Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

Significantly Enhanced Room-Temperature Ferromagnetism in Multiferroic EuFeO3-δ Thin Films.

Regulating the magnetic properties of multiferroics lays the foundation for their prospective application in spintronic devices. Single-phase multiferroics, such as rare-earth ferrites, are promising candidates; however, they typically exhibit weak magnetism at room temperature (RT). Here, we significantly boosted the RT ferromagnetism of a representative ferrite, EuFeO3, by oxygen defect engineering. Polarized neutron reflectometry and magnetometry measurements reveal that saturation magnetization reaches 0.04 µB/Fe, which is approximately 5 times higher than its bulk phase. Combining the annular bright-field images with theoretical assessment, we unravel the underlying mechanism for magnetic enhancement, in which the decrease in Fe-O-Fe bond angles caused by oxygen vacancies (VO) strengthens magnetic interactions and tilts Fe spins. Furthermore, the internal relationship between magnetism and VO was established by illustrating how the magnetic structure and magnitude change with VO configuration and concentration. Our strategy for regulating magnetic properties can be applied to numerous functional oxide materials.

Toward Ultimate Memory with Single-Molecule Multiferroics.

The demand for high-density storage is urgent in the current era of data explosion. Recently, several single-molecule (-atom) magnets and ferroelectrics have been reported to be promising candidates for high-density storage. As another promising candidate, single-molecule multiferroics are not only small in size but also possess ferroelectric and magnetic orderings, which can sometimes be strongly coupled and used as data storage to realize the combination of electric writing and magnetic reading. However, they have been rarely proposed and have never been experimentally reported. Here, by building Hamiltonian models, we propose a new model of single-molecule multiferroics in which electric dipoles and magnetic moments are parallel and can rotate with the rotation of the single molecule. Furthermore, by performing spin-lattice dynamics simulations, we reveal the conditions (e.g., large enough single-ion anisotropy and an appropriate electric field) under which the new single-molecule multiferroic can arise. Based on this model, as well as first-principles calculations, a realistic example of Co(NH3)4N@SWCNT is constructed and numerically confirmed to demonstrate the feasibility of the new single-molecule multiferroic model. Our work not only sheds light on the discovery of single-molecule multiferroics but also provides a new guideline to design multifunctional materials for ultimate memory devices.

Realistic Spin Model for Multiferroic NiI_{2}.

A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i) the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii) the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional Monte Carlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.

Theoretical study on the magnetic properties of cathode materials in the lithium-ion battery.

The layered LiMO2 (M = Co, Ni, and Mn) materials are commonly used as the cathode materials in the lithium-ion battery due to the distinctive layer structure for lithium extraction and insertion. Although their electrochemical properties have been extensively studied, the structural and magnetic properties of LiNiO2 are still under considerable debate, and the magnetic properties of monoclinic LiMnO2 are seldom reported. In this work, a detailed study of LiNiO2, LiMnO2, and a half-doped material LiNi0.5Mn0.5O2 is performed via both first-principles calculations and Monte Carlo simulations based on the effective spin Hamiltonian model. Through considering different structures, it is verified that a structure with a zigzag-type pattern is the most stable one of LiNiO2. Moreover, in order to figure out the magnetic properties, the spin exchange interactions are calculated, and then magnetic ground states are predicted in these three systems. The results show that LiNiO2 forms a spiral order that is caused by the competition from both the short-range and long-range spin exchange interactions, whereas the magnetic ground state of LiMnO2 is collinearly antiferromagnetic due to its nearest and next-nearest neighbor antiferromagnetic spin exchange interactions. However, LiNi0.5Mn0.5O2 is collinearly ferrimagnetic because of the ferromagnetic nearest neighbor Ni-Ni and Mn-Mn exchange interactions. Our work demonstrates the competition between the different exchange interactions in these cathode materials, which may be relevant to the performance of the lithium-ion battery.

Direct experimental evidence of physical origin of electronic phase separation in manganites.

Electronic phase separation in complex oxides is the inhomogeneous spatial distribution of electronic phases, involving length scales much larger than those of structural defects or nonuniform distribution of chemical dopants. While experimental efforts focused on phase separation and established its correlation with nonlinear responses under external stimuli, it remains controversial whether phase separation requires quenched disorder for its realization. Early theory predicted that if perfectly "clean" samples could be grown, both phase separation and nonlinearities would be replaced by a bicritical-like phase diagram. Here, using a layer-by-layer superlattice growth technique we fabricate a fully chemically ordered "tricolor" manganite superlattice, and compare its properties with those of isovalent alloyed manganite films. Remarkably, the fully ordered manganite does not exhibit phase separation, while its presence is pronounced in the alloy. This suggests that chemical-doping-induced disorder is crucial to stabilize the potentially useful nonlinear responses of manganites, as theory predicted.

Two-Dimensional Organic-Inorganic Room-Temperature Multiferroics.

