First Principle Investigations of Long-range Magnetic Exchange Interactions via Polyacene Coupler

The stable organic diradicals that exhibit strong intramolecular ferromagnetic exchange interactions are suitable building blocks for organic magnetic materials (OMMs). Based on the ab initio calculations, here, we report the electronic and magnetic properties of 1,2,4-benzotriazinyl-based mono- and diradicals (known as Blatter’s radicals). The quantum mechanical calculations based on the density functional theory (DFT) reveal the merostability of the superstable Blatter’s radicals. The stability could further be enhanced by tuning the spin densities on the radical centers via the extended π-conjugation. The magnetic exchange interactions (2J) have been investigated for Blatter’s radical coupled to the nitronyl nitroxide radical (i.e., Bl-NN) as the prototypical system that has recently been synthesized by Rajca et al.. The broken-symmetry (BS) approach within the standard DFT and constraint spin-density DFT (CDFT) methods are applied to compute the exchange interactions, while for wave function-based multireference methods, the spin symmetry-adopted (e.g., CASSCF/NEVPT2) approach is applied. It is observed that the CBS-DFT provides much better 2J values as compared to the standard BS-DFT. The multireference calculations based on the minimal active space [i.e., CAS(2,2)] incorporating the delocalized magnetic orbitals provide quite reliable exchange interactions. After validating the applied computational methods, a number of ferromagnetically coupled hybrid diradicals are modeled by coupling Blatter’s monoradical with various known stable organic radicals. A few of them turned out to be quite promising candidates for the building block of OMMs.

${\mathrm{GeCo}}_{2}{\mathrm{O}}_{4}$ is a unique system in the family of cobalt spinels $A{\mathrm{Co}}_{2}{\mathrm{O}}_{4}$ ($A$= Sn, Ti, Ru, Mn, Al, Zn, Fe, etc.) in which magnetic Co ions stabilize on the pyrochlore lattice exhibiting a large degree of orbital frustration. Due to the complexity of the low-temperature antiferromagnetic (AFM) ordering and long-range magnetic exchange interactions, the lattice dynamics and magnetic structure of a ${\mathrm{GeCo}}_{2}{\mathrm{O}}_{4}$ spinel have remained puzzling. To address this issue, here we present theoretical and experimental investigations of the highly frustrated magnetic structure, and the infrared (IR) and Raman-active phonon modes in the spinel ${\mathrm{GeCo}}_{2}{\mathrm{O}}_{4}$, which exhibits an AFM ordering below the N\'eel temperature ${T}_{N}\ensuremath{\sim}21$ K and an associated cubic ($Fd\overline{3}m$) to tetragonal ($I{4}_{1}/amd$) structural phase transition whose location at ${T}_{N}$ vs at a lower ${T}_{S}\ensuremath{\sim}16$ K is controversial. Our density functional theory ($\mathrm{DFT}+U$) calculations reveal that one needs to consider magnetic-exchange interactions up to the third-nearest neighbors to get an accurate description of the low-temperature AFM order in ${\mathrm{GeCo}}_{2}{\mathrm{O}}_{4}$. At room temperature, three distinct IR-active modes (${T}_{1\mathrm{u}}$) are observed at frequencies 680, 413, and 325 ${\mathrm{cm}}^{\ensuremath{-}1}$ along with four Raman-active modes ${A}_{1\mathrm{g}}, {T}_{2\mathrm{g}}$(1), ${T}_{2\mathrm{g}}$(2), and ${E}_{\mathrm{g}}$ at frequencies 760, 647, 550, and 308 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively, which match reasonably well with our $\mathrm{DFT}+U$ calculated values. All the IR-active and Raman-active phonon modes exhibit signatures of moderate spin-phonon coupling. The temperature dependence of various parameters, such as the shift, width, and intensity, of the Raman-active modes is also discussed. Noticeable changes around ${T}_{N}\ensuremath{\sim}21$ K and ${T}_{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}16$ K are observed in the Raman line parameters of the ${E}_{\mathrm{g}}$ and ${T}_{2\mathrm{g}}$(1) modes, which are associated with the modulation of the Co-O bonds in ${\mathrm{CoO}}_{6}$ octahedra during the excitations of these modes.

