Magnetic Superexchange Research Articles

Evolution of tunable energy bandgap and magnetic anisotropy in Mn substituted ferrimagnetic nickel-chromates

We report a detailed study on the composition (x) dependence of structural, electronic, magnetic, and optical studies of nickel chromate spinel (NiCr2O4) at various levels of Mn substitution at B sites. No significant structural distortion from cubic symmetryFd-3m was noticed for all the compositions in the range 0 ⩽x⩽ 1 of Ni(Cr1-xMnx)2O4. However, there is significant alteration in the bond angles∠B-O-B (90.51°-93.86°) and∠A-O-B (122.48°-124.90°) (both of which follow completely opposite trend with increasingx) and bond lengths A-O (1.82-1.94 Å) and B-O (2.02-2.08 Å). The corresponding lattice parameter (a) follows Vegard's law (8.32 ± 0.001 Å ⩽a⩽ 8.45 ± 0.001Å). The electronic structure determined from thex-ray photoelectron spectroscopy reveals the divalent nature of Ni (with spin-orbit splitting energy Δ ∼ 17.62 eV). While the Cr and Mn are stable with trivalent electronic states having Δ=8 and 11.7 eV, respectively. These results are in consonance with the cationic distribution (Ni)A[(Cr1-xMnx)2]BO4obtained from the Rietveld refinement analysis. Interestingly, the current series shows a direct bandgap (EG) semiconducting nature in whichEGvaries from 1.16 to 2.40 eV within the range ofx= 0.85-0. Such variation ofEG(x) is consistent with the compositional variation of the crystal structure data with anomalous change betweenx= 0.25 and 0.6. Beyond this range, theEgmode (140 cm-1) in Raman spectra arising from Mn-O octahedral decreases continuously and vanishes at higher Mn concentrations. Our analysis shows that all the investigated compounds show long-range ferrimagnetic ordering below the Néel temperature,TFNdue to the unequal magnetic moments of the cations. However, both the ordering temperatureTFNand saturation magnetization (MS) increases progressively from 73.3 K (1500 emu mol-1) to 116 K (3600 emu mol-1) with increasing the Mn content from 0 to 1, yet the maximum anisotropy (HK~4.5 kOe,K1~2.5 × 104erg cc-1) shows an opposite trend withx. Such variation is ascribed to the altered magnetic superexchange interactions between the cations located at A and B sites following the trendJBB>JAB>JAA, (JBB/kB=13.36 K).

Electronic and magnetic excitations in La3Ni2O7

High-temperature superconductivity was discovered in the pressurized nickelate La3Ni2O7 which has a unique bilayer structure and mixed valence state of nickel. The properties at ambient pressure contain crucial information of the fundamental interactions and bosons mediating superconducting pairing. Here, using X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we identified that Ni 3dx2−y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\\end{document}, Ni 3dz2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{z}^{2}}$$\\end{document}, and ligand oxygen 2p orbitals dominate the low-energy physics with a small charge-transfer energy. Well-defined optical-like magnetic excitations soften into quasi-static spin-density-wave ordering, evidencing the strong electronic correlation and rich magnetic properties. Based on an effective Heisenberg spin model, we extract a much stronger inter-layer effective magnetic superexchange than the intra-layer ones and propose two viable magnetic structures. Our findings emphasize that the Ni 3dz2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{z}^{2}}$$\\end{document} orbital bonding within the bilayer induces novel electronic and magnetic excitations, setting the stage for further exploration of La3Ni2O7 superconductor.

Tuning Electron Transfer Coupling and Exchange Interaction in Bis-triarylamine Radical Cations and Dications by Bridge Electron Density.

The influence of the electron density of a bridge connecting two redox centers on both the intervalence hole transfer and the magnetic superexchange was investigated in a series of bridged bis-triarylamine mono- and dications. In this series, the bridge was 2,7-fluorenyl, where the bridge electron density was modified by substituents at the 9-position. For the mixed-valence monocations, the observation of both an intervalence charge transfer (IVCT) band and an absorption band associated with an electron transfer from the bridging fluorene to the triarylamine radical cation centers allowed determination of the electron transfer couplings in the framework of the three-state generalized Mulliken-Hush theory. Comparison of the derived couplings with those obtained from a classical two-state approach demonstrates an enhancement of the electronic coupling which increases with decreasing bridge state energy. For the dicationic diradical counterparts, the singlet-triplet gap (exchange interaction) was determined both experimentally and by quantum chemical methods. Hereby, an increase of antiferromagnetic coupling with a lowering of the bridge state energy by electron donating substituents was observed. Analysis of the involved molecular orbitals suggests that the ferromagnetic coupling is inversely proportional to the square of the bridge energy, which is also supported by the experimental findings. This influence of the bridge state energy on both types of interactions, electron transfer and magnetic exchange, provides a design guideline for fine-tuning the properties of electronically coupled organic redox dyads by variation of the bridge electron density.

