Chemical perspectives on heteroanionic compounds: a potential playground for multiferroics

Abstract

Heteroanionic compounds, which host two or more different anions, have emerged as a huge family of functional materials. Different from polyanionic compounds, there is no direct connection between anions within heteroanionic compounds. The connectivity between anions and central atoms constitutes various distorted basic building units (BBUs). The linkage between BBUs further promotes the structural flexibility of heteroanionic compounds. The diverse bonding modes of anion–metal interactions, which originate from the various physical and chemical properties of anions, explain the existence of many important applications of heteroanionic compounds. In this short review, we summarize the synthesis, structures, and physical applications of selected heteroanionic compounds. From a synthesis perspective, a deep understanding of crystal growth mechanisms and a better controlled growth process should be emphasized in future research. The interactions between distinct anions and other featured elements such as elements with lone electron pairs, d⁰ and d¹⁰ transition metals, etc., or other systems such as high entropy systems would further promote more interesting applications. Heteroanionic compounds that exhibit comparable structural features with known multiferroics might be new frameworks for discovering multiferroics. Machine learning and quickly developed calculation capabilities can also aid the study of heteroanionic compounds by understanding growth mechanisms, searching for new compounds, and targeting specific properties.

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Karishma Prasad

Karishma Prasad completed her Master's degree at Goa University, India, in 2019. Following her graduation, she served as an Assistant Professor of Chemistry at Government College Khandola, India. Currently, she is pursuing her PhD at Wichita State University, US, under the guidance of Prof. Jian Wang. Her research interests include two dimensional (2D) magnetic quantum materials.

Vivian Nguyen

Vivian Nguyen is a master's student at Wichita State University. She obtained her bachelor's degree from Wichita State University in Chemistry. She began her research during her undergraduate years working on solid-state nonlinear optical materials with Dr Jian Wang. Her current research interests include crystal growth methods of 2-dimensional polymorphs of metastable transition metal chalcogenides and mixed-metal thiocyanates.

Bingheng Ji

Bingheng Ji is currently pursuing her PhD in Chemistry at Wichita State University, where her research focuses on nonlinear optical materials. She earned her Bachelor of Science degree in Chemistry from Iowa State University in 2019. Her academic interest is the study of semiconductor systems including design and discovery of functional materials and understanding structure–property relationship.

Jasmine Quah

Jasmine Quah is currently a graduate student at the University of Wisconsin Madison pursuing a doctorate in Pharmaceutical Sciences. While in her time at Wichita State University during her Bachelor's of Science in Chemistry and gap year, she focused on the synthesis and analysis of heteroanionic materials, 2-D Dirac quantum materials, and compounds with nonlinear optical properties. Alongside research at WSU, she has worked as a nuclear lab technician, producing radioactive PET imaging drugs for distribution to hospitals around the midwest. She now aims to conduct research in the pharmaceutical field to advance medicine, treatments, and technology.

Danielle Goodwin

Danielle Goodwin obtained her dual Bachelor's degree in Biochemistry and Biological Sciences from Wichita State University. While studying at WSU, she was awarded the ACS Division of Analytical Chemistry Undergraduate Award 2023 and the ACS Division of Inorganic Chemistry Undergraduate Award 2024. She conducted research in the Wang lab during her senior year, focusing on investigation of semiconducting materials and compounds with anisotropic magnetic properties. Goodwin is in her medical school application process, aspiring to advance her knowledge in medicine through research and lectures.

Jian Wang

Jian Wang earned his BS in Materials Science and Engineering from the Changchun University of Science and Technology. His interest in inorganic functional materials led him to pursue a PhD at the State Key Laboratory of Crystal Materials, Shandong University, where he studied from 2008 to 2013. Following his PhD, he completed his postdoctoral training at UC Davis and Iowa State University. In 2019, he joined Wichita State University. His research lab focuses on discovering new inorganic materials, including nonlinear optical materials, 2D metastable phases, 2D magnets, multiferroics, etc.

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1. Introduction

Heteroanionic compounds, which constitute two or more different anions, have attracted growing interest due to their chemical flexibility.^1–15 The chemical flexibility originates from structural flexibility due to the presence of multiple anions. The chemical properties of common anions are tabulated in Table 1. From a structural perspective, the incorporation of two or three distinct anions naturally introduces the probability of intriguing structures plus the flexible connectivity of distinct anions to central metals. The first aspect of flexibility comes from the different chemical properties of anions, such as the ionic radius, electronegativity, oxidation state, charge density, etc., which are shown in Table 1. The distinct anions connect to identical atoms or different atoms with comparable or different chemical bonding modes. Selected compounds are shown in Fig. 1 to elucidate the fundamental building units and bonding modes of heteroanionic compounds. A good example would be Na₃PO_yS_z. As shown in Fig. 1a–c, three units [POS₃], [PO₂S₂], and [PO₃S] act as the major building units of Na₃POS₃,¹⁶ Na₃PO₂S₂,¹⁷ and Na₃PO₃S,¹⁸ respectively. The flexible [PO_yS_z] units account for the structural difference (centrosymmetric vs. noncentrosymmetric) and exotic optical properties of this system.^19–21 The connectivity of different anions to the central metals raises the first degree of freedom of chemical flexibility of heteroanionic compounds. The ordering and tilting of heteroanionic units add additional degrees of freedom to these compounds.^4,22 The variable bond distance increases the distortion of basic building units as shown in Fig. 1d. The La–Br bonds are much longer than the La–O bonds of [LaO₆Br₃] units in LaBrWO₄.^13,23 In addition to the obvious bond length difference, the bonding modes of La–O interactions and La–Br interactions are clearly distinguishable. As shown in Fig. 1e and f, the ICOHP of La–Br interactions is slightly bigger than that of La–O interactions even though the La–O interactions are much shorter than La–Br interactions. The ELF simulations indicate the ionic nature of both La–Br interactions and La–O interactions with the absence of ELF maxima within two adjacent atoms. The ELF maximum around Br is spherical, while the ELF maximum around O is not, as O atoms have a higher electronegativity than Br atoms with smaller sizes. The charge density of O is almost double that of Br as shown in Table 1. Heteroanionic compounds combine all these chemical and structural features in a single lattice, which explains the fantastic physical properties of heteroanionic compounds.

Table 1 Chemical properties of selected anions²⁴

	N	P	O	S	Se	F	Cl	Br	I
Atomic number	7	15	8	16	34	9	17	35	53
Melting point/°C	−210	44	−218	112	217	−220	−101	−7.3	114
Ionic radius/Shannon-Prewitt, Å (C.N.)	1.32(4)	2.12(6)^25	1.26(6)	1.70(6)	1.84(6)	1.19(6)	1.67(6)	1.82(6)	2.06(6)
Electronegativity (Pauling)	3.0	2.1	3.5	2.5	2.4	4.0	3.0	2.8	2.5
Electron affinity/kJ mol^−1	0	−72	−141	−200	−195	−328	−349	−325	−295
Oxidation states (as anions)	−3	−3	−2	−2	−2	−1	−1	−1	−1
Charge density/unit charge/Å	2.27	1.42	1.59	1.18	1.09	0.84	0.60	0.55	0.49

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Fig. 1 (a)–(c) [POS₃] in Na₃POS₃ (Cmc2₁),¹⁶ [PO₂S₂] in Na₃PO₂S₂ (Pbca),¹⁷ and [PO₃S] in Na₃PO₃S (R3c),¹⁸ P: light blue, O: red, S: black; (d) [LaO₆S₃] units in LaBrMoO₄;^13,23 (e) crystal orbital Hamilton population (COHP) analysis of selected La–O and La–Br interactions; and (f) electron localization function (ELF) of LaBrWO₄ with η = 0.6, La: green, O: red, Br: brown.

