Interatomic Exchange Interactions Research Articles

Non-collinear magnetism driven by a hidden multipolar order in PrO2

Standard microscopic approach to magnetic orders is based on assuming a Heisenberg form for inter-atomic exchange interactions. These interactions are considered as the driving force for the ordering transition with magnetic moments serving as the primary order parameter. Any higher-rank multipoles appearing simultaneously with such magnetic order are typically treated as auxiliary order parameters rather than a principal cause of the transition. In this study, we show that these traditional assumptions are violated in the case of PrO2. Evaluating a full set of Pr-Pr superexchange interactions from a first-principles many-body technique we find that its unusual non-collinear 2k magnetic structure stems from high-rank multipolar interactions, and that the corresponding contribution of the Heisenberg interactions is negligible. The observed magnetic order in PrO2 is thus auxiliary to high-rank “hidden” multipoles. Within this picture we consistently account for previously unexplained experimental observations like the magnitude of exchange splitting and the evolution of magnetic structure in external field. Our findings challenge the standard paradigm of observable magnetic moments being the driving force for magnetic transitions.

Enhanced Hydrogen Bonds of the (H2O)n (n = 4-8) Clusters Confined in Uranyl Peroxide Cluster Na20(UO2)20(O2)30.

Water is a basic resource and an essential component of living organisms. It often exhibits some novel properties under confinement. The water clusters (H2O)n (n = 4-8) confined in the cavity of uranyl peroxide cluster Na20(UO2)20(O2)30 (U20) have been computationally investigated by using ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT) calculations in this study. The results show that the confined water clusters can form hydrogen bonds with the internal oxygen atoms (Ouranyl) of U20, and their conformations changed significantly. The average lengths (2.553-2.645 Å) of hydrogen bonds in confined (H2O)n are shorter than those (2.731-2.841 Å) in the corresponding free water clusters. Moreover, these confined hydrogen bonds show better hydrogen bond patterns according to the quantified indices. The natural bond orbital (NBO) calculations determine that there is electron transferring from the U20 to its interior (H2O)n. It is the main reason for enhancing hydrogen bond interactions among the confined water molecules because their oxygen atoms are more negatively charged and their hydrogen atoms are more positively charged. The quantum theory of atoms in molecules (QTAIM) and interacting quantum atoms (IQA) analyses indicate that the confined hydrogen bonds are more covalent, based on the significant electron density ρ(r) and local energy density H(r) at the bond critical points (BCPs), and the stronger energies of interatomic exchange interactions (Vxc). These findings may help to promote the communication of confined water clusters and enrich the understating of confined hydrogen bonds.

Excitonic Order in Strongly Correlated Systems with the Spin Crossover

Features of the formation of the magnetic structure and the exciton Bose–Einstein condensate phase of magnetic excitons in strongly correlated systems near the spin crossover have been considered with the effective Hamiltonian obtained from the two-band Hubbard–Kanamori model. The coexistence of antiferromagnetism and exciton condensate, as well as the appearance of the long-range excitonic antiferromagnetic order even in the absence of the interatomic exchange interaction, has been revealed. The role of the electron–phonon coupling has been considered.

Excitonic ordering in strongly correlated spin crossover systems: Induced magnetism and excitonic excitation spectrum

The effects associated with interatomic hoppings of excitons and the excitonic Bose condensate formation in strongly correlated spin crossover systems are considered in the framework of the effective Hamiltonian for the two-band Kanamori model. The appearance of antiferromagnetic ordering due to the exciton order is found even in the absence of interatomic exchange interaction. The spectrum of excitonic excitations is calculated at various points of the temperature vs crystal field phase diagram. Outside the region of exciton ordering, the spectrum has a gap, which vanishes at the boundary of the exciton condensate phase. The nonuniform spectral weight distribution over the Brillouin zone is found. The role of electron-phonon interaction is discussed as well.

