ions at B-site through targeted adjustments to the positioning of hydrogen bonding. 2) Low dimensional magnetism in ABX 3 -type multiferroic MOFs. From the viewpoint of magnetic states, there are more than 1000 magnetic space groups to describe bulk magnetic structures, which is far more extensive than space groups. Therefore, the exploration of in-depth intrinsic magnetism is very complicated but essential. In particular, the JT effect, which makes the oxygen octahedron significantly distorted, gives rise to the quasi-1D magnetism without exception in some Cu members of multiferroic MOFs. Thus, quantitative characterization with nanometer spatial resolution is in demand and is expected to acquire an in-depth investigating of low dimensional magnetism in multiferroic MOFs. Moreover, some novel and sophisticated techniques for in situ detection, like quantum magnetic imaging technique based on nitrogen-vacancy center, need to be developed to measure the complicated magnetic properties directly. 3) External effects on modifying the multiferroic properties of MOFs. Combined with external fields and pressure effect, the multiferroic properties of MOFs can be further modulated.
Interestingly, magnetoelectric switching based on MOFs, which allows the reversal of the magnetization direction with an electric field or flipping of the electric polarization with an applied magnetic field, is much less understood and is difficult to realize owing to different symmetry properties of the ferroelectric and magnetic orders. Moreover, pressure can drive spin reorientation transition in MOFs magnetic compounds, which is discussed and could become a dramatic topic in the future. In addition, to our knowledge, magnetoelectric and magnetoelastic coupling at higher fields are wholly unexplored, this process made it more intriguing by the presence of a field dependent magnetoelectric coupling mechanism in perovskite MOFs.
In general, the ABX 3 -type perovskite-like MOFs with porous structure and diverse composition can be used as a highly versatile and tunable platform for exploring new functionalities, especially in magnetism, ferroelectricity (antiferroelectricity), multiferroicity, and magnetoelectricity. There are still many challenges in the preparation and application of intrinsically multiferroic MOFs, but we believe that further development will provide more opportunities for the application of multiferroic MOFs for the highly integrated electronic and spintronic devices in digital information manipulation and storage technologies, including lowpower nonvolatile random-access memories.