Heteroanionic compounds are different from polyanionic compounds, where there are anion–anion interactions existing within polyanionic clusters such as polyanionic [AsO₄]³⁻.^2,5,26–31 Heteroanionic compounds do not have direct anion–anion interactions. Heteroanionic compounds can be categorized into two major groups: disordered heteroanionic compounds and ordered heteroanionic compounds. The disordered heteroanionic compounds refer to compounds having two or more anions jointly occupying the same atomic position, such as Cd(SeTe),³² SnO₂:F,³³ and LaFeAsO_1−xF_x.³⁴ The distinct anions occupy independent atomic positions within the ordered heteroanionic compounds such as Na₃MoOF₃,³⁵ LaGaOS₂,³⁶ KBe₂BO₃F₂,³⁷ BiCuSeO,³⁸ CeZnSbO,³⁹etc. The different properties of various anions existing within one crystal lattice greatly enhance the structural flexibility of the heteroanionic compounds. The boundary of heteroanionic compounds was further extended recently via inserting H or C into known compounds such as NdScSiC_x⁴⁰ and CeTiGeH_x.⁴¹ Furthermore, when heteroanionic building units interact with high entropy counterparts, high entropy heteroanionic compounds would be formed as a new functional material family.⁴² Heteroanionic compounds have many emerging physical properties, including nonlinear optical (NLO) properties,^37,43–49 superconducting properties,^34,50–52 photoluminescent response,^53–61 thermoelectric properties,^26,27,62etc.

Hence, in this review, we plan to summarize the synthesis process and structural chemistry of many selected heteroanionic compounds. Important physical properties, such as nonlinear optical (NLO) properties, superconducting properties, photoluminescence response, and thermoelectric properties, were also summarized in this work. We hope to find some linkage from structural chemistry to the physical properties of heteroanionic compounds. We also want to provide an entry-level introduction to any researchers who are wanting to start to work on heteroanionic compounds. Many excellent review articles have been published recently to summarize various chemical properties of heteroanionic compounds.^{1,2,6,63–69} This review briefly summarizes the synthesis, structural chemistry, and potential applications of heteroanionic compounds as multiferroics.

2. Synthesis perspectives on heteroanionic compounds

Functionality arises from synthesis. The presence of more than one anion introduces structural flexibility into target systems while presenting more challenges for synthesis. One challenge is combining various anions within a single crystalline lattice using different sources of anions. Using the synthesis of oxyhalides as an example, it is found that oxides are a good source of oxygen anions. Sometimes carbonates can also be utilized as a source of oxides while taking into consideration of the presence of CO₂. Halides are commonly employed to supply halogen anions. The distinct properties of oxides and halides, such as melting temperature, vapor pressure, reactivity, etc., raise the difficulty of the synthesis process. Another difficulty in synthesizing heteroanionic compounds would be how to control the anion ratios within a single crystalline lattice, which is much harder. The anion ratios are some of the key components of the chemical properties of heteroanionic compounds. The growth of high-quality crystals of heteroanionic compounds is also not easy. The presence of distinct anions raises the difficulty of crystal growth. Hence, during the search for various heteroanionic compounds, many synthetic techniques were employed to target heteroanionic compounds. In this section, common synthetic methods of heteroanionic compounds are summarized.

2.1 Hydrothermal/solvothermal methods

Heating up media, which are used in solvothermal reactions that utilize solvents such as water, alcohol, HF, etc., above their boiling point would generate a high-pressure environment. The presence of high pressure would enhance the solubility of many reactants such as oxides, which have limited solubility in many solvents under ambient conditions. In addition to increasing the solubility and reactivity of reactants, a solvothermal reaction will benefit the crystal growth and the formation of heteroanionic compounds by controlling the temperature, pressure, reactants, type of media, etc. Hence, hydrothermal/solvothermal reactions are widely employed to synthesize heteroanionic compounds. In Table S1 (ESI†),^70–74 some selected compounds represent the heteroanionic compounds synthesized by hydrothermal/solvothermal reactions. The broad applications of hydrothermal/solvothermal synthesis routes to synthesize heteroanionic compounds are also due to their capability of accessing metastable phases, which can be key for preparing heteroanionic compounds.^75,76

2.2 High temperature flux methods

Flux methods were widely employed to form inorganic solids, which can increase the contacting surface areas and improve the diffusion rates.⁷⁷ In addition to promoting chemical reactions, flux can also act as a reactant. For example, halide flux pairs usually have low eutectic temperatures, which are also good sources of halogen anions and flux. Oxides also commonly play a dual role of acting as fluxes and sources of oxygen. Many factors should be considered, such as solubility, inertness, melting temperature, toxicity, reaction vessel, price, etc., when choosing a flux.⁷⁸ We tabulated a few selected heteroanionic compounds in Table S2 (ESI†),^79–83 which were synthesized by flux methods.⁸⁴

2.3 High temperature solid state methods

High temperature solid state reactions are popular methods to synthesize heteroanionic compounds. Solid state reactions have less chance of incorporating foreign elements compared to other methods. The selection of reactants is important for solid state reactions. Binary or ternary compounds made up of two or three different elements, respectively, would dramatically affect final products due to the distinct properties of these reactants and different kinetic processes. The presence of low-melting reactants or reactants in small particle form would help speed up solid state reactions. One factor, which should be considered, would be the containers of solid state reactions. Regular containers such as quartz tubes or carbonized quartz tubes do not tolerate high pressure. In the case of high pressure, sealed metal tubes such as tantalum tubes or niobium tubes would be a good choice. To further prevent possible contamination from metal tubes, a carbon crucible can be used. Sealing carbon crucibles in metal tubes with the protection of a quartz jacket can solve some problems. The sealed environment can efficiently prevent the oxidation of target compounds such as synthesizing oxychalcogenides. In this section, selected heteroanionic compounds synthesized by the solid state method are summarized and are shown in Table S3 (ESI†).^85–89 In Table S3 (ESI†), some compounds are selected to represent the heteroanionic compounds synthesized by high temperature solid state methods.

2.4 Other methods and perspectives

Other methods can also be utilized to synthesize heteroanionic compounds, such as chemical vapor transport (CVT).⁹⁰ The CVT process usually involves chemicals with high vapor pressure. Extreme conditions such as high pressure synthesis were also utilized to synthesize heteroanionic compounds such as A₂NiO₂Ag₂Se₂ (A = Sr, Ba) (7 GPa at 850 °C)⁹¹ and La₂B₂O₅(OH)₂ (30 GPa and ∼2127 °C).⁹² Extreme conditions expand the synthesis boundary from the abovementioned methods. The topochemical reaction is also efficient to synthesize certain groups of heteroanionic compounds.^93–95 To gain a better understanding of the synthesis and crystal growth process of heteroanionic compounds, an in situ study would be a powerful tool.²⁶ The rapid rise of computational power and the development of machine learning may be useful for aiding the crystal growth of heteroanionic compounds.^96–99

3. Structural perspectives on heteroanionic compounds

Heteroanionic compounds are among a few inorganic compounds that exhibit superb flexibility and diverse structural chemistry. The crystal structure of heteroanionic compounds ranges from one-dimensional (1D) chains to two-dimensional (2D) layers and three-dimensional (3D) frameworks. The basic building units of heteroanionic compounds are distorted and flexible due to the presence of two or more anions. The connectivity between these basic building units further promotes the structural diversity of heteroanionic compounds. In this section, we select some heteroanionic compounds to reveal the diverse structural properties of each group. The basic building units are summarized. No comprehensive structural analysis and summary are presented in this section. Many structural factors such as anion-order, anion-disorder, cation coordination environments (heteroleptic or homoleptic) are the dominant driving forces for the chemical flexibility of heteroanionic compounds, which are summarized in many previous works.^{4,29,61,100–102}

3.1 Oxohalides

Oxohalides are any compounds or molecules that constitute both oxygen and halogen atoms as anions, which include oxyfluorides, oxychlorides, oxybromides, and oxyiodides. In this section, some oxohalides were selected to present the diverse structural chemistry of oxohalides. More selected oxohalides are tabulated in Table S4 (ESI†)^{72–74,85,103–147} with an emphasis on basic building units.