Origin of ferromagnetic interactions in NaMnCl3 : How the response theory reconciles with Goodenough-Kanamori-Anderson rules

The on-site Coulomb repulsion $U$ is the key ingredient for describing the magnetic properties of Mott insulators, leading to a popular believe that many limitations of the density-functional theory based methods can be cured by artificially incorporating such on-site interactions for localized electrons in the model form. The layered antiferromagnet NaMnCl$_3$ reveals quite a different story: while the Coulomb $U$ on the Mn sites controls the strength of antiferromagnetic superexchange interactions, an equally important parameter is the Stoner coupling ${\cal I}_{\rm Cl}$ on the ligand sites. The latter is responsible for large ferromagnetic contributions to the interatomic exchange interactions, which in NaMnCl$_3$ nearly cancel the effect of the superexchange interactions. Although such behavior is anticipated from the phenomenological Goodenough-Kamanori-Anderson rules, the quantitative description of the ligand-related contributions remains disputable. Considering NaMnCl$_3$ as an example, we discuss how they can be generally taken into account in the linear response theory to regain the dependence of the exchange interactions on ${\cal I}_{\rm Cl}$. The problem is complicated by the fact that, for the nearly filled Cl $3p$ shell, the parameters ${\cal I}_{\rm Cl}$ are sensitive to the model assumptions.

Longitudinal fluctuations of Co spin moments and their impact on the Curie temperature of the Heusler alloy Co2FeSi

The magnetism of the full Heusler alloy Co2FeSi with its high magnetic ordering temperature is studied on a first-principles basis employing the disordered local moment approximation, the magnetic force theorem and single-site spin fluctuation theory as formulated recently in the framework of the Local Spin Density Approximation. We find that the magnetic moments of Fe and Co in Co2FeSi exhibit a quite distinctive behavior at high temperatures. The Fe moments are well localized and keep their magnitude unchanged with temperature, whereas the Co moments are itinerant and show a temperature dependence. We find that the effects of magnetic disorder strongly renormalize the Fe-Co inter-atomic exchange interactions. Our results suggest a deficiency of the classical Heisenberg model with rigid localized atomic spin moments for the description of magnetism in Co2FeSi. An accurate estimation of the Curie temperature is obtained by taking into the account the thermal longitudinal fluctuations the Co moments.

Microscopic origins and stability of ferromagnetism in Co3Sn2S2

Based on the density functional theory, we examine the origin of ferromagnetism in the Weyl semimetal ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ using different types of response theories. We argue that the magnetism of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ has a dual nature and bears certain aspects of both itineracy and localization. On the one hand, the magnetism is soft, where the local magnetic moments strongly depend on temperature and the angles formed by these moments at different Co sites of the kagome lattice, as expected for itinerant magnets. On the other hand, the picture of localized spins still remains adequate for the description of the local stability of the ferromagnetic (FM) order with respect to the transversal spin fluctuations. For the latter purposes, we employ two approaches, which provide quite different pictures for interatomic exchange interactions: the regular magnetic force theorem and a formally exact theory based on the calculation of the inverse response function. The exact theory predicts ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ to be a three-dimensional ferromagnet with the strongest interaction operating between next-nearest neighbors in the adjacent kagome planes. The ligand states are found to play a very important role by additionally stabilizing the FM order. When the local moments decrease, the interplane interactions sharply decrease, first causing the FM order to become quasi-two-dimensional, and then making it unstable with respect to the spin-spiral order propagating perpendicular to the kagome plane. The latter instability is partly contributed by the states at the Fermi surface and may be relevant to the magnetic behavior of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ near the Curie temperature. Peculiarities of the half-metallic ferromagnetism in ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ are also discussed.

Exchange interactions and magnetic force theorem

We critically reexamine the problem of interatomic exchange interactions, which describe the total energy change caused by infinitesimal rotations of spins near some equilibrium state. For the small variations, such interactions can be always related to the response function. However, the form of this relation can depend on additional approximations. Particularly, the commonly used magnetic force theorem (MFT) prescribes the linear relation between the exchange interactions and the response function, while the exact theory requires this dependence to be inverse. We explore the origin and consequences of these differences in the definition for the wide class of materials: ferromagnetic Ni, antiferromagnetic NiO, half-metallic CrO2, multiferroic HoMnO3, and layered magnets CrCl3 and CrI3. While in most of these cases, MFT produces quite reasonable results and can be rigorously justifies in the long wavelength and strong-coupling limits, the exact formulation appears to be more consistent, especially in dealing with two important issues, which typically arise in the theory of exchange interactions: (i) the treatment of the ligand states, and (ii) the choice of the suitable variable for the description of infinitesimal rotations of spins. Both issues can be efficiently resolved by employing the ideas of adiabatic spin dynamics supplemented with the exact expression for the exchange interactions. Particularly, we propose a simple "downfolding" procedure for the elimination of the ligand spins by transferring their effect to the interaction parameters between the localized spins. Furthermore, we argue that the rotations of spin moments are more suitable for the description of low-energy excitations, while the rotations of the whole magnetization matrix cause much stronger perturbation in the system of spins.

