Direct Exchange Interaction Research Articles

Tunable magnetic interactions in mono-transition metal spinels MgCr2X4 (X=O,S,Se) and ACr2S4 (A=Ca,Sr,Ba)

We investigate the electronic and magnetic properties of the spinel materials $\mathrm{Mg}{\mathrm{Cr}}_{2}{X}_{4}$ ($X$ = O, S, Se) and $A{\mathrm{Cr}}_{2}{\mathrm{S}}_{4}$ ($A$ = Ca, Sr, Ba), a special type of mono-transition metal spinel material. The magnetic properties of these materials are understood by inspecting the competition between the ${90}^{\ensuremath{\circ}}$ ferromagnetic superexchange interactions and the antiferromagnetic direct exchange interactions. We found the direct exchange interaction is extremely sensitive to the distance between the Cr ions, ${d}_{\text{Cr-Cr}}$. The overall magnetic interaction can be transformed from antiferromagnetic at short ${d}_{\text{Cr-Cr}}$ to ferromagnetic at larger ${d}_{\text{Cr-Cr}}$. Therefore, we can realize different magnetic states in the same material by controlling the ${d}_{\text{Cr-Cr}}$ with external strain. Furthermore, the ferromagnetism is strengthened as tensile strain is employed, and a strategy to improve the Curie temperature, which is essential for spintronics devices, is proposed.

Variational Study of Atomic Properties of Ions and Atoms from He to Ne

An extension of the variational approach for the study of atomic properties of ions and atoms containing up to 10 electrons is presented. The study includes exact analytical calculations of all the interaction terms, including direct Coulomb interactions and exchange interactions. Two alternative formulations are considered, with one and with two variational parameters. The exact and numerical values of these parameters are obtained and tabulated. The results of this study are compared with Hartree–Fock calculations. Sample applications to electron-atom scattering and energy losses of ions in Tokamak plasmas are presented.

Ferromagnetic and antiferromagnetic orders in low dimensional PbBiFe1-xMxO4 (M = Mn and Co) solid solutions

A new solid solution of composition PbBiFe1-xMxO4 (M ​= ​Mn and Co, 0 ​≤ ​x ​≤ ​0.15–0.2) with low structural dimensions has been synthesized by solid-state reaction at 873–923 ​K. The crystal structures have been investigated using X-ray and neutron diffraction. The presence of Co2+/Co3+ on the Fe3+ sites and oxygen vacancies in PbBiFe1-xCoxO4 is revealed by its unusual volume increase and TGA, while the volume contraction of PbBiFe1-xMnxO4 indicates the substitution of Mn4+/Mn3+ on the Fe3+ sites. This leads to unexpected greater and smaller metal-metal distances inside the chains for the Co and Mn case, respectively, compared with the undoped materials. All the PbBiFe1-xMxO4 materials display long-range antiferromagnetic order but are suppressed by cationic substitution, as evidenced by a decrease in TN. Additional intrinsic short-range ferro- (or ferri-) magnetic transitions in the Co-doped materials are evidenced by magnetic hysteresis and frequency-dependent χ’ peak around TF. The introduction of ferromagnetic intrachain clusters in PbBiFe1-xCoxO4 is rationalized through a competitive mechanism between direct AFM exchange interaction and 90°- type FM superexchange interactions, which provided insights to tune the magnetic properties and design low dimensional functional materials.

Interaction between magnon and skyrmion: Toward quantum magnonics

In recent years, magnon and spin texture are attracting great interest in condensed matter physics and magnetism. Magnonics is aiming to use magnon as information carriers to realize functions for storage, transmission, and processing. Magnetic skyrmion is representative spin texture due to its topologically nontrivial properties. Since skyrmions are topologically protected, their transformation to other spin configurations requires overcoming additional topological energy barriers. Therefore, skyrmions are more stable than other trivial spin textures. In addition, the characters of nanoscale size, quasiparticle properties, and various excitation modes make them a potential candidate for spintronic application. Magnon and skyrmion, as two fundamental excitations, can coexist in magnetic systems and interplay with each other through direct exchange interactions. In this review, we provide an overview of recent theoretical and experimental studies on magnon–skyrmion interactions. We mainly focus on three kinds of magnon–skyrmion interactions: (i) magnon scattering by skyrmion, (ii) skyrmion motion driven by magnon, and (iii) coupling between magnon and skyrmion modes. The first two kinds of interactions could be clearly explained by the wave-particle interaction model on the classical level. Alternatively, the last kind of interaction could be understood by the coupled harmonic oscillator model on the quantum level, which indicates fast energy exchange and hybrid magnon states. The exploration focused on quantum phenomena of magnon has led to the emerging field of quantum magnonics and promoted applications of magnon in quantum information storage and processing. In the end, we give a perspective on the exploration of magnon–skyrmion interaction in quantum magnonics.