We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the critical phenomena near the lower critical dimension by use of the perturbative functional renormalization group. We compute the analytic fixed points in the one-loop beta functions, and study their stability. We also calculate the critical exponents at the analytical fixed points. We show that the analytic fixed point which governs the phase transition in the system with the long-range correlations of random fields can be destabilized by the nonanalytic perturbation in both cases where the exchange interactions between spins are short ranged and long ranged. For the system with the long-range exchange interactions and uncorrelated random fields, we show that the $d\to d-\sigma$ dimensional reduction at the leading order of the $d-2\sigma$ expansion holds only for $N>2(4+3{\sqrt{3}})\simeq 18.3923\cdots$. Our investigation into the system with the long-range exchange interactions and uncorrelated random fields also gives the value of the boundary between critical behaviors in systems with long-range and short-range exchange interactions, which is identical to that predicted by Sak [Phys. Rev. B {\bf{8}}, 281 (1973)]. For the system with the long-range exchange interactions and the long-range correlated random fields, we show that the $d\to d-\sigma-\rho$ dimensional reduction does not hold within the present framework, as far as $N$ is finite.

Using density-functional theory calculations, we investigated the electronic structure and magnetic exchange interactions of the ordered 3d-5d double perovskite Sr2FeOsO6, which has recently drawn attention for interesting antiferromagnetic transitions. Our study reveals the vital role played by long-range magnetic exchange interactions in this compound. The competition between the ferromagnetic nearest neighbor Os-O-Fe interaction and antiferromagnetic next nearest neighbor Os-O-Fe-O-Os interaction induces strong frustration in this system, which explains the lattice distortion and magnetic phase transitions observed in experiments.

The electronic and magnetic properties of polyacenes become quite fascinating as the number of linearly conjugated benzene rings increases. Higher‐order conjugated polyacenes develop radicaloid characters due to the transition of electronic structures from closed‐shell to the open‐shell system. Here we have investigated the role of such polyacenes as the magnetic coupler when placed between the two spin‐sources based on nitroxy radicals. To do so, the magnetic exchange interactions ( ) are computed employing broken‐symmetry (BS) approach within the density functional theory (DFT). In this approach, various genre of exchange‐ correlation (XC) functionals such as generalized gradient approximation (GGA), meta‐GGA, hybrid functional, constrained spin density (i.e. CDFT) and on‐site Coulomb correlation corrected GGA + U functionals are adopted. All DFT based calculations estimate an exponential increase in values with the length of the couplers. This observation has been understood in terms of increase in number of near‐degenerate or quasi‐degenerate molecular orbitals (MOs), reduction of HOMO‐LUMO energy gap and descend of low‐lying excited states as the number of fused benzene rings are increased.

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT + LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.

Long-range interactions in triple quantum dots (TQDs) in Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3) = (1, 0, 1), a long-range antiferromagnetic exchange interaction (JAF) is demonstrated and induces a continuous phase transition from the separated Kondo singlet (KS) to the long-range spin singlet (LSS) state between edge dots. The expression of JAF is analytically derived and numerically verified, according to which JAF can be conveniently manipulated via gate control of the detuning energy. The long-range entanglement of Kondo clouds are proved to be quite robust at strong inter-dot coupling limit. Under equilibrium condition, it induces an unexpected peak in the spectral function of the middle dot whose singly occupied level keeps much higher than the Fermi level. Under nonequilibrium condition, higher inter-dot tunneling barrier induces an anomalous enhancement of current. These novel features can be observed in routine experiments.