Strain modulation of magnetic coupling in the metallic van der waals magnet Fe3GeTe2

We investigated the strain modulation of the magnetic states and interatomic exchange interactions in layered van der Waals magnet Fe3GeTe2 by detailed first-principles studies. The energy-minimum calculations demonstrate the ground state of bulk Fe3GeTe2 is weak antiferromagnetic coupling, in contrast to most precious reports, and it can be modulated to ferromagnetic coupling under small a-axis distortion (~2%). More importantly, we obtained the variation of exchange coupling parameters Jij and Curie temperature TC under both uniaxial and isotropic strain, and found the TC can be enhanced to room temperature in the case of uniaxial lattice distortion, especially along the a-axis. Our work clarified the role of intra- and inter-layer magnetic coupling in tuning of the ground state magnetism that can be generally applied in two-dimensional layered materials and suggested a paradigm for tuning TC with uniaxial strain in Fe3GeTe2.

Ferromagnetic alloy for high-efficiency photovoltaic conversion in solar cells: first-principles insights when doping SnO2 rutile with coupled Eu-Gd.

From results of first-principles all-electron full-potential augmented spherical-wave calculations within a generalized gradient approximation, a materials design for half-metallic ferromagnetic semiconductors based on (Eu,Gd)-doped SnO2 rutile is proposed. Moreover, their half-metallic ferromagnetic properties are homogenous and energetically stable for different crystallographic directions. Therefore, the interatomic exchange interaction between the spins of double impurity ions is a long-range ferromagnetic interaction that is sharply weakened when the distance between Eu–Gd increases. The double impurities most likely substitute adjacent Sn sites and result in strong ferromagnetic interactions by p–f hybridization between rare earth 4f and Op states. There is great interest in the configuration that has the lowest energy difference, where the double impurity substitutes the nearest neighbor Sn sites along the z-axis of SnO2 rutile. Generalized gradient approximation GGA and GGA+U calculations were performed. According to our revPBE-GGA calculations, the ferromagnetic compound is capable of absorbing 96% from the visible light. Furthermore, the transport properties at room temperature ensure excellent electrical conductivity, low thermal conductivity, and the most optimal figure of merit (ZT), which leads to high thermoelectric performance. As the latter are closely related to free flow charge carriers, we can subsequently predict that the ferromagnetic alloy will be able to be a great power source for highly effective photovoltaic conversion in solar cells. Further experimentation will be necessary to obtain confirmation of our ab initio predictions.

Magnetic and ferroelectric properties of Sr1−xBaxMnO3 from first principles

Density functional theory (DFT) calculations are used to study the magnetic and ferroelectric properties of Sr$_{1-x}$Ba$_{x}$MnO$_3$, with focus on $x=0.5$, under isotropic volume expansion/compression and biaxial strain. Our results indicate that, unexpectedly, Ba substitution alters the electronic structure in a way that, at fixed lattice parameter, notably enhances the interatomic magnetic exchange interactions. However, increasing Ba-content also causes a volume expansion which tends to weaken these interactions, leading to a net effect of weakly suppressed magnetism, as observed in experiments. The ferroelectric properties, on the other hand, are found to be less affected by changes in the electronic structure and can largely be understood in terms of the volume expansion caused by Ba-substitution. The calculated electric polarization as a function of biaxial strain in Sr$_{1-x}$Ba$_{x}$MnO$_3$ for $x=0$ and $x=0.5$, shows that the difference between the two is mainly due to differences in the magnetic order at certain strain values, accompanied by enormous magnetoelectric coupling.