Emergence of Spinmerism for Molecular Spin-Qubits Generation.

Molecular platforms are regarded as promising candidates in the generation of units of information for quantum computing. Herein, a strategy combining spin-crossover metal ions and radical ligands is proposed from a model Hamiltonian first restricted to exchange interactions. Unusual spin states structures emerge from the linkage of a singlet/triplet commutable metal centre with two doublet-radical ligands. The ground state nature is modulated by charge transfers and can exhibit a mixture of triplet and singlet local metal spin states. Besides, the superposition reaches a maximum for , suggesting a necessary competition between the intramolecular and inter-metal-ligand and direct exchange interactions. The results promote spinmerism, an original manifestation of quantum entanglement between the spin states of a metal centre and radical ligands. The study provides insights into spin-coupled compounds and inspiration for the development of molecular spin-qubits.

Strain-tunable Dzyaloshinskii-Moriya interaction and skyrmions in two-dimensional Janus Cr2X3Y3 ( X, Y = Cl, Br, I, X≠Y ) trihalide monolayers

Recently, great effort has been devoted to the search for two-dimensional (2D) ferromagnetic materials with inherent strong Dzyaloshinskii--Moriya interaction (DMI). Here, through a first-principles approach, we systematically investigate the effect of biaxial strain on the DMI, the Heisenberg exchange interaction, and the magnetic anisotropy energy (MAE) of Janus Cr$_{2}$X$_{3}$Y$_{3}$ (X, Y = Cl, Br, I, X $\neq$ Y) monolayers. Both DMI and MAE can be significantly enhanced by tensile strain, while a reversal of the chirality of DMI in Cr$_{2}$Cl$_{3}$Br$_{3}$ and a switch of MAE from off-plane to in-plane in Cr$_{2}$I$_{3}$Cl$_{3}$ are induced by a compressive strain of $2\%$. Microscopically, DMI and MAE are associated mainly with the large spin--orbit coupling of the heavy nonmagnetic halogen atoms rather than that of the magnetic Cr atoms. In particular, the peculiar magnetic transition of Cr$_{2}$I$_{3}$Cl$_{3}$ is explained by competition between direct exchange and superexchange interactions. Micromagnetic simulations show that a small external magnetic field of 65~mT stabilizes a skyrmion with a diameter of 9.8~nm in the Cr$_2$I$_3$Cl$_3$ monolayer. Our results will provide guidance for further research on DMI and skyrmions in 2D Janus materials, as well as a basis for the potential applications in spintronic devices.

Exploring proximity-based recommendation criteria as a tool for information exchange and interactions between locals and tourists

Sharing economy and contemporary tourism are two emerging concepts that urge to be investigated together with new ubiquitous and immersive technologies, in the tourism and hospitality sector. In this rich scenario, we designed and implemented ShareCities, a platform to foster remote direct information exchange and meaningful interactions among tourists and locals. Exploiting ShareCities we here present an extended analysis on the opportunity to use people-to-people recommendation criteria based on proximity. We hence defined three criteria which drove our analysis: i) profile similarity, ii) geographical proximity, and iii) random exploration. Through an online questionnaire, we collect answers from 126 young-adult students, obtaining a general positive interest in the three criteria but also concerns in terms of privacy, trust, and feeling of disorientation.

An intermetallic molecular nanomagnet with the lanthanide coordinated only by transition metals

Magnetic molecules known as molecular nanomagnets (MNMs) may be the key to ultra-high density data storage. Thus, novel strategies on how to design MNMs are desirable. Here, inspired by the hexagonal structure of the hardest intermetallic magnet SmCo5, we have synthesized a nanomagnetic molecule where the central lanthanide (Ln) ErIII is coordinated solely by three transition metal ions (TM) in a perfectly trigonal planar fashion. This intermetallic molecule [ErIII(ReICp2)3] (ErRe3) starts a family of molecular nanomagnets (MNM) with unsupported Ln-TM bonds and paves the way towards molecular intermetallics with strong direct magnetic exchange interactions—a promising route towards high-performance single-molecule magnets.