KBe₂(BO₃)F₂ (KBBF) is a leading deep-ultraviolet nonlinear optical material and has sparked research interest.¹⁴⁸ KBBF crystallizes in the R32 (no. 155) space group. The crystal structure of KBBF is shown in Fig. 2. KBBF is alternatively constructed using [KF] layers and [Be₂BO₃F] layers. The [KF] layers are made of the [KF₆] octahedron via sharing edges. The [Be₂BO₃F] layers are built from planar [BO₃] units and a distorted [BeO₃F] tetrahedron, which are interlinked by sharing vertices. The connectivity between two layers is by ionic K–F interactions, which make the crystal growth of KBBF very challenging.^149–152 KBe₂(BO₃)F₂ has one independent K cation and one independent Be cation. K is homoleptic with six surrounding F atoms and Be is heteroleptic with three surrounding O atoms and one surrounding F atom.

Fig. 2 Ball–stick (left) and polyhedral (right) structural models of KBBF. K: purple, B: blue, Be: light green, O: red, F: black.

Rb₂Bi₂(SeO₃)₃F₂ crystallizes in the Cm (no. 8) space group.⁷² The crystal structure of Rb₂Bi₂(SeO₃)₃F₂ is shown in Fig. 3. The 3D framework of Rb₂Bi₂(SeO₃)₃F₂ is constructed from [Bi₂O₉F₂] chains that are further interconnected by adjacent chains through bridging selenite groups. The basic building units would be [SeO₃] pyramidal units, distorted [BiO₆F₂], and [BiO₅F₂] polyhedra. Rb₂Bi₂(SeO₃)₃F₂ exhibits a high second harmonic generation response of 14.4(2) × KH₂PO₄ (KDP). Rb₂Bi₂(SeO₃)₃F₂ has two independent Bi cations and two independent Rb cations. Bi1 is heteroleptic with six surrounding O atoms and two surrounding F atoms. Bi2 is heteroleptic with three surrounding O atoms and two surrounding F atoms. Rb1 and Rb2 are heteroleptic with eight surrounding O atoms and two surrounding F atoms.

Fig. 3 Ball–stick (left) and polyhedral (right) structural models of Rb₂Bi₂(SeO₃)₃F₂. Rb: purple, Bi: light green, Se: blue, O: red, F: black.

Bi₃(SeO₃)₃(Se₂O₅)F crystallizes in the P2₁ (no. 4) space group,⁷³ which is shown in Fig. 4. The 3D framework of Bi₃(SeO₃)₃(Se₂O₅)F is constructed from [BiO₇], [BiO₆F], [SeO₃], and [Se₂O₅] units, where the connectivity between them is via vertices or edges. Both Bi³⁺ and Se⁴⁺ have stereoactive lone pairs, which significantly contribute to the SHG response. Bi₃(SeO₃)₃(Se₂O₅)F exhibits a large SHG response of 8 × KDP. Bi₃(SeO₃)₃(Se₂O₅)F has three independent Bi cations. Bi1 is homoleptic with five surrounding O atoms. Bi2 is heteroleptic with five surrounding O atoms and one surrounding F atom. Bi3 is homoleptic with six linked O atoms.

Fig. 4 Ball–stick (left) and polyhedral (right) structural models of Bi₃(SeO₃)₃(Se₂O₅)F. Bi: purple, Se: blue, O: red, F: black.

Ba₈SrPb₂₄O₂₄Cl₁₈ crystallizes in the I4/m (no. 87) space group,¹⁵³ which is shown in Fig. 5. The complex 3D framework of Ba₈SrPb₂₄O₂₄Cl₁₈ is constructed from [SrCl₆], [BaO₄Cl₄], and [Pb₃O₅] units. Another view of the crystal structure of Ba₈SrPb₂₄O₂₄Cl₁₈ would be the 2D multimembered-ring layers sandwiched by [SrCl₆] layers. The coexistence of alkali-earth metals Sr and Ba and the stereochemically active lone pair (SCALP) cation Pb lead to rich structural chemistry here. As the first alkali-earth metal lead(II) oxyhalide, Ba₈SrPb₂₄O₂₄Cl₁₈ exhibits a moderate band gap of 3.09 eV and moderate birefringence of 0.014 at 1064 nm. Ba₈SrPb₂₄O₂₄Cl₁₈ has one independent Ba cation, one independent Sr cation, and three independent Pb cations. Ba is heteroleptic with four surrounding O atoms and four surrounding Cl atoms. Sr is homoleptic with six surrounding Cl atoms. Pb1 is heteroleptic with two surrounding O atoms and three surrounding Cl atoms. Pb2 and Pb3 are heteroleptic with three surrounding O atoms and one surrounding Cl atom.

Fig. 5 Ball–stick (left) and polyhedral (right) structural models of Ba₈SrPb₂₄O₂₄Cl₁₈. Ba: purple, Sr: pink, Pb: blue, O: red, Cl: black.

CeBrWO₄ crystallizes in the Pc (no. 7) space group, which is shown in Fig. 6.¹² The 3D framework of CeBrWO₄ is made of two-dimensional (2D) [CeBrO₄]⁶⁻ strips and one-dimensional (1D) [WO₅] strands. The 1D [WO₅] strands are built from distorted [WO₅] trigonal bipyramids, which connect to each other via apical oxygen atoms and run along the [001] direction. The 2D [CeBrO₄]⁶⁻ strips are built from distorted tetracapped trigonal prisms [CeO₆Br₃], where six oxygen atoms and three bromine atoms surround the central Ce atoms. The presence of partially filled 4f orbitals of Ce in CeBrWO₄ is suitable for infrared nonlinear applications compared to isostructural LaBrWO₄, which is a good ultraviolet NLO material.¹³ CeBrWO₄ has two independent Ce cations and two independent W cations. Ce1 and Ce2 are heteroleptic with six surrounding O atoms and three surrounding Br atoms. W1 and W2 are homoleptic with five surrounding O atoms.

Fig. 6 Ball–stick (left) and polyhedral (right) structural models of CeBrWO₄. Ce: purple, W: blue, O: red, Br: black.

(O₂Pb₃)₂(BO₃)I crystallizes in the Pmmn space group (no. 59), which is shown in Fig. 7.¹⁵⁴ (O₂Pb₃)₂(BO₃)I is constructed from 1D [O₂Pb₃] double chains, [BO₃] units, and [IPb₈] units. The 1D [O₂Pb₃] double chains are made of [O₂Pb₆] dimers, which are interconnected by two [OPb₄] tetrahedra via edge-sharing. The 2D ([O₂Pb₃][BO₃]) layers are constructed from 1D [O₂Pb₃] double chains interlinked by [BO₃] units. The I⁻ ions, which are connected to Pb atoms, are located between 2D ([O₂Pb₃][BO₃]) layers. (O₂Pb₃)₂(BO₃)I was predicted to exhibit a moderate birefringence of about 0.072 at 1064 nm. (O₂Pb₃)₂(BO₃)I has four independent Pb cations. Pb1, Pb3 and Pb4 are homoleptic with four surrounding O atoms, and Pb2 is heteroleptic with two surrounding O atoms and two surrounding I atoms.