Two-dimensional (2D) magnetic materials have attracted intensive research interest owing to their extraordinary electronic properties, abundant tunable functionalities and promising device applications. Early experiments attempted to extrinsically introduce magnetism into 2D nonmagnetic materials, for instance, by defect engineering or magnetic proximity. These extrinsic engineering strategies usually lead to weak magnetism and are difficult to control experimentally and thus unfavorable for applications. The discovery of intrinsic ferromagnetism in 2D insulators CrGeTe3 and CrI3 has stimulated great research effort in the field. Besides, different kinds of 2D magnetic materials have been synthesized recently, including itinerant ferromagnets Fe3GeTe2, VSe2 and MnSe x , antiferromagnets NiPS3 and FePS3, and intrinsic magnetic topological material MnBi2Te4. 2D magnetic materials can be used to construct van der Waals heterojunctions to realize novel physical phenomena such as multiferroics and quantum anomalous Hall effect, as well as to develop spintronic devices such as magnetic tunneling junctions and spin-field-effect transistors. On the other hand, first-principles calculations have been widely applied in the study of condensed matter physics and material science. Density functional theory (DFT) in the framework of Kohn-Sham scheme is one of the most popular methods for first-principles calculations. The critical issue of DFT is to use suitable exchange-correlation functional for achieving computational efficiency and accuracy simultaneously. Commonly used exchange-correlation functional, such as local density approximation and generalized gradient approximation, can successfully describe various properties of most compounds comprised of main group elements, such as atomic and electronic structures. However, these local or semi-local functional cannot provide an accurate description of localized or strongly correlated electronic states, including open-shell d and f orbitals. More advanced methods, such as the DFT+ U and hybrid functional methods, are generally desired to study 2D magnetic materials. In this review, we firstly introduced general theoretical background and computational methods on magnetism, including theory of magnetic exchange interactions and magnetic anisotropy. Magnetic exchange interactions determine magnetic orders, which are classified into local magnetic exchange and itinerant magnetic exchange according to electronic properties of the system. Magnetic anisotropy is contributed by shape anisotropy and magnetocrystalline anisotropy, which are originated from magnetic dipolar interaction and spin-orbit coupling, respectively. Then we presented theoretical progresses on the study of 2D magnetic materials, focusing on four representative material systems: (1) 2D magnetic insulators CrGeTe3 and CrI3; (2) 2D ferromagnetic metal Fe3GeTe2; (3) 2D intrinsic magnetic topological material MnBi2Te4; (4) 2D high-temperature quantum anomalous Hall insulator LiFeSe. Through these example studies, we systematically introduced fundamental mechanisms of exchange coupling and magnetic anisotropy, feasible ways to tune electronic and magnetic properties, as well as new physics introduced by the interplay of magnetism and topology. Finally we offered an outlook on future first-principles research of 2D magnetic materials.

Comparative study on effects of bridging and terminal ligands on magnetic exchange interaction in [(NH 3) 5Cr((μ-X)Cr(NH 3) 4L] n+ (X=O, OH; L=OH, OH 2, NH 3; n=4, 5): density functional theory study

We investigate the structural, electronic and magnetic properties of Mn atoms doped two-dimensional (2D) hexagonal GaAs nanosheets (GaAsNSs) using both first-principle calculations and Monte Carlo simulations. The first-principle molecular dynamics is first used to test the structural stability of Mn-doped GaAsNS ((Ga,Mn)AsNS). The analysis of spin-resolved electronic structures and determination of magnetic exchange interactions based on density functional theory (DFT) calculations reveals the existence of long-range exchange interaction in the system. Finally, Metropolis Monte Carlo simulation is employed to estimate Curie temperatures (TCs) of (Ga,Mn)AsNSs with different doping concentrations by different doping strategies. The results indicate that a TC up to 82 K can be obtained in regularly-doped (Ga,Mn)AsNSs and doping strategies have prominent impact on TCs of the systems, which emphasizes the importance of both long-range interactions and doping strategies in reduced dimensional diluted magnetic semiconductors (DMSs).

Low-lying excited states of planarly extended nanographenes are investigated using the long-range corrected (LC) density functional theory (DFT) and the spin-flip (SF) time-dependent density functional theory (TDDFT) by exploring the long-range exchange and double-excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long-range exchange interaction significantly improves the CC bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long-range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long-range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long-range exchange effects, the SF-TDDFT calculations show that the double-excitation correlation effects are negligible in the low-lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long-range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP-EA values. © 2017 Wiley Periodicals, Inc.