Rock salt-type HoO epitaxial thin film as a heavy rare-earth monoxide ferromagnetic semiconductor with a Curie temperature above 130 K

Ho monopnictides (HoPn: Pn = N, P, As, Sb, and Bi) and monochalcogenides (HoCh: Ch = S, Se, and Te) are known to possess a nontrivial magnetic structure, while solid-phase HoO has not been synthesized yet. In this study, a rock salt-type HoO epitaxial thin film was grown by using the pulsed laser deposition method, which had a bandgap of 0.11 eV and tunable electrical conduction via its oxygen nonstoichiometry. Its Curie temperature, above 130 K, was much higher than those of HoPn and HoCh, most likely due to an enhanced direct exchange interaction. Similar to HoPn and HoCh, a HoO thin film showed a metamagnetic behavior below the Curie temperature in spite of its dominant ferromagentic ordering.

Enhanced Curie Temperature of Two-Dimensional Cr(II) Aromatic Heterocyclic Metal-Organic Framework Magnets via Strengthened Orbital Hybridization.

Two-dimensional (2D) metal-organic frameworks (MOFs) with room-temperature magnetism are highly desirable but challenging due to the weak superexchange interaction between metal atoms. For this purpose, strengthening the hybridization between metal ion and organic linkage presents an experiment-feasible chemical solution to enhance the Curie temperature. Here, we report three 2D Cr(II) aromatic heterocyclic MOF magnets with enhanced Curie temperature by bridging Cr(II) ions with pyrazine, 1,4-diphosphinine, and 1,4-diarsenin linkers, i.e., Cr(pyz)2, Cr(diphos)2, and Cr(diarse)2, and using first-principles calculations. Our results show that Cr(pyz)2, Cr(diphos)2, and Cr(diarse)2 are ferrimagnetic semiconductors. In particular, the Curie temperature of Cr(pyz)2 is estimated to be about 344 K and could be enhanced to 512 and 437 K in Cr(diphos)2 and Cr(diarse)2 by strengthening the hybridization between Cr ions and organic linkers via d-π* direct exchange interaction. This study presents a prototype to obtain room-temperature magnetism in 2D Cr(II)-based MOF magnets for nanoscale spintronics applications.

Competing magnetic states in transition metal dichalcogenide moiré materials

Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moir\'e bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metallic and insulating states that appear under different control conditions at a density of one-electron per moir\'e period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state near the model phase diagram's metal-insulator phase-transition line. Ferromagnetic insulating states, stabilized by non-local direct exchange interactions, are surprisingly prominent.

Designing Two-Dimensional Versatile Room-Temperature Ferromagnets via Assembling Large-Scale Magnetic Quantum Dots.

Two-dimensional (2D) ferromagnets possess astonishing potential in new-concept spintronics. However, most of the reported intrinsic 2D ferromagnets show a low Curie temperature far below room temperature. Here, we propose a series of 2D magnetic covalent and metal organic frameworks (COFs/MOFs) by assembling triangular zigzag graphene quantum dots (TZGDs) with various linkages, involving small-sized TZGDs, nonmetal atoms, magnetic metal atoms, and molecules. Upon first-principles calculations, we demonstrate 2D magnetic semiconductors with an enhanced Curie temperature of up to 472 K can be realized through the strong p(d)-p direct exchange interaction between TZGDs and linkages. Particularly, the TZGD size hardly affects the Curie temperature, whereas linkages can modulate the Curie temperature significantly. The TZGD size and linkages can regulate the electronic and magnetic properties of TZGD-based 2D ferromagnets. Our results confirm the possibility of designing 2D ferromagnets based on TZGDs and motivate the research of 2D ferromagnets on magnetic quantum dots and molecular magnets.

Newtype two-dimensional Cr2O3 monolayer with half-metallicity, high curie temperature, and magnetic anisotropy

Due to 100% spin polarization, half-metallic systems play a great role in the development of nanoscale spintronic devices. We conduct extensive calculations within spin-polarized density functional theory to design a newtpye two-dimensional Cr2O3 monolayer. The monolayer demonstrates robust stability as verified by formation energy, phonon spectrum, elastic constants, and molecular dynamics simulation. Each Cr2O3 unit cell gives rise to a total magnetic moment of 6.0 μB, mainly resulting from Cr sites due to the cooperation between crystal-field effect and Hund’s exchange. The monolayer is identified as a half-metallic ferromagnet with Curie temperature up to 460 K and 100% spin polarization. The super-exchange mechanism and direct exchange interaction are responsible for the ferromagnetic coupling. Moreover, the system shows large magnetic anisotropy with the easy axis in the basal plane. The excellent stability, half-metallicity, high Curie temperature, and magnetic anisotropy endow the monolayer with great potential in spintronic devices. This work provides a new pathway for designing ferromagnetic material with half-metallicity and high Curie temperature.