Controlling Noncollinear Ferromagnetism in van der Waals Metal-Organic Magnets.

Van der Waals (vdW) magnets both allow exploration of fundamental 2D physics and offer a route toward exploiting magnetism in next generation information technology, but vdW magnets with complex, noncollinear spin textures are currently rare. We report here the syntheses, crystal structures, magnetic properties and magnetic ground states of four bulk vdW metal-organic magnets (MOMs): FeCl2(pym), FeCl2(btd), NiCl2(pym), and NiCl2(btd), pym = pyrimidine and btd = 2,1,3-benzothiadiazole. Using a combination of neutron diffraction and bulk magnetometry we show that these materials are noncollinear magnets. Although only NiCl2(btd) has a ferromagnetic ground state, we demonstrate that low-field hysteretic metamagnetic transitions produce states with net magnetization in zero-field and high coercivities for FeCl2(pym) and NiCl2(pym). By combining our bulk magnetic data with diffuse scattering analysis and broken-symmetry density-functional calculations, we probe the magnetic superexchange interactions, which when combined with symmetry analysis allow us to suggest design principles for future noncollinear vdW MOMs. These materials, if delaminated, would prove an interesting new family of 2D magnets.

Copper(II) salts and complexes of 2-amino-5-nitropyridine*

Four new copper compounds of 2-amino-5-nitropyridine/pyridinium (5NAP/5NAPH) have been prepared and characterized: (5NAPH)2[CuBr4], 2; (d2-5NAPD)2[CuBr4], 2a; (5NAP)2CuCl2, 3; (5NAP)2CuBr2, 4. Compounds 2 and 2a are isomorphous and crystallize in the triclinic space group P-1. Packing is stabilized by hydrogen/deuterium bonds. Short Br…Br contacts provide potential magnetic superexchange pathways, but only very weak antiferromagnetic exchange is observed (J/kB∼-2 K). Compounds 3 and 4 are also isomorphous and crystallize in the monoclinic space group P21/c. The molecules are linked into chains by bihalide bridges, and the chains linked into rectangular/square layers by short X…X. contacts. Variable temperature magnetic data were best fit by the S = ½ antiferromagnetic rectangular model for 3 (C = 0.429(1) emu-K/mol-Oe, J/kB = −9.38(6) K, J’/kB = −5.91(4) K). Variable temperature magnetic susceptibility data for 4 were best fit by the two-dimensional antiferromagnetic square lattice model (C = 0.43(1) emu-K/mol-Oe, J/kB = −36.5(2) K).

Regulating the dopant clustering in LiZnAs-based diluted magnetic semiconductor

Tuning of the magnetic interaction plays the vital role in reducing the clustering of magnetic dopant in diluted magnetic semiconductors (DMS). Due to the not well understood magnetic mechanism and the interplay between different magnetic mechanisms, no efficient and universal tuning strategy is proposed at present. Here, the magnetic interactions and formation energies of isovalent-doped (Mn) and aliovalent (Cr)-doped LiZnAs are studied based on density functional theory (DFT). It is found that the dopant–dopant distance-dependent magnetic interaction is highly sensitive to the carrier concentration and carrier type and can only be explained by the interplay between two magnetic mechanisms, i.e., super-exchange and Zener’s p–d exchange model. Thus, the magnetic behavior and clustering of magnetic dopant can be tuned by the interplay between two magnetic mechanisms. The insensitivity of the tuning effect to U parameter suggests that our strategy could be universal to other DMS.

First-Principles Studies on the Structural and Electronic Properties of α-Na2FePO4F with Strong Antisite Disorder.

