Observation of Magnetoelectric Multiferroicity in a Cubic Perovskite System: LaMn(3)Cr(4)O(12)

High-pressure synthesis of A-site ordered perovskite PbMn3(CrMn3)O12 with long-range antiferromagnetic ordering and a spin glass transition

An AA'3B4O12-type perovskite oxide PbMn3(CrMn3)O12 was synthesized by high-pressure solid-state reactions at 8 GPa and 1373 K. Synchrotron X-ray diffraction shows a cubic crystal structure with the space group Im3̄. The charge states are verified by X-ray photoelectron spectroscopy to be PbMn3+3(Cr3+Mn3+2Mn4+)O12, where the Pb2+ and Mn3+ are 1 : 3 ordered respectively at A and A' sites, while the Cr3+, Mn3+ and Mn4+ are disorderly distributed at the B site. PbMn3(CrMn3)O12 features a long-range antiferromagnetic order of A'-site Mn3+ spins at about 66 K and a subsequent spin glass transition around 36 K due to the randomly distributed Cr3+, Mn3+, and Mn4+ cations at the B site. This unique stepwise order of A' and B-site spins indicates weak A'-B site spin interactions, which are dominated by the difference in the B-site Mn3+/Ni2+ and Mn4+ number in the quadruple perovskites AMn3B4O12.

High-Pressure Synthesis of Semiconducting PbCu3Mn4O12 with Near-Room-Temperature Ferrimagnetic Order

A transition-metal oxide of PbCu3Mn4O12 was prepared at 1523 K and 10 GPa. An A-site-ordered quadruple perovskite structure with the space group Im3̅ is assigned for this compound. Based on bond-valence-sum calculations and X-ray absorption spectroscopy, the charge combination is determined to be PbCu32+Mn44+O12. Due to Cu2+(↑)-Mn4+(↓) antiferromagnetic coupling, a near-room-temperature ferrimagnetic phase transition is observed at approximately 287 K. PbCu3Mn4O12 exhibits a semiconducting electric transport property with the energy band gap Eg ≈ 0.2 eV. In addition, considerable low-field magnetoresistance effects are observed at lower temperatures. This study provides an intrinsic near-room-temperature ferrimagnetic semiconductor that exhibits potential applications in next-generation spintronic devices.

High-Pressure Synthesis of Quadruple Perovskite Oxide CaCu3Cr2Re2O12 with a High Ferrimagnetic Curie Temperature

An AA'3B2B'2O12-type quadruple perovskite oxide of CaCu3Cr2Re2O12 was synthesized at 18 GPa and 1373 K. Both an A- and B-site ordered quadruple perovskite crystal structure was observed, with the space group Pn-3. The valence states are verified to be CaCu32+Cr23+Re25+O12 by bond valence sum calculations and synchrotron X-ray absorption spectroscopy. The spin interaction among Cu2+, Cr3+, and Re5+ generates a ferrimagnetic transition with the Curie temperature (TC) at about 360 K. Moreover, electric transport properties and specific heat data suggest the presence of a half-metallic feature for this compound. The present study provides a promising quadruple perovskite oxide with above-room-temperature ferrimagnetism and possible half-metallic properties, which shows potential in the usage of spintronic devices.

Robust Crystal Phase Separation with Distinct Charge, Orbital, and Spin Orders in AgMn7O12

An AA'3B4O12-type A-site-ordered quadruple perovskite oxide AgMn7O12 was prepared by high-pressure and high-temperature methods. At room temperature, the compound crystallizes into a cubic Im3̅ symmetry with a charge distribution of AgMn33+Mn43.5+O12. With the temperature decreasing to TCO,OO ≈ 180 K, the compound undergoes a structural phase transition toward a monoclinic C2/m symmetry, giving rise to a B-site charge- and orbital-ordered AgMn33+Mn23+Mn24+O12 phase. Moreover, this charge-/orbital-ordered main phase coexists with the initial cubic AgMn33+Mn43.5+O12 phase in the wide temperature range we measured. The charge-/orbital-ordered phase shows two antiferromagnetic phase transitions near 125 and 90 K, respectively. Short-range ferromagnetic correlations are found to occur for the initial B-site mixed cubic phase around 35 K. Because of the robust phase separation, considerable magnetoresistance effects are observed below TCO,OO in AgMn7O12.