Improved performance of wide bandwidth neutron-spin polarizer due to ferromagnetic interlayer exchange coupling

Ferromagnetic (FM) interlayer exchange coupling of ion-beam sputtered Fe/Ge multilayers was investigated by off-specular polarized neutron scattering measurements. We observed a monotonously growing correlation of magnetic moments in the out-of-plane direction with decreasing Ge thickness. The magnetic properties of the multilayers with and without the FM interlayer exchange coupling agree well with the three- and two-dimensional random anisotropy model, respectively, assuming an FM interlayer exchange coupling comparable to the direct exchange interaction within the sample plane. The results of the Fe/Ge multilayers were used to invoke FM interlayer exchange coupling in a neutron polarizing supermirror in order to extend its bandwidth. Typically, the bandwidth is limited due to a Curie temperature close to room temperature of the thinnest Fe layers with less than 3 nm. We propose a modified layer sequence of the neutron polarizing supermirror, where the minimum Fe thickness was set to 3.5 nm, whereas the Ge thickness was reduced. A performance test of the neutron polarizing supermirror showed that the FM interlayer exchange coupling contributed to the presence of the magnetization comparable to the bulk and resulted in a marked extension in the bandwidth.

Enhanced Magnetic Interaction by Face-Shared Hydride Anions in 6H-BaCrO2H.

Studies on magnetic oxyhydrides have been almost limited to perovskite-based lattices with corner-sharing octahedra with a M-H-M (M: transition metal) angle of θ ∼ 180°. Using a high-pressure method, we prepared BaCrO2H with a 6H-type hexagonal perovskite structure with corner- and face-sharing octahedra, offering a unique opportunity to investigate magnetic interactions based on a θ ∼ 90° case. Neutron diffraction for BaCrO2H revealed an antiferromagnetic (AFM) order at TN ∼ 375 K, which is higher than ∼240 K in BaCrO3-xFx. The relatively high TN of BaCrO2H can be explained by the preferred occupancy of H- at the face-sharing site that provides AFM superexchange in addition to AFM direct exchange interactions. First-principles calculations on BaCrO2H in comparison with BaCrO2F and BaMnO3 further reveal that the direct Cr-Cr interaction is significantly enhanced by shortening the Cr-Cr distance due to the covalent nature of H-. This study provides a useful strategy for the extensive control of magnetic interactions by exploiting the difference in the covalency of multiple anions.

Recent progress on 2D magnets: Fundamental mechanism, structural design and modification

The two-dimensional (2D) magnet, a long-standing missing member in the family of 2D functional materials, is promising for next-generation information technology. The recent experimental discovery of 2D magnetic ordering in CrI3, Cr2Ge2Te6, VSe2, and Fe3GeTe2 has stimulated intense research activities to expand the scope of 2D magnets. This review covers the essential progress on 2D magnets, with an emphasis on the current understanding of the magnetic exchange interaction, the databases of 2D magnets, and the modification strategies for modulation of magnetism. We will address a large number of 2D intrinsic magnetic materials, including binary transition metal halogenides; chalogenides; carbides; nitrides; oxides; borides; silicides; MXene; ternary transition metal compounds CrXTe3, MPX3, Fe-Ge-Te, MBi2Te4, and MXY (M = transition metal; X = O, S, Se, Te, N; Y = Cl, Br, I); f-state magnets; p-state magnets; and organic magnets. Their electronic structure, magnetic moment, Curie temperature, and magnetic anisotropy energy will be presented. According to the specific 2D magnets, the underlying direct, superexchange, double exchange, super-superexchange, extended superexchange, and multi-intermediate double exchange interactions will be described. In addition, we will also highlight the effective strategies to manipulate the interatomic exchange mechanism to improve the Curie temperature of 2D magnets, such as chemical functionalization, isoelectronic substitution, alloying, strain engineering, defect engineering, applying electronic/magnetic field, interlayer coupling, carrier doping, optical controlling, and intercalation. We hope this review will contribute to understanding the magnetic exchange interaction of existing 2D magnets, developing unprecedented 2D magnets with desired properties, and offering new perspectives in this rapidly expanding field.

Two-Dimensional Cr2X3S3 (X = Br, I) Janus Semiconductor with Intrinsic Room-Temperature Magnetism.