With ongoing efforts to synthesize super-stable Blatter's diradicals having strong ferromagnetic exchange interactions, all the 10 possible isomers of di-Blatter diradical coupled through the fused benzene rings are investigated. A variety of electronic structure theory such as broken-symmetry methods in density functional theory (DFT), spin-constraint DFT (CDFT), and wave function-based multi-configurational methods, e.g., CASSCF/NEVPT2 are applied to compute the magnetic exchange interactions. Surprisingly, anti-ferromagnetic interactions are revealed for all the stable isomers of di-Blatter diradicals. Indeed, it is commensurate with the experimental observations for the only available synthesized isomer. However, the other nine isomeric diradicals in the series are yet to be synthesized. Despite a good match between theory and experiment, the anti-ferromagnetic exchange interactions could not be explained based on the spin alternation rule due to unique spin distributions in the triazinyl ring. Thus, we propose the zonal spin-alternation rule, which explains the observed ground spin-state for the conjugated di-Blatter diradicals quite accurately. Further, the fractional spin-moment localization on the N-atoms activates multiple exchange pathways and the dominating exchange interactions render anti-ferromagnetic interactions in the conjugated isomers. The study further reveals that, due to strong steric hindrance in certain coupled isomers, the exchange interaction switches from anti-ferromagnetic to weak ferromagnetic interactions with the cost of stabilization energy of the radicals. Thus, it questions the possibility of synthesizing ferromagnetic di-Blatter diradicals.

We investigate the far-from-equilibrium nature of magnetic anisotropy and exchange interactions between molecular magnets embedded in a tunnel junction. By mapping to an effective spin model, these magnetic interactions can be divided into three types: isotropic Heisenberg, anisotropic Ising, and anisotropic Dzyaloshinski-Moriya contributions, which are attributed to the background nonequilibrium electronic structures. We further demonstrate that both the magnetic self- and exchange interactions can be controlled either electrically by gating and tuning the voltage bias, or thermally by adjusting the temperature bias. We show that the Heisenberg and Ising interactions scale linearly, while the Dzyaloshinski-Moriya interaction scales quadratically, with the molecule-lead coupling strength. The interactions scale linearly with the effective spin polarizations of the leads and the molecular coherence. Our results pave a way for smart control of magnetic exchange interactions at atomic and molecular levels.

We study the electronic structure and magnetic interactions in methylamine-intercalated orthorhombic alkali-doped fullerene $({\mathrm{CH}}_{3}{\mathrm{NH}}_{2}){\mathrm{K}}_{3}{\mathrm{C}}_{60}$ within the density functional theory. As in the simpler ammonia intercalated compound $({\mathrm{NH}}_{3}){\mathrm{K}}_{3}{\mathrm{C}}_{60}$, the orthorhombic crystal-field anisotropy $\ensuremath{\Delta}$ lifts the ${t}_{1}\mathrm{u}$ triple degeneracy at the $\ensuremath{\Gamma}$ point and drives the system deep into the Mott-insulating phase. However, the computed $\ensuremath{\Delta}$ and conduction electron bandwidth $W$ cannot alone account for the abnormally low experimental N\'eel temperature, ${T}_{\mathrm{N}}=11$ K, of the methylamine compound, compared to the much higher value ${T}_{\mathrm{N}}=40$ K of the ammonia one. Significant interactions between ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$ and ${\mathrm{C}}_{60}^{3\ensuremath{-}}$ are responsible for the stabilization of particular fullerene-cage distortions and the ensuing low-spin $S=1/2$ state. These interactions also seem to affect the magnetic properties, as interfullerene exchange interactions depend on the relative orientation of deformations of neighboring ${\mathrm{C}}_{60}^{3\ensuremath{-}}$ molecules. For the ferro-orientational order of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$-K${}^{+}$ groups we find an apparent reduced dimensionality in magnetic exchange interactions, which may explain the suppressed N\'eel temperature. The disorder in exchange interactions caused by orientational disorder of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{2}$-K${}^{+}$ groups could further contribute to this suppression.

First-principles studies of the magnetic structure and exchange interactions in the frustrated multiferroic [formula omitted