High-pressure single crystal growth and magnetoelectric properties of CdMn7O12

The concurrent presence of large electric polarization and strong magnetoelectric coupling is quite desirable for potential applications of multiferroics. In this paper, we report the growth of CdMn₇O₁₂single crystals by flux method under a high pressure of 8 GPa for the first time. An antiferromagnetic (AFM) order with a polar magnetic point group is found to occur at the onset temperature ofT_N1= 88 K (AFM1 phase). As a consequence, the pyroelectric current emerges atT_N1and gradually increases and reaches its maximum atT_set= 63 K, at which the AFM1 phase finally settles down. BelowT_set, CdMn₇O₁₂single crystal exhibits a large ferroelectric polarization up to 2640µC m^-2. Moreover, the spin-induced electric polarization can be readily tuned by applying magnetic fields, giving rise to considerable magnetoelectric coupling effects. Thus, the current CdMn₇O₁₂single crystal acts as a rare multiferroic system where both large polarization and strong magnetoelectric coupling merge concurrently.

BaTiO3/NixZn1−xFe2O4 (x = 0, 0.5, 1) Composites Synthesized by Thermal Decomposition: Magnetic, Dielectric and Ferroelectric Properties

To investigate the influence of spinel structure and sintering temperature on the functional properties of BaTiO3/NixZn1−xFe2O4 (x = 0, 0.5, 1), NiFe2O4, ZnFe2O4, and Ni0.5Zn0.5Fe2O4 were in situ prepared by thermal decomposition onto BaTiO3 surface from acetylacetonate precursors. As-prepared powders were additionally sintered at 1150 °C and 1300 °C. X-ray powder diffraction (XRPD) and scanning electron microscopy (SEM) coupled with electron dispersive spectroscopy (EDS) were used for the detailed examination of phase composition and morphology. The magnetic, dielectric, and ferroelectric properties were investigated. The optimal phase composition in the BaTiO3/NiFe2O4 composite, sintered at 1150 °C, resulted in a wide frequency range stability. Additionally, particular phase composition indicates favorable properties such as low conductivity and ideal-like hysteresis loop behavior. The favorable properties of BaTiO3/NiFe2O4 make this particular composite an ideal material choice for further studies on applications of multi-ferroic devices.

Comparative Study on the Magnetic and Transport Properties of B-Site Ordered and Disordered CaCu3Fe2Os2O12

The B-site Fe/Os ordered and disordered quadruple perovskite oxides CaCu₃Fe₂Os₂O₁₂ were synthesized under different high-pressure and high-temperature conditions. The B-site ordered CaCu₃Fe₂Os₂O₁₂ is a system with a very high ferrimagnetic ordering temperature of 580 K having the Cu²⁺(↑)Fe³⁺(↑)Os⁵⁺(↓) charge and spin arrangement. In comparison, the highly disordered CaCu₃Fe₂Os₂O₁₂ has a reduced magnetic transition temperature of about 350 K. The Cu²⁺Fe³⁺Os⁵⁺ charge combination remains the same without any sign of changes in the valence state of the constituent ions. Although the average net moments of each sublattice are reduced, the average ferrimagnetic spin arrangement is unaltered. The robustness of the basic magnetic properties of CaCu₃Fe₂Os₂O₁₂ against site disorder may be taken as an indication of the tendency to maintain the short-range order of the atomic constituents.

Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn₃Cr₄O₁₂ (A = La and Tb) reside on the topological Roman surface—a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.

A non-orientable surface can mirror reflecting the man travelling on it. Realizing such topological object is fascinating. Here, the authors discover that antiferromagnetic-induced polarization in a solid can realize a non-orientable Roman surface.

Direct Evidence for an Intermediate Multiferroic Phase in LiCuFe2(VO4)3

Magnetic susceptibility, specific heat, dielectric, and electric polarization of LiCuFe₂(VO₄)₃ have been investigated. Two sequential antiferromagnetic transitions at T_N1 ∼ 9.95 K and T_N2 ∼ 8.17 K are observed under zero magnetic field. Although a dielectric peak at T_N1 is clearly identified, the measured pyroelectric current also exhibits a sharp peak at T_N1, implying the magnetically relevant ferroelectricity. Interestingly, another pyroelectric peak around T_N2 with an opposite signal is observed, resulting in the disappearance of electric polarization below T_N2. Besides, the electric polarization is significantly suppressed in response to external magnetic field, evidencing a remarkable magnetoelectric effect. These results suggest the essential relevance of the magnetic structure with the ferroelectricity in LiCuFe₂(VO₄)₃, deserving further investigation of the underlying mechanism.