Polyanionic Na2FePO4F is one of the most important cathode materials for sodium-ion batteries. The orthorhombic β-Na2FePO4F material has been studied extensively and intensively since it was proposed. In this article, a novel monoclinic sodium phosphate fluoride α-Na2FePO4F is concerned. Kirsanova's experiment showed that Na and Fe ions in α-Na2FePO4F are prone to antisite, leading to strong antisite disorder. Through first-principle calculations, we show that the steric effect, the magnetic exchange and superexchange interactions between transition-metal cations are shown to be the main driving forces for Na+/Fe2+ antisite disorder. We first calculated the crystal structures, electronic properties, and cohesive energies of all the 10 antisite phases of α-Na2FePO4F and β-Na2FePO4F. Then, we compared the difference charge densities, magnetism, binding energies, and electrostatic potentials of α-Na2FePO4F and β-Na2FePO4F materials in the antisite and pristine phases. In α-Na2FePO4F, the binding energy of the antisite phase with the lowest binding energy is almost degenerate with that of the pristine phase. Moreover, only small differences of the electrostatic potential and the charge density distribution are found between the antisite (with lowest energy) and the pristine phases of α-Na2FePO4F, which also helped elaborate the facile formation of Na+/Fe2+ antisite in the α-Na2FePO4F material. Our research contributes to the understanding of the mechanism of Na+/Fe2+ antisite and the development of high-performance polyanionic cathode materials.

Ag(II) as Spin Super-Polarizer in Molecular Spin Clusters.

Using quantum mechanical calculations, we examine magnetic (super)exchange interactions in hypothetical, chemically reasonable molecular coordination clusters containing fluoride-bridged late transition metals or selected lanthanides, as well as Ag(II). By referencing to analogous species comprising closed-shell Cd(II), we provide theoretical evidence that the presence of Ag(II) may modify the magnetic properties of such systems (including metal-metal superexchange) to a surprising degree, specifically both coupling sign and strength may markedly change. Remarkably, this happens in spite of the fact that the fluoride ligand is the least susceptible to spin polarization among all monoatomic ligands known in chemistry. In an extreme case of an oxo-bridged Ni(II)2 complex, the presence of Ag(II) leads to a nearly 17-fold increase of magnetic superexchange and switching from antiferro (AFM)- to ferromagnetic (FM) coupling. Ag(II)─with one hole in its d shell that may be shared with or transferred to ligands─effectively acts as spin super-polarizer, and this feature could be exploited in spintronics and diverse molecular devices.

New CuSO4‐related high‐temperature polymorph of AgIISO4**

AbstractSilver(II) compounds exhibit powerful oxidizing properties and strong magnetic superexchange, but most of them comprise fluoride ligands. AgSO4 is a rare fluorine‐free salt of Ag(II) which found some application in organic chemistry. Here, we report a discovery of a new AgSO4 polymorph (β). The distinct nature of the two polytypes of AgSO4 is established using powder X‐ray diffraction, vibrational spectroscopy and theoretical calculations. The β polymorph crystallizes in the monoclinic system (P21/n) and shows structural similarities with CuSO4. DFT calculations indicate very small differences in the energy of the two AgSO4 polymorphs and that the relative stability of the β polymorph should increase with temperature. The monoclinic distortion of the orthorhombic CuSO4 prototype originates from an unprecedented strong antiferromagnetic interaction between Ag sites along the unit cell diagonal.

Structure and magnetism across the Sr2−xBaxNiOsO6 phase diagram: Understanding magnetic superexchange between first and third row transition metal ions

The crystal chemistry and magnetism of compositions in the Sr2−xBaxNiOsO6 phase diagram have been investigated to better understand the superexchange interactions between 3d and 5d transition metal ions. Compositions with x ​< ​1.35 crystallize with the double perovskite structure, while those with x ​> ​1.83 crystallize in a trigonal structure that is a cation ordered variant of the 6H hexagonal perovskite structure. The Sr-rich double perovskites undergo a cubic to tetragonal distortion upon cooling that is driven by out-of-phase octahedral tilting. The tetragonal distortion occurs upon cooling below 650 ​K in Sr2NiOsO6. The temperature of this transition decreases as the barium content increases and is completely suppressed for x ​≥ ​1.2. All compositions in the double perovskite region become spin glasses below Tg ​≈ ​40 ​K, due to the competition between ferromagnetic Ni–Os and antiferromagnetic Ni–Ni and Os–Os superexchange interactions. The double perovskite compositions that are rich in barium, like Sr0.8Ba1.2NiOsO6 show some signs of magnetic ordering in small clusters, but the presence of Ba/Sr disorder inhibits long-range magnetic order. Trigonal Ba2NiOsO6 orders ferrimagnetically below TC ​= ​108 ​K. The magnetic structure of this compound contains ferromagnetic ∼180° Ni–O–Os interactions and antiferromagnetic ∼90° Ni–O–Os interactions, both in agreement with the Goodenough-Kanamori rules.