Organic-inorganic multiferroics are promising for the next generation of electronic devices. To date, dozens of organic-inorganic multiferroics have been reported; however, most of them show a magnetic Curie temperature much lower than room temperature, which drastically hampers their application. Here, by performing first-principles calculations and building effective model Hamiltonians, we reveal a molecular orbital-mediated magnetic coupling mechanism in two-dimensional Cr(pyz)2 (pyz = pyrazine) and the role that the valence state of the molecule plays in determining the magnetic coupling type between metal ions. Based on these, we demonstrate that a two-dimensional organic-inorganic room-temperature multiferroic, Cr(h-fpyz)2 (h-fpyz = half-fluoropyrazine), can be rationally designed by introducing ferroelectricity in Cr(pyz)2 while keeping the valence state of the molecule unchanged. Our work not only reveals the origin of magnetic coupling in 2D organic-inorganic systems but also provides a way to design room-temperature multiferroic materials rationally.

Convert Widespread Paraelectric Perovskite to Ferroelectrics.

While nature provides a plethora of perovskite materials, only a few exhibit large ferroelectricity and possibly multiferroicity. The majority of perovskite materials have the nonpolar CaTiO_{3}(CTO) structure, limiting the scope of their applications. Based on the effective Hamiltonian model as well as first-principles calculations, we propose a general thin-film design method to stabilize the functional BiFeO_{3}(BFO)-type structure, which is a common metastable structure in widespread CTO-type perovskite oxides. It is found that the improper antiferroelectricity in CTO-type perovskite and ferroelectricity in BFO-type perovskite have distinct dependences on mechanical and electric boundary conditions, both of which involve oxygen octahedral rotation and tilt. The above difference can be used to stabilize the highly polar BFO-type structure in many CTO-type perovskite materials.

Cooperative Nature of Ferroelectricity in Two-Dimensional Hybrid Organic-Inorganic Perovskites.

Two-dimensional (2D) ferroelectric (FE) hybrid organic-inorganic perovskites (HOIPs) are promising for potential applications as miniaturized flexible ferroelectric/piezoelectric devices. Recently, several 2D HOIPs [e.g., Ruddlensden-Popper type HOIP BA2PbCl4 (BA = C6H5CH2NH3+)] were reported to possess room-temperature ferroelectricity. However, the underlying microscopic mechanisms for ferroelectricity in 2D HOIPs remain elusive. Here, by performing first-principles calculations and symmetry mode analysis, we demonstrate that there exists a cooperative coupling between A-site organic molecules and B-site inorganic Pb2+ ions that is essential to the ferroelectricity in 2D BA2PbCl4. The nonpolar ground state of the closely related compounds BA2PbBr4 and BA2PbI4 can also be explained in terms of the weakened cooperative coupling. We further predict that 2D BA2PbF4 displays in-plane ferroelectricity with a higher Curie temperature and larger electric polarization. Our work not only reveals the unusual FE mechanism in 2D HOIPs but also provides a solid theoretical basis for the rational design of 2D multifunctional materials.

Spin Hamiltonians in Magnets: Theories and Computations.

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Magnetic-Domain-Wall-Induced Electrical Polarization in Rare-Earth Iron Garnet Systems: A First-Principles Study.

First-principles methods are employed to understand the existence of magnetic-domain-wall-induced electric polarization observed in rare-earth iron garnets. In contrast with previous beliefs, it is found that the occurrence of such polarization neither requires the local magnetic moments of the rare-earth ions nor noncollinear magnetism. It can rather be understood as originating from a magnetoelectric effect arising from ferromagnetic interactions between octahedral and tetrahedral Fe ions at the domain walls, and the mechanism behind is found to be a symmetric exchange-striction mechanism.

Electric-Field Switching of Magnetic Topological Charge in Type-I Multiferroics.

Applying electric field to control magnetic properties is a very efficient way for spintronics devices. However, the control of magnetic characteristics by electric fields is not straightforward, due to the time-reversal symmetry of magnetism versus spatial inversion symmetry of electricity. Such fundamental difficulty makes it challenging to modify the topology of magnetic skyrmionic states with electric field. Here, we propose a novel mechanism that realizes the electric-field (E) switching of magnetic topological charge (Q) in a controllable and reversible fashion, through the mediation of electric polarization (P) and Dzyaloshinskii-Moriya interaction (D). Such a mechanism is coined here EPDQ. Its validity is demonstrated in a multiferroic VOI_{2} monolayer, which is predicted to host magnetic bimerons. The change in magnetic anisotropy is found to play a crucial role in realizing the EPDQ process and its microscopic origin is discussed. Our study thus provides a new approach toward the highly desired electric-field control of magnetism.

Linear Versus Nonlinear Electro-Optic Effects in Materials.

Two schemes are proposed to compute the nonlinear electro-optic (EO) tensor for the first time. In the first scheme, we compute the linear EO tensor of the structure under a finite electric field, while we compute the refractive index of the structure under a finite electric field in the second scheme. Such schemes are applied to Pb(Zr,Ti)O_{3} and BaTiO_{3} ferroelectric oxides. It is found to reproduce a recently observed feature, namely, why Pb(Zr_{0.52}Ti_{0.48})O_{3} adopts a mostly linear EO response while BaTiO_{3} exhibits a strongly nonlinear conversion between electric and optical properties. Furthermore, the atomistic insight provided by the proposed ab initio scheme reveals the origin of such qualitatively different responses, in terms of the field-induced behavior of the frequencies of some phonon modes and of some force constants.