Emergent physical properties of perovskite-type oxides prepared under high pressure

The perovskite ABO₃ family demonstrates a wide variety of structural evolutions and physical properties and is arguably the most important family of complex oxides. Chemical substitutions of the A- and/or B-site and modulation of oxygen content can effectively regulate their electronic behaviors and multifunctional performances. In general, the BO₆ octahedron represents the main unit controlling the electronic and magnetic properties while the A-site ion is often not involved. However, a series of unconventional perovskite materials have been recently synthesized under high pressure, such as the s-d level controlled Pb-based perovskite family and quadruple perovskite oxides containing transition metal ions at the A-site. In these compounds, the intersite A-B correlations play an important role in electronic behaviors and further induce many emergent physical properties.

High-Pressure Synthesis and Magnetism of the 4H-BaMnO3 Single Crystal and Its 6H-Type Polymorph

A 4H-type BaMnO₃ single crystal was prepared by combining the floating zone method with high-pressure treatment at 5 GPa and 1023 K. The crystal crystallizes to a hexagonal structure with space group P6₃/mmc and lattice parameters a = 5.63723(5) Å and c = 9.22355(8) Å. In this structure, face-sharing MnO₆ octahedral dimers connect with each other by corner O atoms along the c-axis direction, forming an -A-B-A-C-type 4H arrangement. A long-range antiferromagnetic (AFM) phase transition is found to occur at T_N ≈ 263 K. When the synthesis pressure increases to 20 GPa, a new polymorphic phase is obtained. This higher-pressure phase still possesses the hexagonal P6₃/mmc symmetry, but the lattice parameters change to be a = 5.61349(2) Å and c = 13.66690(9) Å with a unit cell volume reduction of 2.05%. In this new phase, the c-axis MnO₆ dimers are separated by MnO₆ octahedral layers in the ab plane, forming an -A-B-C-A-C-B-type 6H structure. The 6H phase exhibits two long-range AFM orderings at T_N1 ≈ 220 K and T_N2 ≈ 25 K, respectively. The different magnetic properties are discussed on the basis of the detailed structural constitutions of 4H- and 6H-BaMnO₃.

Metamagnetic Behavior in a Quadruple Perovskite Oxide

A cubic quadruple perovskite oxide CeMn₃Cr₄O₁₂ has been synthesized under high-pressure and high-temperature conditions of 8 GPa and 1273 K. The X-ray absorption spectroscopy reveals that the Ce ions are in a trivalent state, as represented by the ionic model of Ce³⁺Mn³⁺₃Cr³⁺₄O₁₂. The magnetic study demonstrates three independent antiferromagnetic transitions attributed to Ce (∼10 K), Mn (46 K), and Cr (133 K) ions. Furthermore, a magnetic field-induced antiferromagnetic-to-ferromagnetic (metamagnetic) transition of Ce³⁺ 4f moments is observed at low temperatures below 20 K, exhibiting a rare example of metamagnetism in the Ce³⁺-oxides. This finding represents that the 3d-electron magnetic sublattices play a role in the metamagnetism of 4f-electron magnetic moments, demonstrating a new aspect of the 3d-4f complex electron systems.

Os Doping Suppressed Cu-Fe Charge Transfer and Induced Structural and Magnetic Phase Transitions in LaCu3Fe4-xOsxO12 (x = 1 and 2)