Complex interplay of magnetic interactions in 5f -electron systems: The case of U2Ni2Sn

Recent experiments on a single crystal of ${\mathrm{U}}_{2}{\mathrm{Ni}}_{2}\mathrm{Sn}$ established a strong uniaxial magnetic anisotropy and an unusual magnetic structure that is antiferromagnetic both inside the U layers and between the layers. We apply fully relativistic first-principles calculations to investigate various magnetic configurations of the system. The calculations confirmed both the character of the magnetic anisotropy and the type of the ground-state magnetic structure. The study of the electron density of states shows that the lowest energy of the ground-state structure is related to the doubling of the magnetic unit cell and corresponding reduction of the Brillouin zone, leading to the formation of the energy gaps in the electronic structure. The mapping of the energies of the magnetic structures on the Heisenberg Hamiltonian of interacting atomic moments leads to a surprising result that only one of the interatomic exchange interactions is antiferromagnetic. We explain how this one antiferromagnetic interaction competing with several ferromagnetic interactions leads to the simultaneous presence of two types of antiferromagnetic behavior. We provide a simple mean-field estimate of the N\'eel temperature and conclude that short-range magnetic order, neglected on the mean-field level, may play an important role at temperatures around the critical temperature. We demonstrate the existence of self-consistent noncollinear magnetic states that limits the accuracy of treating ${\mathrm{U}}_{2}{\mathrm{Ni}}_{2}\mathrm{Sn}$ as a pure Ising magnet. We apply $\mathrm{GGA}+U$ method to examine the influence of the Hubbard parameter $U$ on the magnetic moments and energies of the magnetic configurations. An estimation of the influence of the contraction of the lattice on the magnetic properties is reported.

Ferromagnetic quasi-atomic electrons in two-dimensional electride

An electride, a generalized form of cavity-trapped interstitial anionic electrons (IAEs) in a positively charged lattice framework, shows exotic properties according to the size and geometry of the cavities. Here, we report that the IAEs in layer structured [Gd2C]2+·2e− electride behave as ferromagnetic elements in two-dimensional interlayer space and possess their own magnetic moments of ~0.52 μB per quasi-atomic IAE, which facilitate the exchange interactions between interlayer gadolinium atoms across IAEs, inducing the ferromagnetism in [Gd2C]2+·2e− electride. The substitution of paramagnetic chlorine atoms for IAEs proves the magnetic nature of quasi-atomic IAEs through a transition from ferromagnetic [Gd2C]2+·2e− to antiferromagnetic Gd2CCl caused by attenuating interatomic exchange interactions, consistent with theoretical calculations. These results confirm that quasi-atomic IAEs act as ferromagnetic elements and trigger ferromagnetic spin alignments within the antiferromagnetic [Gd2C]2+ lattice framework. These results present a broad opportunity to tailor intriguing ferromagnetism originating from quasi-atomic interstitial electrons in low-dimensional materials.

Magnetic susceptibility, EPR, NEXAFS and XPS spectra of Fe-doped CaBi2Nb2O9

In order to study the electronic state of Fe atoms and interatomic exchange interactions in solid solutions of Bi2CaNb2−2xFe2xO9−δ with perovskite structure, methods of magnetic dilution, NEXAFS, XPS and EPR spectroscopy were used. Increased values of the magnetic moment of iron atoms in solid solutions compared to pure spin values for Fe(III) are explained by the presence of clusters of Fe(III) atoms predominantly with antiferromagnetic type of exchange. Exchange parameters and cluster distribution in Bi2CaNb2−2xFe2xO9−δ solid solutions depending on the Fe content were calculated according to the Heisenberg–Dirac–van Vleck model. The effect of calcium atoms on the clusterization degree and intensity of Fe interatomic exchange interactions was displayed. XPS spectra of Bi2CaNb2-2xFe2xO9-δ, were identified to enable estimation of the effective charge of the atoms composing it. The analysis of the NEXAFS Fe2p-spectra of iron oxides and the iron-containing solid solutions revealed that Fe atoms were mainly in an oxidation state of +3. EPR spectra of Fe containing solid solution powder show an intense asymmetric line in the low-field part of the spectra at g=4.27 with weakly manifested shoulder g∼8–10 and a broad component in the g∼2 range with a high-field wing.