Crystal Engineering and Photomagnetic Studies of CN-Bridged Coordination Polymers Based on Octacyanidometallates(IV) and [Ni(cyclam)]2.

A series of new CN-bridged coordination networks of different dimensionality and topology was obtained through the modification of reaction conditions between [Ni(cyclam)]2+ (cyclam = 1,4,8,11-tetraazacyclotetradecane) and [W(CN)8]4–. The factors determining the reaction pathway are temperature and addition of the LiCl electrolyte. The products include three negatively charged frameworks incorporating Li+ guests: the 1D Li2[Ni(cyclam)][W(CN)8]·6H2O (1) straight chain, the 1D Li2[Ni(cyclam)][W(CN)8]·2H2O (2) zigzag chain, and the 2D Li2[Ni(cyclam)]3[W(CN)8]2·24H2O (3) honeycomb-like network, as well as the 3D two-fold interpenetrating [Ni(cyclam)]5[Ni(CN)4][W(CN)8]2·11H2O (4) network and the 1D [Ni(cyclam)][Ni(CN)4]·2H2O (5) chain, which result from partial decomposition of the starting complexes. Together with the previously characterized 3D [Ni(cyclam)]2[W(CN)8]·16H2O (6) network, they constitute the largest family of CN-bridged coordination polymers obtained from the same pair of building blocks. All compounds exhibit paramagnetic behavior because of the separation of paramagnetic nickel(II) centers through the diamagnetic polycyanidometallates. However, the presence of the photomagnetically active octacyanidotungstate(IV) ions allowed observation of the magnetic superexchange after the violet light excitation (405 nm) for compound 3, which constitutes the first example of the photomagnetic effect in a NiII–[WIV(CN)8] system. The photomagnetic investigations for fully hydrated and dehydrated sample of 3, as well as for the isostructural octacyanidomolybdate(IV)-based network are discussed.

Effect of Eu3+ on the Structural, Magnetic and Mössbauer Spectroscopy Studies of Copper Ferrite

Here, theoretical and practical methods were used to study the impact of Eu3+ substitution on copper ferrites. The spinel cubic structure of the synthesised samples is crystalline, and XRD analysis revealed the presence of a trace amount of the impurity Fe2O3 phase. The range of the estimated crystallite sizes is between 18 and 27 nm. FTIR spectra of the ferrites exhibited the presence of functional groups of spinel ferrites. The temperature-dependent Mössbauer spectra of CuFe2-xEuxO4 (x = 0, 0.01, 0.02, 0.03) (CEF) were collected at 300 K, 200 K, 100 K, and 14 K. Room temperature spectra consist of asymmetrically broadened sextets and quadruple split lines. The intensity of quadrupole split lines decreases along with the reduction in temperature. The observed changes in the structure of the Mössbauer spectra are typical of nanosized particles. The presence of paramagnetic lines at temperatures lower than the Curie temperature, asymmetric lines with sharp external fronts, and significantly diffused internal fronts is a sign of superparamagnetic relaxation. The partial substitution of Fe3+ ions by Eu3+ ions causes the redistribution of A and B cations, which leads to the alteration in angle and bond length of magnetic superexchange links. DFT calculations support the preference for octahedral Eu-doping in combination with the CuFe2O4 matrix, which results in local structural disorders that affect both the material's magnetic and electrical characteristics. The size, shape, interaction with the matrix, and crystallite characteristics all affect the material's magnetic properties. A weak ferromagnetic characteristic is indicated by the magnetic properties, and the magnetization values increase as Eu increases as a result of changes in crystallite size. As a result, our findings imply that synthesised samples are appropriate for applications involving hyperthermia.

Magnetic Superexchange Induced Quantum Phase Transition in Cr2B2 MBene

Stable long-range magnetic order in low-dimensional semiconductors up to room temperature has long been the pursuit of researchers for their potential applications in the field of spintronic and memory devices. However it is a great challenge to achieve magnetic phase transition together with a controllable band structure in two-dimensional magnetic materials simultaneously. Through fully terminated oxygen group adsorption, the transformation from ferromagnetic metal to antiferromagnetic semiconductor with a high Néel temperature (425 K) has been achieved in Cr2B2 MBene, which is attributed to superexchange interaction between the interlayer magnetic chromium (Cr) atoms. Furthermore, exotic quantum phase transition between two different antiferromagnetic states of Cr2B2O2, together with the transition from semiconductor to metal, is observed when applying compressive strain. Interestingly, ferromagnetic half-metal and ferromagnetic semiconductor states are achieved by nonuniform oxygen group adsorption, resulting from electrical potential difference between the Cr atomic layers and thus built-in electric field. Our results reveal the origin of magnetic phase transition in Cr2B2 MBene and offer a new avenue to obtain magnetic multifunctional materials for spintronic devices.