B-site Os-doped quadruple perovskite oxides LaCu₃Fe_4-xOs_xO₁₂ (x = 1 and 2) were prepared under high-pressure and high-temperature conditions. Although parent compound LaCu₃Fe₄O₁₂ experiences Cu-Fe intermetallic charge transfer that changes the Cu³⁺/Fe³⁺ charge combination to Cu²⁺/Fe^3.75+ at 393 K, in the Os-doped samples, the Cu and Fe charge states are found to be constant 2+ and 3+, respectively, indicating the complete suppression of charge transfer. Correspondingly, Os⁶⁺ and mixed Os^4.5+ valence states are determined by X-ray absorption spectroscopy for x = 1 and x = 2 compositions, respectively. The x = 1 sample crystallizes in an Fe/Os disordered structure with the Im3̅ space group. It experiences a spin-glass transition around 480 K. With further Os substitution up to x = 2, the crystal symmetry changes to Pn3̅, where Fe and Os are orderly distributed in a rocksalt-type fashion at the B site. Moreover, this composition shows a long-range Cu²⁺(↑)Fe³⁺(↑)Os^4.5+(↓) ferrimagnetic ordering near 520 K. This work provides a rare example for 5d substitution-suppressed intermetallic charge transfer as well as induced structural and magnetic phase transitions with high spin ordering temperature.

Observation of novel charge ordering and spin reorientation in perovskite oxide PbFeO3

PbMO₃ (M = 3d transition metals) family shows systematic variations in charge distribution and intriguing physical properties due to its delicate energy balance between Pb 6s and transition metal 3d orbitals. However, the detailed structure and physical properties of PbFeO₃ remain unclear. Herein, we reveal that PbFeO₃ crystallizes into an unusual 2a_p × 6a_p × 2a_p orthorhombic perovskite super unit cell with space group Cmcm. The distinctive crystal construction and valence distribution of Pb²⁺_0.5Pb⁴⁺_0.5FeO₃ lead to a long range charge ordering of the -A-B-B- type of the layers with two different oxidation states of Pb (Pb²⁺ and Pb⁴⁺) in them. A weak ferromagnetic transition with canted antiferromagnetic spins along the a-axis is found to occur at 600 K. In addition, decreasing the temperature causes a spin reorientation transition towards a collinear antiferromagnetic structure with spin moments along the b-axis near 418 K. Our theoretical investigations reveal that the peculiar charge ordering of Pb generates two Fe³⁺ magnetic sublattices with competing anisotropic energies, giving rise to the spin reorientation at such a high critical temperature.

Polarization-Sensitive Halide Perovskites for Polarized Luminescence and Detection: Recent Advances and Perspectives

While halide perovskites (HPs) have achieved enormous success in the field of optoelectronic applications, much attention has been recently drawn to the unique polarization sensitivity of HPs, either intrinsic or extrinsic, which makes HPs a potential candidate for innovative applications in directly polarized luminescence and detection. Herein, the research status in the field of polarization-sensitive HPs, including linear polarization and circular polarization, is comprehensively summarized. To evaluate the effectiveness of HPs in generating and detecting linearly or circularly polarized light, the principles and characterization methods of polarized luminescence and detection are introduced. Sequentially, the state-of-the-art development of the strategies that induce the linear or circular polarization characteristics of HPs is systematically reviewed, based on which the application of polarization-sensitive HPs in the field of polarization luminescence and detection are summarized. Moreover, the current challenges and opportunities are discussed, and prospects of the future development in this promising field are outlined.

A combinatory ferroelectric compound bridging simple ABO3 and A-site-ordered quadruple perovskite

The simple ABO₃ and A-site-ordered AA′₃B₄O₁₂ perovskites represent two types of classical perovskite functional materials. There are well-known simple perovskites with ferroelectric properties, while there is still no report of ferroelectricity due to symmetry breaking transition in A-site-ordered quadruple perovskites. Here we report the high pressure synthesis of an A-site-ordered perovskite PbHg₃Ti₄O₁₂, the only known quadruple perovskite that transforms from high-temperature centrosymmetric paraelectric phase to low-temperature non-centrosymmetric ferroelectric phase. The coordination chemistry of Hg²⁺ is changed from square planar as in typical A-site-ordered quadruple perovskite to a rare stereo type with 8 ligands in PbHg₃Ti₄O₁₂. Thus PbHg₃Ti₄O₁₂ appears to be a combinatory link from simple ABO₃ perovskites to A-site-ordered AA′₃Ti₄O₁₂ perovskites, sharing both displacive ferroelectricity with former and structure coordination with latter. This is the only example so far showing ferroelectricity due to symmetry breaking phase transition in AA′₃B₄O₁₂-type A-site-ordered perovskites, and opens a direction to search for ferroelectric materials.