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2.

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.

Ultra-High-Temperature Ferromagnetism in Intrinsic Tetrahedral Semiconductors.

Ferromagnetic semiconductors exhibit novel spin-dependent optical, electrical, and transport properties, which are promising for next-generation highly functional spintronic devices. However, the possibility of practical applications is hindered by their low Curie temperature. Currently, whether semiconducting ferromagnetism can exist at room temperature is still unclear because of the absence of a solid physical mechanism. Here, on the basis of tight-binding model analysis and first-principles calculations, we report that ferromagnetism in a tetrahedral semiconductor originating from superexchange interactions can be strong enough to survive at room temperature because of the weakening of antiferromagnetic direct-exchange interactions. On the basis of the explored mechanism, a zinc-blende binary transition metal compound, chromium carbide, is predicted to be an intrinsic ferromagnetic tetrahedral semiconductor with a Curie temperature that is as high as ∼1900 K. These findings not only expand the understandings of magnetism in semiconductors but also are of great interest for room-temperature spintronic applications.

Designing Multifunctionality via Assembling Dissimilar Materials: Epitaxial AlN/ScN Superlattices.

First-principles calculations are performed to investigate the effect of epitaxial strain on energetic, structural, electrical, electronic, and optical properties of 1×1 AlN/ScN superlattices. This system is predicted to adopt four different strain regions exhibiting different properties, including optimization of various physical responses such as piezoelectricity, electro-optic and elasto-optic coefficients, and elasticity. Varying the strain between these four different regions also allows the creation of an electrical polarization in a nominally paraelectric material, as a result of a softening of the lowest optical mode, and even the control of its magnitude up to a giant value. Furthermore, it results in an electronic band gap that cannot only change its nature (direct vs indirect), but also cover a wide range of the electromagnetic spectrum from the blue, through the violet and near ultraviolet, to the middle ultraviolet. These findings thus point out the potential of assembling two different materials inside the same heterostructure to design multifunctionality and striking phenomena.

Electric-Field Control of Magnetization, Jahn-Teller Distortion, and Orbital Ordering in Ferroelectric Ferromagnets.

Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the PbTiO_{3}/LaTiO_{3} (PTO/LTO) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making PTO/LTO of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

Ferroelectricity with Asymmetric Hysteresis in Metallic LiOsO_{3} Ultrathin Films.

Bulk LiOsO_{3} was experimentally identified as a "ferroelectric" metal where polar distortions coexist with metallicity [Shi et al., Nat. Mater. 12, 1024 (2013)NMAACR1476-112210.1038/nmat3754]. It is generally believed that polar displacements in a ferroelectric metal cannot be switched by an external electric field. Here, via comprehensive density functional theory calculations, we demonstrate that a two-unit cell-thick LiOsO_{3} thin film exhibits a ferroelectric ground state having an out-of-plane electric dipole moment that can be switched by an external electric field. Moreover, its dipole moment-versus-electric field hysteresis loop is asymmetric because only surface Li ions' displacements are reversed by the external electric field whereas the field-induced force on inner Li atoms is nearly fully screened by itinerant electrons. As a relevant by-product of our study, we also extend the concept of "Born effective charge" to finite metallic systems, and show its usefulness to rationalize the observed effects.

Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions.

Magnetic ions M in discrete molecules and extended solids form MLn complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex MLn prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the MLn complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔLz| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of MLn chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔLz| = 0 but perpendicular to the z axis (⊥z) when |ΔLz| = 1.

Unusual Ferroelectricity in Two-Dimensional Perovskite Oxide Thin Films.

Two-dimensional (2D) ferroelectricity have attracted much attention due to their applications in novel miniaturized devices such as nonvolatile memories, field effect transistors, and sensors. Since most of the commercial ferroelectric (FE) devices are based on ABO3 perovskite oxides, it is important to investigate the properties of 2D ferroelectricity in perovskite oxide thin films. Here, based on density functional theory (DFT) calculations, we find that there exist three kinds of in-plane FE states that originate from different microscopic mechanisms: (i) a proper FE state with the polarization along [110] due to the second-order Jahn-Teller effect related to the B ion with empty d-orbitals; (ii) a robust FE state with the polarization along [100] induced by the surface effect; (iii) a hybrid improper FE state with the polarization along [110] that is induced by the trilinear coupling between two rotational modes and the A-site displacement. Interestingly, the ferroelectricity in the latter two cases becomes stronger along with decreasing the thin film thickness, in contrast to the usual behavior. Moreover, the latter two FE states are compatible with magnetism since their stability does not depend on the occupation of the d-orbitals of the B-ion. These two novel 2D FE mechanisms provide new avenues to design 2D multiferroics, as we demonstrated in SrVO and CaFeO thin film cases. Our work not only reveals new physical mechanisms of 2D ferroelectricity in perovskite oxide thin films but also provides a new route to design the high-performance 2D FE and multiferroics.