Discovery of twin orbital-order phases in ferromagnetic semiconducting VI3 monolayer.

Spontaneous orbital symmetry breaking in crystals gives rise to abundant novel and interesting physical properties, which sometimes are concealed by the absence of geometrical distortions. We show that a recently discovered 3d2 system, namely the layered VI3 ferromagnetic semiconductor, is a strongly correlated and orbital ordering system. Our analysis reveals that in a VI3-like system, there could be two types of orbital splitting, which are stabilized respectively by strong electronic correlation and inter-atomic exchange interactions. Consequently, on the basis of first-principles calculations, two competing low-energy phases of VI3 monolayer (denoted as twin orbital-order phases) are discovered, in which the metal-insulator transition is driven by strong electronic correlation, and the orbital symmetry breaking is robust against geometrical distortions. In addition, similar phenomena are also observed in other VI3-like systems. These findings shed light on the unusual electronic behavior of a strongly correlated 2D system and will be interesting for nanoscale multi-functional spintronic applications.

Microscopic toy model for magnetoelectric effect in polar Fe2Mo3O8

The kamiokite, Fe$_2$Mo$_3$O$_8$, is regarded as a promising material exhibiting giant magnetoelectric (ME) effect at the relatively high temperature $T$. Here, we explore this phenomenon on the basis of first-principles electronic structure calculations. For this purpose we construct a realistic model describing the behavior of magnetic Fe $3d$ electrons and further map it onto the isotropic spin model. Our analysis suggests two possible scenaria for Fe$_2$Mo$_3$O$_8$. The first one is based on the homogeneous charge distribution of the Fe$^{2+}$ ions amongst tetrahedral ($t$) and octahedral ($o$) sites, which tends to low the crystallographic P6$_3$mc symmetry through the formation of an orbitally ordered state. Nevertheless, the effect of the orbital ordering on interatomic exchange interactions does not seem to be strong, so that the magnetic properties can be described reasonably well by averaged interactions obeying the P6$_3$mc symmetry. The second scenario, which is supported by obtained parameters of on-site Coulomb repulsion and respects the P6$_3$mc symmetry, implies the charge disproportionation involving somewhat exotic $1+$ ionization state of the $t$-Fe sites (and $3+$ state of the $o$-Fe sites). Somewhat surprisingly, these scenarios are practically indistinguishable from the viewpoint of exchange interactions, which are practically identical in these two cases. However, the spin-dependent properties of the electric polarization are expected to be different due to the strong difference in the polarity of the Fe$^{2+}$-Fe$^{2+}$ and Fe$^{1+}$-Fe$^{3+}$ bonds. Our analysis uncovers the basic aspects of the ME effect in Fe$_2$Mo$_3$O$_8$. Nevertheless, the quantitative description should involve other ingredients, apparently related to the lattice and orbitals degrees of freedom.

Systematic understanding of half-metallicity of ternary compounds in Heusler and Inverse Heusler structures with 3d and 4d elements

Employing ab initio electronic structure calculations, we extensively study ternary Heusler compounds with the chemical formula X2X′Z, where X = Mn, Fe or Co; Z = Al or Si; and X′ changes along the row of 4d transition metals. A comprehensive overview of these compounds, addressing the trends in structural, electronic, magnetic properties and Curie temperature, is presented here along with the search for new materials for spintronics applications. A simple picture of hybridization of the d-orbitals of the neighboring atoms is used to explain the origin of the half-metallic gap in these compounds. We show that arrangements of the magnetic atoms in different Heusler lattices are largely responsible for the interatomic exchange interactions that are correlated with the features in their electronic structures as well as the possibility of half-metallicity. We find seven half-metallic magnets with 100% spin polarization. We identify a few other compounds with high spin polarization as ‘near half-metals’ which could be of potential use in applications as well. We find that the major features in the electronic structures remain intact if a 3d X′ constituent is replaced with an isoelectronic 4d, implying that the total number of valence electrons can be used as a predictor of half-metallic nature in compounds from the Heusler family.