There are few reports of ferroelectricity due to symmetry breaking transition in A-site-ordered quadruple perovskites. Here, the authors find one with phase transition from a high-temperature centrosymmetric paraelectric phase to a low-temperature non-centrosymmetric ferroelectric phase in a high pressure synthesized compound.

Prediction of two-dimensional antiferromagnetic ferroelasticity in an AgF2 monolayer

Two-dimensional multiferroics, simultaneously harboring antiferromagneticity and ferroelasticity, are essential and highly sought for miniaturized device applications, such as high-density data storage, but thus far they have rarely been explored. Herein, using first principles calculations, we identified two-dimensional antiferromagnetic ferroelasticity in an AgF₂ monolayer that is dynamically and thermally stable, and can be easily fabricated from its bulk. The AgF₂ monolayer is an antiferromagnetic semiconductor with large spin polarization, and with great structural distortion due to its intrinsic Jahn-Teller effect when thinning the AgF₂ down to a monolayer. Additionally, it features excellent ferroelasticity with high transition signal and a low switching barrier, rendering the room-temperature nonvolatile memory accessible. Such coexistence of antiferromagneticity and ferroelasticity is of great significance to the study of two-dimensional multiferroics and also renders the AgF₂ monolayer a promising platform for future multifunctional device applications.

Magnetic Structures of Mn11Ta4O21 and Interpretation as an Hexagonal A-site Manganite

Mn₁₁Ta₄O₂₁ is presented as the first hexagonal A-site manganite. Based on simple rules, the structure is compatible with a 14H-layer (cchchch)₂ stacking sequence that is related to BaVO₃ and BaCrO₃ high-pressure polymorphs. The A-site overstoichiometry is explained through difference in ionic radii sizes between Ba and Mn. Magnetic properties show two transitions at T_N1 = 88 K and T_N2 = 56 K. Neutron powder diffraction evidence two magnetic structures with purely antiferromagnetic and ferrimagnetic orders below T_N1 and T_N2, respectively. A complementary description with 14H-(hhccccc)₂ sequence of only Mn octahedra provides a direct comparison with BaMnO_3-δ hexagonal perovskites and naturally explains the AFM order. Below T_N2 a magneto-elastic coupling along with uniaxial negative thermal expansion are observed.

High-Pressure Synthesis of a B-site Co2+/Mn4+ Disordered Quadruple Perovskite LaMn3Co2Mn2O12

A new oxide, LaMn₃Co₂Mn₂O₁₂, was synthesized under high-pressure (7 GPa) and high-temperature (1423 K) conditions. The compound crystallizes in an AA'₃B₄O₁₂-type quadruple perovskite structure with space group Im3̅. The Rietveld structural analysis combined with soft X-ray absorption spectroscopy reveals the charge combination to be LaMn³⁺₃Co²⁺₂Mn⁴⁺₂O₁₂, where the La³⁺ and Mn³⁺ are 1:3 ordered respectively at the A and A' sites, whereas the Co²⁺ and Mn⁴⁺ are disorderly distributed at the B site. This is in sharp contrast to R₂Co²⁺Mn⁴⁺O₆ (R = La and rare earth) double perovskites, in which the Co²⁺ and Mn⁴⁺ charge states are always orderly distributed with a rocksalt-type fashion, giving rise to a long-range magnetic ordering. As a result, LaMn₃Co₂Mn₂O₁₂ displays spin glassy magnetic properties due to the random Co²⁺ and Mn⁴⁺ distribution, as demonstrated by dc and ac magnetic susceptibility as well as specific heat measurements. Possible factors that affect the B-site degree of order in perovskite structures are discussed.