Pressure Control of the Structure and Multiferroicity in a Hydrogen-Bonded Metal-Organic Framework.

Multiferroic materials with the cross-coupling of magnetic and ferroelectric orders provide a new platform for physics study and designing novel electronic devices. However, the weak coupling strength of ferroelectricity and magnetism is the main obstacle for potential applications. The recent research focuses on enhancing the coupling effect via synthesizing novel materials in a chemical route or tuning the multiferroicity in the physical way. Among them, pressure is an effective method to modify multiferroic materials, especially when the chemical doping has reached its tuning limit. In this work, we systemically studied the multiferroic properties in a hydrogen-bonded metal-organic framework (MOF) [(CH3)2NH2]Ni(HCOO)3 under high pressure. X-ray diffraction and Raman scattering reveal that a structural phase transition occurs in a pressure region of 6-9 GPa, and the crystal structure is greatly modified by pressure. With the ac magnetic susceptibility, pyroelectric current, and dielectric constant measurements, we obtain the multiferroic property evolution under high pressure and create a temperature-pressure phase diagram. Our study demonstrates that the pressure can modify the magnetic superexchange interaction and hydrogen bonding simultaneously in these perovskite-like MOFs. The multiferroic phase region has been expanded to higher temperature due to the pressure-enhanced spin-phonon coupling effect.

Structural Phase Transitions and Magnetic Superexchange in MI AgII F3 Perovskites at High Pressure.

Pressure‐induced phase transitions of MIAgIIF3 perovskites (M=K, Rb, Cs) have been predicted theoretically for the first time for pressures up to 100 GPa. The sequence of phase transitions for M=K and Rb consists of a transition from orthorhombic to monoclinic and back to orthorhombic, associated with progressive bending of infinite chains of corner‐sharing [AgF6]4− octahedra and their mutual approach through secondary Ag⋅⋅⋅F contacts. In stark contrast, only a single phase transition (tetragonal→triclinic) is predicted for CsAgF3; this is associated with substantial deformation of the Jahn–Teller‐distorted first coordination sphere of AgII and association of the infinite [AgF6]4− chains into a polymeric sublattice. The phase transitions markedly decrease the coupling strength of intra‐chain antiferromagnetic superexchange in MAgF3 hosts lattices.

Temperature and pressure driven spin transitions and piezochromism in a Mn-based hybrid perovskite

Hybrid perovskites have been at the forefront of condensed matter research particularly in context of device applications primarily in relation to applications in the field of solar cells. In this article, we demonstrate that several new functionalities may be added to the arsenal of hybrid perovskites, in terms of external stimuli driven spin transitions as well as piezochromism. As an example, we study Dimethylammonium Manganese Formate (DMAMnF), a hybrid perovskite investigated quite extensively experimentally. We show by employing first principles DFT+U calculations with the aid of ab initio molecular dynamics calculations that DMAMnF shows temperature and pressure driven spin transitions, from a low spin $S=1/2$ to a high spin $S=5/2$ state. This transition is accompanied by a hysteresis, and we find that this hysteresis and the transition temperature are quite close to room temperature, which is desirable for device applications particularly in memory, display, and switching devices. The operating pressure is a few GPa, which is accessible in standard laboratory settings. We find that the cooperative behaviour showing up as hysteresis accompanying the transition is driven primarily by elastic interactions, assisted by magnetic superexchange between Mn atoms. Last but not least we demonstrate that the spin transition is associated with piezochromism which could also be important for applications.