Microscopic origin of ferromagnetism in the trihalides CrCl3 and CrI3

Microscopic origin of the ferromagnetic (FM) exchange coupling in CrCl$_3$ and CrI$_3$, their common aspects and differences, are investigated on the basis of density functional theory combined with realistic modeling approach for the analysis of interatomic exchange interactions. We perform a comparative study based on the pseudopotential and linear muffin-tin orbital methods by treating the effects of electron exchange and correlation in GGA and LSDA, respectively. The results of ordinary band structure calculations are used in order to construct the minimal tight-binding type models describing the behavior of the magnetic Cr $3d$ and ligand $p$ bands in the basis of localized Wannier functions, and evaluate the effective exchange coupling ($J_{\rm eff}$) between two Cr sublattices employing four different technique: (i) Second-order Green's function perturbation theory for infinitesimal spin rotations of the LSDA (GGA) potential at the Cr sites; (ii) Enforcement of the magnetic force theorem in order to treat both Cr and ligand spins on a localized footing; (iii) Constrained total-energy calculations with an external field, treated in the framework of self-consistent linear response theory. We argue that the ligand states play crucial role in the ferromagnetism of Cr trihalides, though their contribution to $J_{\rm eff}$ strongly depends on additional assumptions, which are traced back to fundamentals of adiabatic spin dynamics. Particularly, by neglecting ligand spins in the Green's function method, $J_{\rm eff}$ can easily become antiferromagnetic, while by treating them as localized, one can severely overestimate the FM coupling. The best considered approach is based on the constraint method, where the ligand states are allowed to relax in response to each instantaneous reorientation of the Cr spins, controlled by the external field.

Magnetic phase transitions induced by pressure and magnetic field: The case of antiferromagnetic USb2

Fascinating phenomena observed under applied pressure and magnetic field are attracting much research attention. Recent experiments have shown that application of the pressure or magnetic field to the ${\mathrm{USb}}_{2}$ compound induce the transformations of the ground-state antiferromagnetic (AFM) structure $(+\ensuremath{-}\ensuremath{-}+)$ to, respectively, ferromagnetic (FM) or ferrimagnetic structures. Remarkably, the magnetic critical temperature of the FM state, induced by pressure, is more than two times smaller than the N\'eel temperature of the AFM ground state. We performed density-functional theory (DFT) and DFT+$U$ studies to reveal the origin of the unusual magnetic ground state of the system and the driving mechanisms of the phase transitions. We investigate both the magnetic anisotropy properties and the parameters of the interatomic exchange interactions. To study pressure-induced effects we carry out calculations for reduced volume and demonstrate that the existence of the AFM-FM phase transformation depends on the peculiar features of the magnetic anisotropy. We discuss why the magnetic field that couples directly to the magnetic moments of atoms leads to the phase transition to the ferrimagnetic state whereas the pressure that does not couple directly to magnetic moments results in the FM structure. Our work demonstrates how the competition of different physical factors leads to variety of unusual properties of the antiferromagnetic ${\mathrm{USb}}_{2}$.

Europium Cyclooctatetraene Nanowire Carpets: A Low-Dimensional, Organometallic, and Ferromagnetic Insulator.

We investigate the magnetic and electronic properties of europium cyclooctatetraene (EuCot) nanowires by means of low-temperature X-ray magnetic circular dichroism (XMCD) and scanning tunneling microscopy (STM) and spectroscopy (STS). The EuCot nanowires are prepared in situ on a graphene surface. STS measurements identify EuCot as an insulator with a minority band gap of 2.3 eV. By means of Eu M5,4 edge XMCD, orbital and spin magnetic moments of (-0.1 ± 0.3)μB and (+7.0 ± 0.6)μB, respectively, were determined. Field-dependent measurements of the XMCD signal at the Eu M5 edge show hysteresis for grazing X-ray incidence at 5 K, thus confirming EuCot as a ferromagnetic material. Our density functional theory calculations reproduce the experimentally observed minority band gap. Modeling the experimental results theoretically, we find that the effective interatomic exchange interaction between Eu atoms is on the order of millielectronvolts, that magnetocrystalline anisotropy energy is roughly half as big, and that dipolar energy is approximately ten times lower.