Fig. 7 Ball–stick (left) and polyhedral (right) structural models of (O₂Pb₃)₂(BO₃)I. Pb: purple, B: light green, O: red, I: black.

3.2 Oxysulfides and oxyselenides

Oxychalcogenides are any compounds or molecules that constitute both oxygen and chalcogen atoms as anions including oxysulfides and oxyselenides. Oxygen and other chalcogen elements have the same oxidation states with different atomic sizes or electronegativity, which still results in flexible structures. Selected compounds are presented herein to showcase the structures of oxychalcogenides. More compounds are listed in Table S5 (ESI†).^91,155–162

CaOFeS crystallizes in the P6₃mc space group (no. 186), which is shown in Fig. 8.¹⁶³ The 3D framework of CaOFeS is constructed from alternating layers of [CaO] and [FeS], which exhibit clear layered features. The basic building units are [FeS₃O] tetrahedra and [CaS₃O₃] octahedra. CaOFeS shows the existence of two-dimensional (2D) short-range ordering. The geometrically frustrated compound condenses into a partial long-range ordered state with AFM coupled Fe layers below T_n = 40.6 K. CaOFeS belongs to the CaOZnS structure family with many isostructural compounds known. CaOFeS has one independent Ca cation and one independent Fe cation. Ca is heteroleptic with four surrounding S atoms and three surrounding O atoms, and Fe is heteroleptic with three surrounding S atoms and one surrounding O atom.

Fig. 8 Ball–stick (left) and polyhedral (right) structural models of CaOFeS. Ca: purple, Fe: light green, O: red, S: black.

Ce₃NbO₄S₃ crystallizes in the Pbam (no. 55) space group, which is shown in Fig. 9.¹⁶⁴ The 3D framework of Ce₃NbO₄S₃ is constructed from highly distorted [NbO₃S₃] octahedra and [CeO₃S₅] and [CeO₄S₄] units. Certain oxygen and sulfur atoms are not connected to niobium but are exclusively surrounded by cerium. All polyhedra are connected to each other through the vertex. Magnetic susceptibility measurements indicated a weak antiferromagnetic coupling within Ce₃NbO₄S₃ with a Weiss-constant (θ_p) of −12(1) K. No magnetic ordering was detected above 2 K. Ce₃NbO₄S₃ has two independent Ce atoms and one independent Nb atom. Ce1 is heteroleptic with five surrounding S atoms and three surrounding O atoms, and Ce2 is heteroleptic with four surrounding S atoms and four surrounding O atoms. Nb is heteroleptic with one S atom and three O atoms as the coordination environment.

Fig. 9 Ball–stick (left) and polyhedral (right) structural models of Ce₃NbO₄S₃. Ce: purple, Nb: light green, O: red, S: black.

Zn₄B₆O₁₂S crystallizes in the I4̄3m (no. 217) space group, which belongs to the Zn₄B₆O₁₃ structure type as shown in Fig. 10.⁸¹ Tetrahedra are basic building units of Zn₄B₆O₁₂S. A truncated octahedron was constructed from the quadrangles and hexagons via sharing corners. All Zn atoms locate toward alternating hexagonal faces. Zn₄B₆O₁₂S has a SHG around 1.9 × KDP at 1.604 μm, and its photo-current is 2.1 μA cm⁻². Zn₄B₆O₁₂S has one independent Zn cation and one independent B cation. Zn is heteroleptic with one surrounding S atom and three surrounding O atoms, and B is homoleptic with four surrounding O atoms.

Fig. 10 Ball–stick (left) and polyhedral (right) structural models of Zn₄B₆O₁₂S. Zn: purple, B: light green, O: red, S: black.

Ag₃S(NO₃) crystallizes in the P2₁3 (no. 198) space group, which is shown in Fig. 11.¹⁶⁵ The 3D positively charged [Ag₃S]⁺ frameworks were constructed from the [SAg₆] octahedron, where [NO₃]⁻ fills all cavities. The [Ag₃S]⁺ cationic framework is formed by two crystallographically independent atoms, sulfur and silver. Ag₃S(NO₃) shows semiconducting behavior with a band gap of ca. 1.2 eV. Ag₃S(NO₃) has one independent Ag cation and one independent N cation. Ag is heteroleptic with two surrounding S atoms and one surrounding O atom, and N is homoleptic with three surrounding O atoms.

Fig. 11 Ball–stick (left) and polyhedral (right) structural models of Ag₃S(NO₃). Ag: purple, N: light green, O: red, S: black.

YSeBO₂ crystallizes in the Cmc2₁ (no. 36) space group, which is presented in Fig. 12.¹⁶¹ The 3D framework of YSeBO₂ is built from two basic building units, [BO₃]³⁻ planar triangles and [YO₃Se₄]¹¹⁻ pentagonal bipyramids, which are interlinked via sharing edges. The structure of YSeBO₂ features the [YSeBO₂]_n planar belt. YSeBO₂ has a large bandgap of 3.45 eV. YSeBO₂ is a type-I phase matching material. YSeBO₂ has one independent Y cation and one independent B cation. Y is heteroleptic with four surrounding Se atoms and three surrounding O atoms, and B is homoleptic with three linked O atoms.

Fig. 12 Ball–stick (left) and polyhedral (right) structural models of YSeBO₂. Y: purple, B: light green, O: red, Se: black.

Ba₂NiO₂Ag₂Se₂ crystallizes in the I4/mmm (no. 139) space group, which is shown in Fig. 13.⁹¹ The 3D framework of Ba₂NiO₂Ag₂Se₂ contains clear layered features. The [Ag₂Se₂] layers and [NiO₂] layers are interconnected by Ba–Se and Ba–O interactions, which feature a NiO₂ square net. Ba atoms are sandwiched between [NiO₂] layers and [Ag₂Se₂] layers. Each Ba is connected to four oxygen and four selenium atoms. Ba₂NiO₂Ag₂Se₂ exhibits a G-type spin order at 130 K and has strong in-plane antiferromagnetic interaction. Ba₂NiO₂Ag₂Se has one independent Ba cation, one independent Ni cation, and one independent Ag cation. Ni is homoleptic with four surrounding O atoms, and Ag is homoleptic with four surrounding Se atoms.

Fig. 13 Ball–stick (left) and polyhedral (right) structural models of Ba₂NiO₂Ag₂Se₂. Ba: purple, Ni: blue, Ag: gray, O: red, Se: light blue.

3.3 Oxypnictides

Oxypnictides refer to compounds that constitute both oxygen and pnictogen elements as anions including anion groups of O–N, O–P, O–As, etc. Oxygen and other pnictogen elements have different oxidation states with different atomic sizes or electronegativities, which results in diverse structures. Selected compounds are presented herein to showcase the structures of oxypnictides. More compounds are listed in Table S6 (ESI†).^{82,87,89,166–248}

NbON crystallizes in the P2₁/c (no. 14) space group, which is shown in Fig. 14.²⁴⁹ There is only one basic building unit of [NbO₃N₄] within NbON. The [NbO₃N₄] units connect to each other via sharing edges to form the 3D framework of NbON. NbON exhibits promising electrochemical behavior versus Li. The stabilized capacity was 250 A h kg⁻¹ with a cutoff potential of 0.05 V. NbON has one independent Nb cation, which is heteroleptic with three surrounding O and four surrounding N atoms.

Fig. 14 Ball–stick (left) and polyhedral (right) structural models of NbNO. Nb: purple, O: red, N: black.