Sequential Spin State Transition and Intermetallic Charge Transfer in PbCoO3

Spin state transitions and intermetallic charge transfers can essentially change material structural and physical properties while excluding external chemical doping. However, these two effects have rarely been found to occur sequentially in a specific material. In this article, we show the realization of these two phenomena in a perovskite oxide PbCoO₃ with a simple ABO₃ composition under high pressure. PbCoO₃ possesses a peculiar A- and B-site ordered charge distribution Pb²⁺Pb⁴⁺₃Co²⁺₂Co³⁺₂O₁₂ with insulating behavior at ambient conditions. The high spin Co²⁺ gradually changes to low spin with increasing pressure up to about 15 GPa, leading to an anomalous increase of resistance magnitude. Between 15 and 30 GPa, the intermetallic charge transfer occurs between Pb⁴⁺ and Co²⁺ cations. The accumulated charge-transfer effect triggers a metal-insulator transition as well as a first-order structural phase transition toward a Tetra.-I phase at the onset of ∼20 GPa near room temperature. On further compression over 30 GPa, the charge transfer completes, giving rise to another first-order structural transformation toward a Tetra.-II phase and the reentrant electrical insulating behavior.

High-Pressure Synthesis of Two Polymorphic HgMnO3 Phases and Distinct Magnetism from 2D to 3D

An ilmenite-like monoclinic phase of HgMnO₃ with space group P2₁/c was prepared using high-pressure and high-temperature methods at 18 GPa and 1473 K. The MnO₆ octahedra form a two-dimensional (2D) network in the bc plane, leading to a long-range antiferromagnetic ordering with a low Néel temperature of T_N ∼ 32 K. As the synthesis pressure increases to 20 GPa, a new perovskite-like rhombohedral phase with space group R3̅c was found to occur. The rhombohedral phase exhibits a three-dimensional (3D) network for the MnO₆ octahedra, giving rise to an antiferromagnetic ordering at T_N ∼ 60 K. X-ray absorption spectroscopy confirms the invariable Mn⁴⁺ charge state in these two polymorphic phases, in agreement with the Curie-Weiss and bond valence sum analysis. HgMnO₃ provides an interesting example to study the magnetic properties from 2D to 3D by varying synthesis pressure.

Near-Room-Temperature Ferrimagnetic Ordering in a B-Site-Disordered 3d-5d-Hybridized Quadruple Perovskite Oxide, CaCu3Mn2Os2O12

A new 3d-5d hybridization oxide, CaCu₃Mn₂Os₂O₁₂ (CCMOO), was prepared by high-pressure and high-temperature synthesis methods. The compound crystallizes to an A-site-ordered but B-site-disordered quadruple perovskite structure with a space group of Im3̅ (No. 204). The charge states of the transition metals are determined to be Cu²⁺/Mn^3.5+/Os^4.5+ by X-ray absorption spectroscopy. Although most B-site-disordered perovskites possess lower spin-ordering temperatures or even nonmagnetic transitions, the current CCMOO displays a long-range ferrimagnetic phase transition with a critical temperature as high as ∼280 K. Moreover, a large saturated magnetic moment is found to occur [7.8 μ_B/formula units (f.u.) at 2 K]. X-ray magnetic circular dichroism shows a Cu²⁺(↑)Mn^3.5+(↑)Os^4.5+(↓) ferrimagnetic coupling. The corner-sharing Mn/OsO₆ octahedra with mixed Mn and Os charge states make the compound metallic in electrical transport, in agreement with a specific heat fitting at low temperature. This work provides a rare example with high spin-ordering temperature and a large magnetic moment in B-site-disordered 3d-5d hybridization perovskite oxides.

Single-phase multiferroics: new materials, phenomena, and physics

Multiferroics, where multiple ferroic orders coexist and are intimately coupled, promise novel applications in conceptually new devices on one hand, and on the other hand provide fascinating physics that is distinctly different from the physics of high-T_C superconductors and colossal magnetoresistance manganites. In this mini-review, we highlight the recent progress of single-phase multiferroics in the exploration of new materials, efficient roadmaps for functionality enhancement, new phenomena beyond magnetoelectric coupling, and underlying novel physics. In the meantime, a slightly more detailed description is given of several multiferroics with ferrimagnetic orders and double-layered perovskite structure and also of recently emerging 2D multiferroics. Some emergent phenomena such as topological vortex domain structure, non-reciprocal response, and hybrid mechanisms for multiferroicity engineering and magnetoelectric coupling in various types of multiferroics will be briefly reviewed.

Group-theoretical analysis of 1:3 A-site-ordered perovskite formation

The quadruple perovskites AA'₃B₄X₁₂ are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu₃Ti₄O₁₂, CaCu₃Ga₂Sn₂O₁₂, CaMn₃Mn₄O₁₂, Ce_1/2Cu₃Ti₄O₁₂, LaMn₃Mn₄O₁₂, BiMn₃Mn₄O₁₂ and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.