The exploration of two-dimensional (2D) semiconductors with intrinsic room-temperature magnetism for use in nanoscale spintronic devices is of particular interest. Recently, the ferromagnetic CrX3 monolayer (X = Br, I) has received growing attention, but low critical temperature hinders its practical applications in spintronics. Here, using first-principles calculations, we report 2D Cr2X3S3 (X = Br, I) Janus semiconductors with room-temperature magnetism by replacing one layer of halogon atoms with sulfur atoms in CrX3 monolayer. Our results demonstrate that Cr2Br3S3 and Cr2I3S3 Janus crystals are ferrimagnetic semiconductors, that maintain their magnetic order, with a direct bandgap of 1.19 and 0.61 eV and high critical temperature of 387 and 447 K, respectively. The residual unpaired p electrons on the S anions lead to a strong direct-exchange interaction between the Cr and S atoms. Moreover, their room-temperature magnetism is robust under biaxial strain, while the bandgap can be remarkably modulated with strain. The novel magnetic properties in 2D Cr2X3S3 Janus magnetic semiconductors give them promising applications in spintronics.

Mixed-cation driven magnetic interaction of interstitial electrons for ferrimagnetic two-dimensional electride

Magnetism of pure electrons is fundamental for understanding diverse magnetic phenomena in condensed matters but has not been fully investigated in experiments due to the lack of a tractable model system. Such an exotic material necessitates an exclusive magnetic interaction of electrons being devoid of orbital and lattice degrees of freedom. Here, we report the two-dimensional mixed-cation [YGdC]2+∙2e− electride, showing ferrimagnetic nature from the direct exchange interaction of magnetic interstitial electrons in interlayer space. We identify that magnetic interstitial electrons are periodically localized in octahedral and tetrahedral cavities between 2D cationic Y2−xGdx arrays. The mixed configuration of non-magnetic and magnetic cations in cavities induces divergent spin states and interactions of magnetic interstitial electrons, in which their direct exchange interaction overwhelms the interactions with magnetic cations, triggering the ferrimagnetic spin-alignment. This discovery facilitates further exploration of magnetic electrides and nurtures the study of two-dimensional magnetism of layered crystals and electron phases.

Ultra-low Young’s modulus and high super-exchange interactions in monolayer CrN: A promising candidate for flexible spintronic applications* *Project supported by the National Natural Science Foundation of China (Grant No. 61888102), the National Key Research and Development Program of China (Grant No. 2016YFA0202300), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000).

Monolayer CrN has been predicted to be half-metallic ferromagnet with high Curie temperature. Due to bulk CrN’s biocompatibility, the monolayer is a promising candidate for bio-related devices. Here, using first-principles calculations based on density functional theory, we find that the formation energy of the bulk CrN stacking from layers with square lattice is only 68 meV/atom above the convex hull, suggesting a great potential to fabricate the monolayer CrN in a square lattice by using molecular beam epitaxy method. The monolayer CrN is then proved to be a soft material with an ultra-low Young’s modulus and can sustain very large strains. Moreover, the analysis of the projected density of states demonstrates that the ferromagnetic half-metallicity originates from the splitting of Cr-d orbitals in the CrN square crystal field, the bonding interaction between Cr–N, and that between Cr–Cr atoms. It is worth noting that the super-exchange interaction is much larger than the direct-exchange interaction and contributes to the ultra-high Curie temperature, which is obtained from Monte Carlo simulations based on Heisenberg model. Our findings suggest that the monolayer CrN can be an indispensable candidate for nanoscale flexible spintronic applications with good biocompatibility and is considerable appealing to be realized in experiment.

Numerical simulation of magnetic skyrmions on flat lattices

We studied several types of flat lattices with direct exchange and Dzyaloshinskii-Moriya interaction between spins: a honeycomb lattice with 3 nearest neighbours (NN), a square lattice with 4 NN and a hexagonal or triangular lattice with 6 NN. For the analysis of data obtained during the Monte Carlo simulation, a convolutional neural network was used for the recognition of different phases of the spin system which was dependent on simulation parameters such as DMI and external magnetic field (Hz). Based on these data, the phase diagrams (Hz, D) for the different lattices were plotted. The various states of the systems under observation were visualised and the boundaries between the different phases were defined as a spiral, a skyrmion and others. The data from the numerical experiments will be used in further studies to determine the model parameters of the systems for the formation of a stable skyrmion state and the development of methods for controlling skyrmions in a magnetic film.