YZnPO crystallizes in the R3̄m (no. 166) space group, which is shown in Fig. 15.²⁵⁰ The 3D framework of YZnPO is constructed from [ZnP] layers and [YO] layers. The basic building units within YZnPO are [ZnP₄] tetrahedral and [YO₄P₃] units. [ZnP] layers are made of [ZnP₄] tetrahedra linked by edge-sharing and corner-sharing. Y atoms connect to oxygen atoms via edge-sharing and corner-sharing to form [YO] layers. Other isostructural compounds are REZnAsO (RE = Y, La–Nd, Sm, Gd–Er). YZnPO has one independent Y cation and one independent Zn cation. Y is heteroleptic with three surrounding P atoms and four surrounding O atoms. Zn is homoleptic with four connected P atoms.

Fig. 15 Ball–stick (left) and polyhedral (right) structural models of YZnPO. Y: purple, Zn: light blue, O: red, P: black.

GdFeAsO crystallizes in the P4/nmm (no. 129) space group, which is shown in Fig. 16.¹⁸² GdFeAsO belongs to the ZrCuSiAs structure type. GdFeAsO is built from two alternating [ZnAs] layers and [GdO] layers. The square planar [GdO₄] units construct the [GdO] layers via edge-sharing. The [ZnAs] layers are constructed from [ZnAs₄] tetrahedra. The layered structural features host very rich physical properties for many isostructural compounds such as ThFeAsN with superconducting properties,²⁵¹ LaCuSO with diamagnetic properties,²⁵² and EuCuSF with optical properties.²⁵² GdFeAsO has one independent Gd cation and one independent Fe cation. Gd is homoleptic with four coordinated O atoms, and Fe is homoleptic with four coordinated As atoms.

Fig. 16 Ball–stick (left) and polyhedral (right) structural models of GdFeAsO. Gd: purple, Fe: light blue, O: red, As: black.

Sr₂Mn₃Sb₂O₂ crystallizes in the I4/mmm (no. 139) space group, which is shown in Fig. 17.¹⁸⁷ Sr₂Mn₃Sb₂O₂ contains a CuO₂-type layer created by square planar corner-sharing MnO₄ units. Mn forms tetrahedra with four Sb atoms, which edge-share with three other tetrahedra to create a BaAl₄-type layer. These [MnO₂] and [Mn₂Sb₂] layers sandwich Sr atoms. Sr₂Mn₃Sb₂O₂ has one independent Sr cation and two independent Mn cations. Sr is homoleptic with four coordinated O atoms. Mn1 is homoleptic with four coordinated O atoms, and Mn2 is homoleptic with three coordinated Sb atoms.

Fig. 17 Ball–stick (left) and polyhedral (right) structural models of Sr₂Mn₃Sb₂O₂. Sr: purple, Mn: light green, O: red, Sb: black.

Ce₂O₂Bi crystallizes in the I4/mmm (no. 139) space group, which belongs to the Th₂TeN₂ structure type (anti-ThCr₂Si₂)²²² as shown in Fig. 18. Ce is coordinated by four oxygen atoms in a distorted square planar geometry. These [CeO₄] units connect together by edge-sharing through O atoms, which creates a CeO layer. CeO layers are separated by a Bi square net layer. Ce₂O₂Bi exhibited metallic properties. Ce₂O₂Bi has one independent Ce cation. Ce is homoleptic with four coordinated O atoms.

Fig. 18 Ball–stick (left) and polyhedral (right) structural models of Ce₂O₂Bi. Ce: purple O: red, Bi: black.

3.4 Other heteroanionic combinations (N–Cl, S–Cl, Se–Cl, P–Cl, P–Br, etc.)

As stated in the introduction, many possible combinations of various anions result in more heteroanionic compounds beyond oxygen-containing materials. In this section, we selected a few samples to present the flexible structural chemistry. Selected examples are shown in Table S7 (ESI†).^{79,83,253–289}

Zn₂NCl crystallizes in the Pna2₁ (no. 33) space group, which is shown in Fig. 19.^83,290 The basic building units of Zn₂NCl are distorted [ZnN₂Cl₂] tetrahedra. The highly distorted [ZnN₂Cl₂] tetrahedra connect to each other via sharing N and Cl atoms to form the 3D framework. Zn₂NCl exhibits balanced NLO properties (bandgap: 3.21 eV, SHG: 0.9× AGS). Zn₂NCl has two independent Zn cations. Zn1 is heteroleptic with two surrounding N atoms and two surrounding Cl atoms, and Zn2 is heteroleptic with two surrounding N atoms and one surrounding Cl atom.

Fig. 19 Ball–stick (left) and polyhedral (right) structural models of Zn₂NCl. Zn: purple, N: red, Cl: black.

Hg₃ZnS₂Cl₄ crystallizes in the P6₃mc (no. 186) space group, which is shown in Fig. 20.^79,291 Hg₃ZnS₂Cl₄ features a 2D layered structure. The 12-membered [Hg₆S₃Cl₃] rings are interconnected to form 2D slabs with chair-like conformation. The 2D layers are adjacent to [ZnSCl₃] tetrahedra. The basic building units of Hg₃ZnS₂Cl₄ are linear [HgSCl] units and [ZnSCl₃] tetrahedra. Hg₃ZnS₂Cl₄ is a semiconductor with an experimentally measured bandgap of 2.65 eV. Hg₃ZnS₂Cl₄ has one independent Hg cation and one independent Zn cation. Hg is heteroleptic with one surrounding S atom and one surrounding Cl atom. Zn is heteroleptic with one surrounding S atom and three linked Cl atoms.

Fig. 20 Ball–stick (left) and polyhedral (right) structural models of Hg₃ZnS₂Cl₄. Hg: purple, Zn: light green, S: red, Cl: black.

La₃Zn₄P₆Cl crystallizes in the orthorhombic space group Cmcm (no. 63), which is shown in Fig. 21.²⁷² In La₃Zn₄P₆Cl, 2D [Zn₄P₆] layers sandwich 1D [La₃Cl] chains. 2D [Zn₄P₆] layers are constructed from 1D [Zn₄P₄] tubes linked to each other via homoatomic P–P bonds. La₃Zn₄P₆Cl is constructed from trigonal planar [ZnP₃] units, [ZnP₄] tetrahedra, and [ClLa₄] tetrahedra. La₃Zn₄P₆Cl is a small bandgap (0.24 eV) semiconductor. La₃Zn₄P₆Cl has two independent La cations and two independent Zn cations. La1 is heteroleptic with six surrounding P atoms and one surrounding Cl atom, and La2 is heteroleptic with six surrounding P atoms and two surrounding Cl atoms. Zn1 is homoleptic with four connected P atoms, and Zn2 is homoleptic with three surrounding P atoms.

Fig. 21 Ball–stick (left) and polyhedral (right) structural models of La₃Zn₄P₆Cl. La: purple, Zn: light green, P: red, Cl: black.

La₃AsS₅Br₂ crystallizes in the acentric monoclinic space group Cc (no. 9), which is shown in Fig. 22.¹⁴ The 3D framework of La₃AsS₅Br₂ is constructed from [LaS₅Br₃] bicapped trigonal prisms, [La₃S₇] capped trigonal prisms, and [AsS₃] trigonal pyramids, which are linked to each other. La₃AsS₅Br₂ is a semiconductor with a bandgap of 2.83 eV and a moderate SHG response of 0.23× AGS for the sample of 150–200 μm particle size. La₃AsS₅Br₂ has three independent La cations and one independent As cation. La1 is heteroleptic with four surrounding S atoms and three surrounding Br atoms, La2 is heteroleptic with five surrounding S atoms and two surrounding Br atoms, La3 is homoleptic with seven surrounding S atoms. As is homoleptic with three surrounding S atoms.

Fig. 22 Ball–stick (left) and polyhedral (right) structural models of La₃AsS₅Br₂. La: purple, As: light green, S: red, Br: black.