Magnetoelectricity in multiferroics: a theoretical perspective

The key physical property of multiferroic materials is the existence of coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on mainstream physical mechanisms in both single-phase multiferroics and magnetoelectric heterostructures. The most recent tendencies addressing possible new magnetoelectric mechanisms will also be briefly outlined.

Spin-reorientation-induced magnetodielectric coupling effects in two layered perovskite magnets

Spin-reorientation-induced magnetodielectric coupling effects were discovered in two layered perovskite magnets, [C6H5CH2CH2NH3]2[MCl4] (M = Mn2+ and Cu2+), via isothermal magnetodielectric measurements on single-crystal samples. Specifically, peak-like dielectric anomalies and spin-flop transitions appeared simultaneously at around ±34 kOe for the canted antiferromagnet (M = Mn2+) at below 44.3 K, while a low-field (1 kOe) controlled magnetodielectric effect was observed in the "soft" ferromagnet (M = Cu2+) at below 9.5 K. These isothermal magnetodielectric effects are highly reproducible and synchronous with the field-induced magnetization at different temperatures, well confirming the essential role of spin reorientation on inducing magnetodielectric coupling effects. These findings strongly imply that the layered perovskite magnets are new promising organic-inorganic hybrid systems to host magnetodielectric coupling effects.

A suite-level review of the neutron powder diffraction instruments at Oak Ridge National Laboratory

The suite of neutron powder diffractometers at Oak Ridge National Laboratory (ORNL) utilizes the distinct characteristics of the Spallation Neutron Source and High Flux Isotope Reactor to enable the measurements of powder samples over an unparalleled regime at a single laboratory. Full refinements over large Q ranges, total scattering methods, fast measurements under changing conditions, and a wide array of sample environments are available. This article provides a brief overview of each powder instrument at ORNL and details the complementarity across the suite. Future directions for the powder suite, including upgrades and new instruments, are also discussed.

A group-theoretical approach to enumerating magnetoelectric and multiferroic couplings in perovskites

A group-theoretical approach is used to enumerate the possible couplings between magnetism and ferroelectric polarization in the parent Pm{\overline 3}m perovskite structure. It is shown that third-order magnetoelectric coupling terms must always involve magnetic ordering at the A and B sites which either transforms both as R-point or both as X-point time-odd irreducible representations (irreps). For fourth-order couplings it is demonstrated that this criterion may be relaxed allowing couplings involving irreps at X-, M- and R-points which collectively conserve crystal momentum, producing a magnetoelectric effect arising from only B-site magnetic order. In this case, exactly two of the three irreps entering the order parameter must be time-odd irreps and either one or all must be odd with respect to inversion symmetry. It is possible to show that the time-even irreps in this triad must transform as one of: X1+, M3,5- or R5+, corresponding to A-site cation order, A-site antipolar displacements or anion rocksalt ordering, respectively. This greatly reduces the search space for type-II multiferroic perovskites. Similar arguments are used to demonstrate how weak ferromagnetism may be engineered and a variety of schemes are proposed for coupling this to ferroelectric polarization. The approach is illustrated with density functional theory calculations on magnetoelectric couplings and, by considering the literature, suggestions are given of which avenues of research are likely to be most promising in the design of novel magnetoelectric materials.

Realization of Large Electric Polarization and Strong Magnetoelectric Coupling in BiMn3 Cr4 O12

Magnetoelectric multiferroics have received much attention in the past decade due to their interesting physics and promising multifunctional performance. For practical applications, simultaneous large ferroelectric polarization and strong magnetoelectric coupling are preferred. However, these two properties have not been found to be compatible in the single-phase multiferroic materials discovered as yet. Here, it is shown that superior multiferroic properties exist in the A-site ordered perovskite BiMn₃ Cr₄ O₁₂ synthesized under high-pressure and high-temperature conditions. The compound experiences a ferroelectric phase transition ascribed to the 6s² lone-pair effects of Bi³⁺ at around 135 K, and a long-range antiferromagnetic order related to the Cr³⁺ spins around 125 K, leading to the presence of a type-I multiferroic phase with huge electric polarization. On further cooling to 48 K, a type-II multiferroic phase induced by the special spin structure composed of both Mn- and Cr-sublattices emerges, accompanied by considerable magnetoelectric coupling. BiMn₃ Cr₄ O₁₂ thus provides a rare example of joint multiferroicity, where two different types of multiferroic phases develop subsequently so that both large polarization and significant magnetoelectric effect are achieved in a single-phase multiferroic material.