Electronic phase separation in the hexagonal perovskite Ba3SrMo2O9

Competition between exotic magnetic and electronic ground states underpins the properties of strongly correlated transition metal oxides and can result in electronic phase separation (EPS). The 6H-perovskite ${\mathrm{Ba}}_{3}{\mathrm{SrMo}}_{2}{\mathrm{O}}_{9}$ exhibits no magnetic order down to 1.6 K and EPS is observed at 230 K. The ground state of this material contains a complex mixture of spin-singlet ${\mathrm{Mo}}_{2}{\mathrm{O}}_{9}$ dimers and quasimolecular ${\mathrm{Mo}}_{2}{\mathrm{O}}_{9}$ clusters. Segregation in ${\mathrm{Ba}}_{3}{\mathrm{SrMo}}_{2}{\mathrm{O}}_{9}$ emerges due to competition between direct Mo--Mo bonding and Mo--O--Mo magnetic superexchange, comprising an unusual mechanism of EPS in transition-metal oxides.

Sorption and Magnetic Properties of Oxalato-Based Trimetallic Open Framework Stabilized by Charge-Assisted Hydrogen Bonds.

We report a new structure of {[Co(bpy)2(ox)][{Cu2(bpy)2(ox)}Fe(ox)3]}n·8.5nH2O NCU-1 presenting a rare ladder topology among oxalate-based coordination polymers with anionic chains composed of alternately arranged [Cu2(bpy)2(ox)]2+ and [Fe(ox)3]3− moieties. Along the a axis, they are separated by Co(III) units to give porous material with voids of 963.7 Å3 (16.9% of cell volume). The stability of this structure is assured by a network of stacking interactions and charge-assisted C-H…O hydrogen bonds formed between adjacent chains, adjacent cobalt(III) units, and alternately arranged cobalt(III) and chain motifs. The soaking experiment with acetonitrile and bromobenzene showed that water molecules (8.5 water molecules dispersed over 15 positions) are bonded tightly, despite partial occupancy. Water adsorption experiments are described by a D’arcy and Watt model being the sum of Langmuir and Dubinin–Serpinski isotherms. The amount of primary adsorption sites calculated from this model is equal 8.2 mol H2O/mol, being very close to the value obtained from the XRD experiments and indicates that water was adsorbed mainly on the primary sites. The antiferromagnetic properties could be only approximately described with the simple CuII-ox-CuII dimer using H = −J·S1·S2, thus, considering non-trivial topology of the whole Cu-Fe chain, we developed our own general approach, based on the semiclassical model (SC) and molecular field (MF) model, to describe precisely the magnetic superexchange interactions in NCU-1. We established that Cu(II)-Cu(II) coupling dominates over multiple Cu(II)-Fe(III) interactions, with JCuCu = −275(29) and JCuFe = −3.8(1.6) cm−1 and discussed the obtained values against the literature data.

Magnetic superexchange couplings in Sr2IrO4

We investigate the magnetic couplings in ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ in the Mott-insulating picture, combining density-functional theory, dynamical mean-field theory, and many-body perturbation theory. We first determine the form of the ${j}_{\mathrm{eff}}=1/2$ pseudospin via the local-density-approximation $+$ dynamical mean-field theory approach. Next we study the magnetic interactions in the strong-to-intermediate coupling regime. To this end, we calculate the superexchange pseudospin tensors ${\mathrm{\ensuremath{\Gamma}}}_{1}, {\mathrm{\ensuremath{\Gamma}}}_{2}$, and ${\mathrm{\ensuremath{\Gamma}}}_{3}$ up to fourth order and analyze their dependence on the screened Coulomb interaction integrals $U$ and $J$. We show that, due to term cancellations, the experimental nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{1}$ is reasonably well reproduced for a whole range of realistic $(U,J)$ values. We show that increasing the Hund's rule coupling $J$ (within the window of realistic values) can lead to large fourth-order contributions, which could explain the ferromagnetic next-nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{2}$ extracted from the spin-wave dispersion. This regime is characterized by a sizable ring exchange $K$. For $(U,J)$ values that yield a Mott insulator with a half-filled ${j}_{\mathrm{eff}}=1/2$ state, however, fourth-order terms remain minor even if the gap is small. For no realistic parameters, we find a sizable next-next-nearest-neighbor coupling ${\mathrm{\ensuremath{\Gamma}}}_{3}\ensuremath{\sim}|{\mathrm{\ensuremath{\Gamma}}}_{2}|$. Possible implications are discussed.

Formate-mediated magnetic superexchange in the model hybrid perovskite [(CH3)2NH2]Cu(HCOO)3: applicability criteria for the GKA rules

Formate-mediated magnetic superexchange in the model hybrid perovskite [(CH₃)₂NH₂]Cu(HCOO)₃: applicability criteria for the GKA rules