4. Selected physical applications of heteroanionic compounds

4.1 Nonlinear optical (NLO) properties

One important way to expand the laser frequency is via the second harmonic generation (SHG) process, where two photons of the same frequency interact with nonlinear optical (NLO) materials to generate a new photon of doubled frequency. The NLO materials are the core materials for the SHG process. Based on the application spectrum range, NLO materials can be categorized into deep-ultraviolet NLO materials, ultraviolet-visible NLO materials, infrared NLO materials, far-infrared NLO materials, etc. A good NLO material should balance a long list of properties such as a large second harmonic generation coefficient (SHG, d_ij >AgGaS₂ for infrared NLO materials), moderate birefringence (Δn) for phase matchability, high laser damage threshold (LDT > AgGaS₂), large bandgap for a good transmission range in a desired spectrum range and good thermal-, air-, and chemical stability. However, most importantly, NLO materials should crystallize in noncentrosymmetric (NC) space groups. The presence of distinct anions increases the degree of distortion of basic building units, which enables heteroanionic compounds to ‘easily’ form NC structures. In addition to contributing to formation of NC structures, a higher degree of distortion also benefits the enhancement of SHG coefficients.^15,292–299 The chemical property difference among different anions makes the bandgap of heteroanionic compounds adjustable. For example, oxyhalides, especially oxyfluorides, are the best candidates for deep-ultraviolet NLO applications due to the presence of highly electronegative O²⁻ and F⁻, which results in very large bandgap solids.^300,301 As shown in Fig. 23, the bandgap of oxyflourides spans the largest range from ∼2 eV to ∼6.5 eV. The bandgap is an important parameter for many optical and optoelectronic applications. As shown in Fig. 23, heteroanionic compounds exhibit variable bandgaps, which originate from structural flexibility. Employing appropriate strategies, the bandgap of heteroanionic compounds can be suppressed to be suitable for visible NLO materials or even IR NLO materials.^293–299 For example, one successful strategy to create good oxyhalide IR NLO materials is to incorporate heavy metals like Pb, resulting in Pb₁₈O₈Cl₁₅I₅,³⁰² Pb₁₃O₆Cl₄Br₁₀,³⁰³ and Pb₁₇O₈Cl₁₈.³⁰⁴ Another good method to employ oxyhalides as IR NLO materials is to add more anions such as [Ba₂F₂][Ge₂O₃S₂].³⁰⁵ Our recent work on employing the partially filled 4f orbitals of cerium atoms also successfully developed the CeHaVIO₄ (Ha = Cl, Br; VI = Mo, W) system suitable for IR NLO materials.¹² The high chance of forming NC structures coupled with tunable band gaps makes heteroanionic compounds appealing for NLO material research. Moving forward, heteroanionic compounds can be advanced by using other chemical strategies such as the mixed-cation strategy to further enlarge bandgaps or using elements containing stereochemically active lone pairs to enhance SHG response.^294–299

Fig. 23 A summary of bandgap of seven groups of heteroanionic compounds; V–VII represents heteroanionic compounds constituting main group five and main group seven elements.

4.2 Superconducting properties

Superconductors have been always an important research topic due to their scientific importance and potential applications.^34,51 A number of superconductor materials were reported, including elements such as lead³⁰⁶ and tin,³⁰⁷ alloys such as Nb–Ti³⁰⁸ and Ge–Nb,^309,310 organic compounds such as (TMTSF)₂PF₆ (TMTSF = tetramethyltetraselenafulvalene, P = 1.1 GPa)³¹¹ and A₃C₆₀ (A = K, Rb, Cs),^312,313 oxides such as LiTi₂O₄³¹⁴ and YBCO,³¹⁵ superhydrides under high pressure such as LaH₁₀,³¹⁶ sulfides such as H₃S,³¹⁷ heteroanionic compounds and others. Among all of these compounds, heteroanionic compounds do not play a negligible role. Heteroanionic superconducting compounds belong to the unconventional superconductor family of materials such as LaFePO³¹⁸ and REFeAsO (RE = rare earth),^34,319,320 (Sr₂VO₃)₂Fe₂As,³²¹ Ba₂Ti₂Fe₂As₄O,³²² (Sr₃Sc₂O₅)Fe₂As₂,³²³etc. The well-studied LaFePO³¹⁸ and REFeAsO (RE = rare earth) compounds belong to the ‘1-1-1-1’ phase system and crystallize in the ZrCuSiAs structure type.^34,319,320 There are more than one hundred quaternary oxypnictides reported within the ‘1-1-1-1’ phase system. Among the heteroanionic superconducting compounds belonging to the ‘1-1-1-1’ phase system, the two-dimensional [FeAs] layers seem to be a common structure. As discussed in the section on the structure of heteroanionic compounds, there are more compounds containing 2D [FePn]_Pn=P,As layers that await further studies. Combining the [FePn]_Pn=P,As tetrahedra with other heteroanionic building blocks may result in the discovery of new compounds that possess intriguing physical properties. The central element of [TPn]_{T=transition metals,Pn=P,As} tetrahedra can also expand to heteroanionic compounds containing other transition metals, such as heteroanionic La₂NiO₃F, which also contains 2D [NiO₃] layers.

4.3 Photoluminescence response

Photoluminescent (PL) materials emit light in response to higher energy light exposure. Based on how long emitting light lasts, there are two types of photoluminescent processes: fluorescence and phosphorescence. Phosphorescent materials can continually emit light from less than a second to several hours after the removal of the light resource. Fluorescent materials immediately stop emission after the removal of the exciting light. The difference between fluorescence and phosphorescence originates from the different electron-transfer paths. PL materials have many important applications such as emissive displays,³²⁴ LEDs,³²⁵ and X-ray detection.³²⁶ For visible light emission from PL materials, ultraviolet light is the common excitation light resource. To absorb UV light, materials are required to have a large bandgap, which falls into the realm of many heteroanionic compounds. The combination of strong electronegative anions, such as O, S, F, and Cl, and metals can generate ionic metal–anion interactions. The ionic interaction can produce large bandgaps for many systems. Only a large bandgap is not sufficient. Many inorganic systems do not emit light without doping of “light emitting centers”, which are normally rare earth or transition metals incorporated into the crystal lattice.¹³ A feasible structural feature would add additional benefits for an inorganic system to be selected as a PL material. Good ambient stability of PL materials is also essential, which explains why many oxyhalides (Table S4, ESI†) and oxynitrides (Table S6, ESI†) were widely studied as PL materials. In the future, studying PL materials coupled with other physical properties would open new research directions. Among their applications, the use of luminescence in biological systems is efficient to understand cellular structures and diagnose diseases. Uncovering new materials that have high PL efficiency and are biologically compatible and the use of light in the regions where tissues and cells have low absorption would be the targets for the future.^327–329 The heteroanionic compounds are less commonly utilized for biological applications, generally due to the presence of heavy elements. The high stability and excellent PL properties of heteroanionic compounds still keep the door open for biological application purposes. Constructing heteroanionic compounds with light elements or even organic heteroanionic compounds may be a good way to expand the boundary of heteroanionic compounds. The solid-state LEDs have been developed well for low-energy applications. On the other hand, the high energy PL materials, which can be utilized for high-energy output applications such as lasers, are still underdeveloped.^330–332 The high energy output PL materials require high thermal stability and thermal conductivity of heteroanionic compounds, which can conduct heat out quickly. The three-dimensional crystal structure and the presence of light elements coupled with strong bonding interactions can guarantee the high thermal conductivity of heteroanionic compounds, which indicates that heteroanionic compounds are good candidates for high-energy output PL materials.^330–332