Non-collinear magnetic structure of manganese quadruple perovskite CdMn7O12

We report on the magnetic structure of CdMn₇O₁₂ determined by powder neutron diffraction. We were able to measure the magnetic structure of this Cd containing and highly neutron absorbing material by optimizing the sample geometry and by blending the CdMn₇O₁₂ with Aluminum powder. Below its Néel temperature T_N1 all magnetic reflections can be indexed by a single commensurate propagation vector k = (0, 0, 1). This is different to the case of CaMn₇O₁₂ where the propagation vector is incommensurate and where an in-plane helical magnetic structure has been found. We observe a commensurate non-collinear magnetic structure in CdMn₇O₁₂ with in-plane aligned magnetic moments resembling the ones in CaMn₇O₁₂. However, the commensurate propagation vector prevents the appearance of a helical magnetic structure in CdMn₇O₁₂. Finally, we also observe a third structural phase transition below ~60 K that can be attributed to phase separation.

Improper electric polarization in simple perovskite oxides with two magnetic sublattices

ABO₃ perovskite oxides with magnetic A and B cations offer a unique playground to explore interactions involving two spin sublattices and the emergent effects they may drive. Of particular interest is the possibility of having magnetically driven improper ferroelectricity, as in the much studied families of rare-earth orthoferrites and orthochromites; yet, the mechanisms behind such effects remain to be understood in detail. Here we show that the strongest polar order corresponds to collinear spin configurations and is driven by non-relativistic exchange-strictive mechanisms. Our first-principles simulations reveal the dominant magnetostructural couplings underlying the observed ferroelectricity, including a striking magnetically driven piezoelectric effect. Further, we derive phenomenological and atomistic theories that describe such couplings in a generic perovskite lattice. This allows us to predict how the observed effects can be enhanced, and even how similar ones can be obtained in other perovskite families.

Magnetically-driven ferroelectricity holds the key for novel multiferroic effects in perovskite oxides, but it remains poorly understood. Here, Zhao et al. determine the dominant magnetostructural couplings that yield improper ferroelectricity in a generic perovskite with two spin sublattices.

Ferroelectricity of domain walls in rare earth iron garnet films

In this paper, we report on electric polarization arising in a vicinity of Bloch-like domain walls in rare-earth iron garnet films. The domain walls generate an intrinsic magnetic field that breaks an antiferroelectric structure formed in the garnets due to an exchange interaction between rare earth and iron sublattices. We explore 180° domain walls whose formation is energetically preferable in the films with perpendicular magnetic anisotropy. Magnetic and electric structures of the 180° quasi-Bloch domain walls have been simulated at various relations between system parameters. Singlet, doublet ground states of rare earth ions and strongly anisotropic rare earth Ising ions have been considered. Our results show that electric polarization appears in rare earth garnet films at Bloch domain walls, and the maximum of magnetic inhomogeneity is not always linked to the maximum of electric polarization. A number of factors including the temperature, the state of the rare earth ion and the type of a wall influence magnetically induced electric polarization. We show that the value of polarization can be enhanced by the shrinking of the Bloch domain wall width, decreasing the temperature, and increasing the deviations of magnetization from the Bloch rotation that are regulated by impacts given by magnetic anisotropies of the films.

Symmetry conditions for type II multiferroicity in commensurate magnetic structures

Type II multiferroics are magnetically ordered phases that exhibit ferroelectricity as a magnetic induced effect. We show that in single-k magnetic phases the presence in the paramagnetic phase of non-symmorphic symmetry combined with some specific type of magnetic propagation vector can be sufficient for the occurrence of this type of multiferroic behaviour. Other symmetry scenarios especially favourable for spin driven multiferroicity are also presented. We review and classify known type II multiferroics under this viewpoint. In addition, some other magnetic phases which due to their symmetry properties can exhibit type II multiferroicity are pointed out.