4.4 Thermoelectric properties

The increased need for clean energy sources continues to fuel the research on thermoelectric materials, which can convert heat flow into electrical power through the Seebeck effect or conversely change electrical power into heat flow via the Peltier effect.²⁷² The performance of a thermoelectric material is evaluated through the dimensionless figure-of-merit zT = S²T/ρκ, where S is the Seebeck thermopower, T is the absolute temperature, ρ is the electrical resistivity, and κ is the thermal conductivity. A state-of-the-art thermoelectric material should combine high Seebeck coefficients, high electrical conductivity, and low thermal conductivity. All three parameters are intrinsically correlated via carrier concentration and electronic structures.³³³ Thermal conductivity arises from two components, lattice thermal conductivity and carrier thermal conductivity, K_total = K_lattice + K_carrier. The carrier thermal conductivity is determined by carrier concentration and carrier mobility.³³³ The lattice thermal conductivity is independent of carrier concentration, which is the major target of research. Many strategies such as including heavy elements, the presence of rattling elements and defects, and reducing the dimensionality of the crystal lattice have proved to be efficient in reducing lattice thermal conductivity. Some heteroanionic compounds such as BiCuSeO and LaZnSbO, which combine the 2D crystal lattice with defects to tune electrical and thermal conductivities, achieve a high figure of merit.^334–336 As discussed in the section on the structure of heteroanionic compounds, there are more heteroanionic compounds that feature 2D layered structures. Even some known compounds, which crystallize in the ZrCuSiS structure type, remain unexplored for thermoelectric applications. With the quick development of machine learning and calculation power, more thermoelectric materials may be explored.

4.5 Other applications

The flexible structural chemistry of heteroanionic compounds results in a wide range of applications such as photocatalysis applications,³³⁷ battery materials,³³⁸etc., which are summarized in related papers. Exploring new compounds with flexible structures, which result in important applications, is always exciting for research.

4.6 Can heteroanionic compounds be new playgrounds for discovering multiferroics?

The data that are created daily in 2024 are about 2.5 quintillion (10¹⁸) bytes!³³⁹ More data are expected in the future. Processing and storing these huge amounts of data remain a big challenge. Developing more compact, faster, and secure storage methods is crucial for our society. Multiferroics are considered as good candidates for next-generation storage materials, which could be utilized to fabricate smaller, faster, and secure storage devices.^340–345 Multiferroics refer to materials that exhibit more than one ferroic order simultaneously as shown in Fig. 24. In addition to data storage, multiferroics find applications such as sensors,^346–350 energy devices,^351–355 radio and high-frequency devices,^356–358etc. The broad range of applications of multiferroics require single-phase multiferroics with transition temperature above room temperature, which has become the bottleneck for implementing those materials in technology. Seeking multiferroics is challenging because multiferroics combine two or more ferroic states within a single lattice, where some ferroic states naturally oppose each other. Even though the concept of multiferroics was developed many years ago, only a limited number of chemical systems were found to be multiferroics. The physicists roll the ball back to the chemists. The chemistry question arises: Which chemical systems can host multiferroic states? Alternatively, what is a good chemical methodology to discover new multiferroics? Finding new chemical systems that have the same microscopic building units with known multiferroics and good chemical flexibility, should be a good strategy. The highly flexible heteroanionic compounds that share common structural features with known multiferroics might be new playgrounds for discovering multiferroics.

Fig. 24 (a) Spontaneous polarization, which can be switched by an external electric field in ferroelectrics. (b) Spontaneous magnetization, which can be switched by an external magnetic field in ferromagnetic materials. (c) A Venn diagram of ferroelectricity and ferromagnetism combined to create multiferroics. (d) The [d⁰O₆]_d⁰=Nb/Fe octahedral within perovskites; the green arrow indicates the displacement of the central atom; O: red. (e) Crystal structure of 1T-CrTe₂,^359–361 a room-temperature ferromagnetic material (T_c = ∼320 K), the green arrows present the potential alignment of magnetic moments of Cr atoms, Cr: red, Te: black. The inset shows the 1T-CrTe₂ crystals grown in the PI's lab attracted to the magnetic stir bar at room temperature. (f) Crystal structure of BiFeO₃,^362,363 a well-known multiferroic compound, Bi: pink, Fe: black, O: red.

Multiferroics refer to materials that exhibit the coexistence of two or more ferroic states (ferroelectricity (Fig. 24a and d), ferromagnetism (Fig. 24b and e), ferroelasticity, and ferrotoroidicity).^364–376 Multiferroics were found in various forms including single-phase crystals mainly oxides,^377–379 thin films,^380–383 composite materials,^384–386 organics,³⁸⁷ and organic–inorganic hybrid materials^388–390 Multiferroics are not new to the research community. The study of multiferroics can date back to around 1974 and they were studied by Aizu.³⁹¹ The study of magnetoelectric materials, which exhibit interplay between electrical and magnetic properties, began much earlier.³⁹² Not all magnetoelectric materials can be categorized into multiferroics. In rigid terms, multiferroics are materials in which ferroelectricity and ferromagnetism coexist (Fig. 24c and f). The magnetoelectric effect refers to magnetization induced by an applied electric field or vice versa, i.e., the electric polarization induced by an applied magnetic field. Multiferroic materials reignited more and more research interest over the past few decades due to many exotic properties that originate from the combination of ferroic states.^{340–358,364–390} The list of applications of multiferroics keeps growing.^{346–358,364–378}

Why heteroanionic compounds are a good fit for multiferroics?

(1) Higher chance of forming acentric crystal structure: ferroelectricity can only be found within certain space groups.³⁶⁵ These space groups should belong to one of the ten polar point groups (1, 2, 3, 4, 6, m, mm2, 3m, 4mm, and 6mm). These 10 polar point groups are also subsets of 21 acentric point groups. Hence, an acentric crystal structure would be the first requirement to probe possible ferroelectrics. Macroscopic symmetry is determined by microscopic structures. Our previous study has found that distortion of tetrahedra,^293,393,394 mixed-cation strategy,²⁹⁷ and alignment of lone pairs⁷³ are useful strategies to form acentric crystal structures. The presence of distinct anions increases the degree of distortion of basic building units, which enables heteroanionic compounds to ‘easily’ form acentric structures.^1–3

(2) Highly distorted BBUs without inversion centers: the acentric crystal structures cannot guarantee the presence of ferroelectricity. The presence of spontaneous polarization would be the key to achieving ferroelectricity. Understanding the origin of ferroelectricity from a chemical perspective, especially from a crystal structure viewpoint, would help us find new materials. The ferroelectricity of perovskite materials originates from the ‘off-center’ movement of cations (usually d⁰ metals) (Fig. 24d), which is caused by the interactions between center cations and the surrounding anions.^365–376 The presence and alignment of lone pairs of Bi³⁺ play a key role in contributing to the ferroelectricity of BiFeO₃.^362,363 Using the Valence Shell Electron Pair Repulsion (VSEPR) theory, the lone pairs of Bi³⁺ can be treated as one domain. Bi³⁺ is also located in a highly distorted tetrahedron (Fig. 25c). Nevertheless, in h-YMnO₃, the movement of [MnO₅] bipyramids, which results in the displacement of Y cations, is the dominant factor for its ferroelectricity (Fig. 25a).^395,396 Distorted bipyramids are also the common features of many compounds such as our recently discovered REHaVIO₄, where [WO₅] bipyramids are also present (Fig. 25b).^12,13 The presence of various anions coupled with lone-pair active elements such as Sb³⁺, Bi³⁺, and Te⁴⁺ would introduce distinct distorted building units into the target system. The heteroanionic compounds share many comparable structural features with known multiferroics.

(3) Highly tunable crystal structure to adjust magnetic properties: ferromagnetic materials primarily include single elements like cobalt (Co) and iron (Fe), their alloys, and rare earth compounds such as neodymium iron boron (NdFeB). The transition temperature of a ferromagnetic material is mainly determined by its crystal structure and its constituent magnetic elements. Recent studies on two-dimensional (2D) ferromagnetic materials have advanced our understanding of the origins and mechanisms of ferromagnetism.^359–361 As shown in Fig. 24e, room-temperature 2D 1T-CrTe₂ features a simple crystal structure. Cr atoms are separated from adjacent Cr atoms by 4.0193 Å. Each Cr atom is surrounded by six Te atoms that form a close packing within the Cr layers. The Cr lattice accounts for the room-temperature ferromagnetic properties of bulk and thin-layer CrTe₂ samples. To be honest, how to find a new ferromagnetic material is a challenging question. A chemically flexible lattice, where multiple atomic positions can accommodate magnetic elements such as rare earth or transition metals, provides a promising foundation for discovering ferromagnetic materials. Heteroanionic compounds provide a good platform for chemical flexibility. For a quaternary system A–B–C–D (A and B represent metals and C and D are distinct anions), the presence of two metal atomic sites provides structural flexibility. Both A and/or B can be replaced by magnetic elements, which introduces magnetic properties into heteroanionic compounds. Within a heteroanionic compound lattice, the distances between magnetic elements can vary and are adjustable. One example would be our recent study of the REHaVIO₄ system; the RE atomic position can be occupied by magnetic 4f elements such as Ce–Yb. Another degree of flexibility comes from the substitution of group VI elements. The ionic sizes of Re⁶⁺ and W⁶⁺ are 74 pm and 69 pm, respectively, for a six-coordination environment. W⁶⁺ does not have any 5d electrons. Re⁶⁺ has one 5d electron (5d¹), which introduces magnetism into the target system (Fig. 25b). As shown in Fig. 25c, the lone pairs of Bi³⁺ and their alignment within BiFeO₃ are crucial for its ferroelectricity. Lone pair active elements are also common constituent elements for heteroanionic compounds. One of example systems, Bi₄Te₂O₉Br₂, possesses two lone pair active elements, Bi³⁺ and Te⁴⁺. The highly distorted [TeO₄] unit and [TeO₅Br₂] unit within Bi₄Te₂O₉Br₂ are shown in Fig. 25d and e, respectively. Bi₄Te₂O₉Br₂ was proven to show pyroelectric properties.³⁹⁷

Fig. 25 (a) [MnO₅] bipyramids in h-RMnO₃.^395,396 (b) [WO₅] bipyramids in LaBrWO₄;^12,13 the arrow shows that W⁶⁺ can be replaced by Re⁶⁺, where the unpaired 5d¹ electron of Re⁶⁺ can introduce magnetic properties into the system. (c) [BiO₃] unit with lone pairs within BiFeO₃^362,363 (d) [TeO₄] unit and (e) [TeO₅Br₂] unit within Bi₄Te₂O₉Br₂.³⁹⁷ O: red.

(4) High stability and chemical flexibility of heteroanionic compounds: the three-dimensional structure constructed by strong chemical bonding will enable heteroanionic compounds to show very good water-, air- and chemical stability. One example would be our recently reported REHaVIO₄ system remaining unchanged in air for many months. The crystals were collected after water treatment to remove salt flux.^12,13 The chemical property difference among different anions makes the bandgap of heteroanionic compounds adjustable. For example, oxyhalides, especially oxyfluorides, have much bigger bandgaps than oxides, which enables them to show good transmission of visible light or even deep-ultraviolet light (Fig. 23).¹³ Employing appropriate strategies, the bandgap of heteroanionic compounds can be suppressed to be suitable for the transmission of infrared radiation.¹² Adjustable bandgaps add another flexibility to the heteroanionic compounds since many physical processes are directly correlated to the bandgap of solids (Fig. 23). Ferroelectricity typically exists within insulating materials characterized by a large bandgap, whereas ferromagnetic materials are often found in metals, which generally have no bandgap. This is another reason why it is extremely hard to combine both ferroic states within one lattice. In the chemistry language: a polar crystal lattice with distorted building units is necessary to achieve ferroelectricity; a crystal lattice with magnetic elements interacting with tunable distances and coordination environments would be another prerequisite for ferromagnetic properties. Heteroanionic compounds satisfy both requirements. In summary, heteroanionic compounds are ideal systems for multiferroics.

A brief history of research on heteroanionic compounds as multiferroics is provided. Not too many multiferroic heteroanionic compounds have been discovered. However, interestingly, the heteroanionic compound Ni₃B₇O₁₃I was the first experimentally verified magnetic ferroelectric, which was discovered by Asher et al. back in 1966.³⁹⁸ This system was further expanded later in ref. 399. Another heteroanionic compound CuO₂Cl₂ was discovered as a multiferroic material with ferroelectricity below 70 K.⁴⁰⁰ Theoretical studies also predicted that some heteroanionic compounds such as Eu₄Sb₂O⁴⁰¹ and YCaFe₂O₅F⁴⁰² might be potential multiferroics and are awaiting experimental studies. Since 1966, not too many heteroanionic compounds have been explored as multiferroics (or not too many successful examples). This short part aims to highlight the structural similarity between heteroanionic compounds and known multiferroics, which might reignite the spark of searching for new multiferroics within heteroanionic compounds.

5. Summary and outlook

In this review, we summarized the synthesis, selected crystal structures presenting the diverse and feasible structural chemistry, and selected applications of heteroanionic compounds.

1. Synthesis: the incorporation of distinct anions introduces structural complexity into heteroanionic compounds, and thus, raises the difficulty of the synthesis process. Growing high-quality crystals still relies on a ‘trial-and-error’ model. Another challenge would be to control the ratio of different anions. Looking into the crystal growth mechanisms of heteroanionic compounds via in situ studies and theoretical simulation is becoming more and more important. The quickly developed AI techniques might also aid in the synthesis of heteroanionic compounds.

2. Structure of heteroanionic compounds: as discussed in the second section, selected examples verify the diverse structural chemistry of heteroanionic compounds. The rich structural chemistry of heteroanionic compounds originates from flexible basic building units and their connecting manner. How these anions connect to central atoms is one important factor for the structures. Another factor would be the connectivity between these basic building units. Letting distinct anions interact with other structural features, such as lone pair electrons and d⁰ or d¹⁰ transition metals, partially occupied 4f/5f orbitals, might open a new realm for related research topics. Both new compounds and known compounds of heteroanionic compounds are worth expecting to be discovered and show exotic physical properties. Exploring new compounds can push the boundaries of heteroanionic compounds forward. Understanding the structure plus the controlled growth of many known heteroanionic compounds would also be a good add-on to solid-state chemistry.

3. Properties of heteroanionic compounds: as briefly discussed in Section 3, heteroanionic compounds exhibit many intriguing physical properties. It seems that heteroanionic compounds are naturally suitable for certain applications. Superconductive and thermoelectric materials favor layered structures, where many heteroanionic compounds find their place. The tunable bandgap of heteroanionic compounds also places them in a good position for NLO applications. Furthermore, external stimuli such as high pressure or strain might introduce more important applications for heteroanionic compounds.

4. Research on new single-phase multiferroics is more and more crucial due to their important applications. The heteroanionic compounds, which have a high degree of chemical flexibility, might be a potential platform for studying multiferroics.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article and its ESI.†

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This research was supported by the National Science Foundation (DMR-2316811).

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Footnotes

† Electronic supplementary information (ESI) available: Synthesis details, structural chemistry and physical properties of selected heteroanionic compounds. See DOI: https://doi.org/10.1039/d4qm00454j

‡ Contributed equally.

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