Exchange Coupling Constants Research Articles

Pragmatic Improvement of Magnetic Exchange Couplings from Subsystem Density-Functional Theory through Orthogonalization of Subsystem Orbitals

We explore a pragmatic way of correcting magnetic exchange coupling constants from subsystem density-functional theory (sDFT). Our previous work [ Faraday Discuss. 2020, 224, 201−226] showed that s...

Direct and Inverse Magnetocaloric Effects in FeRh Alloy: A Theoretical Study

There are two types of magnetocaloric effects that are the so-called direct and inverse effects originating from ferromagnetic-paramagnetic (FM-PM) and antiferromagnetic--ferromagnetic (AFM-FM) phase transitions, respectively. Here, the magnetocaloric effects of FeRh alloy, which exhibit both the direct and inverse effects, have been studied by combining first-principles calculations and Monte-Carlo simulations. The magnetic exchange coupling constants in the AFM and FM phases are evaluated by first-principles calculations based on the Liechtenstein formula. The Monte-Carlo calculations considering the two-phase mixtures of AFM and FM well reproduce the experimental magnetization curves at zero external magnetic field. It is also shown that the isothermal magnetic entropy changes near the AFM-FM transition temperature under magnetic fields are successfully reproduced based on the Maxwell relation. The entropy changes in a wide range of the magnetic fields near the AFM-FM and FM-PM transition temperatures are investigated and the direct and inverse magnetocaloric effects of FeRh are discussed. The giant relative cooling power of FeRh alloy is achieved due to the large saturation magnetizations and the first-order AFM-FM phase transition.

Synthesis and Magneto‐Structural Study of Distorted Octahedral CoII Complexes with Picolinamide and Azide (μ1,1)‐Bridge

AbstractTwo compounds [Co2(pa)2(μ1,1‐N3)2]n (1) and [Co4(pa)6(μ1,1‐N3)6] (2), (pa=picolinamide) were obtained and studied by electronic and magnetic spectroscopies. 1 is a polymer and 2 is a tetramer of mixed‐valence CoII/III. The N3− anions act as bridges between cobalt ions in the μ1,1 coordination mode. UV‐Vis spectrum analysis showed the octahedral distortion of the compounds. ESR solution spectra revealed a low‐spin ground state, s=1/2 ( ) for CoII. The energy gap was J> between levels, to , of 2; consequently, its transition would not be observed. 1 showed zero‐field splitting of the excited level with D∼0.31 cm−1. Hyperfine (59Co, I=7/2) and superhyperfine (14N, I=1) couplings were observed. Magnetic susceptibility studies (3–300 K) revealed antiferromagnetic exchange interactions in 1 and 2 with exchange coupling constants, J1=−108 cm−1 and J2=−20 cm−1, g=2 and s= , for the Co(2)‐Co(2) magnetic exchange pathways.

Synthesis, Structural Features and Physical Properties of a Family of Triply Bridged Dinuclear 3d-4f Complexes

New dinuclear MII-LnIII complexes of general formulas [Cu(µ-L)(µ-OAc)Ln(NO3)2]·CH3CN·H2O (LnIII = Gd (1), Tb (2), Dy (3) and Er (4)), [Ni(CH3CN)(µ-L)(µ-OAc)Ln(NO3)2]·CH3CN (LnIII = Nd (5), Gd (6), Tb (7), Dy (8), Er (9) and Y (10)) and [Co(CH3CN)(µ-L)(µ-OAc)Ln(NO3)2]·CH3CN (LnIII = Gd (11), Tb (12), Dy (13), Er (14) and Y (15)) were prepared from the compartmental ligand N,N′-dimethyl-N,N′-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine (H2L). In all these complexes, the transition metal ions occupy the internal N2O2 coordination site of the ligand, whereas the LnIII ions lie in the O4 external site. Both metallic ions are connected by an acetate bridge, giving rise to triple mixed diphenoxido/acetate bridged MIILnIII compounds. Direct current (dc) magnetic measurements allow the study of the magnetic exchange interactions between the 3d and 4f metal ions, which is supported by density functional theory (DFT) theoretical calculations for the GdIII-based counterparts. Due to the weak ferromagnetic exchange coupling constants obtained both experimentally and theoretically, the magneto-thermal properties of the less anisotropic systems (compounds 1 and 6) are also studied. Alternating current (ac)magnetic measurements reveal the occurrence of slight frequency dependency of the out-of-phase signal for complexes 8, 9 and 13, while complex 15 displays well-defined maximums below ~6 K.

Thresholding of the Elliott-Yafet spin-flip scattering in multi-sublattice magnets by the respective exchange energies

How different microscopic mechanisms of ultrafast spin dynamics coexist and interplay is not only relevant for the development of spintronics but also for the thorough description of physical systems out-of-equilibrium. In pure crystalline ferromagnets, one of the main microscopic mechanism of spin relaxation is the electron-phonon (el-ph) driven spin-flip, or Elliott-Yafet, scattering. Unexpectedly, recent experiments with ferro- and ferrimagnetic alloys have shown different dynamics for the different sublattices. These distinct sublattice dynamics are contradictory to the Elliott-Yafet scenario. In order to rationalize this discrepancy, it has been proposed that the intra- and intersublattice exchange interaction energies must be considered in the microscopic demagnetization mechanism, too. Here, using a temperature-dependent x-ray emission spectroscopy (XES) method, we address experimentally the element specific el-ph angular momentum transfer rates, responsible for the spin-flips in the respective (sub)lattices of Fe_{20}Ni_{80}, Fe_{50}Ni_{50} and pure nickel single crystals. We establish how the deduced rate evolution with the temperature is linked to the exchange coupling constants reported for different alloy stoichiometries and how sublattice exchange energies threshold the related el-ph spin-flip channels. Thus, these results evidence that the Elliott-Yafet spin-flip scattering, thresholded by sublattice exchange energies, is the relevant microscopic process to describe sublattice dynamics in alloys and elemental magnetic systems.

Effect of non-Heisenberg magnetic interactions on defects in ferromagnetic iron

Fundamental flaws in the Heisenberg Hamiltonian are highlighted in the context of its application to bcc Fe, including the particular issues arising when modeling lattice defects using spin dynamics. Exchange integrals are evaluated using the magnetic force theorem. The bilinear exchange coupling constants are calculated for all the interacting pairs of atomic magnetic moments in large simulation cells containing defects, enabling a direct mapping of the magnetic energy onto the Heisenberg Hamiltonian and revealing its limitations. We provide a simple procedure for extracting the Landau parameters from density-functional theory calculations to construct a Heisenberg-Landau Hamiltonian. We quantitatively show how the Landau terms correct the exchange-energy hypersurface, which is essential for the accurate evaluation of energies and migration barriers of defects.

Substituent Effects on Exchange Coupling and Magnetic Relaxation in 2,2'-Bipyrimidine Radical-Bridged Dilanthanide Complexes.

Systematic analysis of related compounds is crucial to the design of single-molecule magnets with improved properties, yet such studies on multinuclear lanthanide complexes with strong magnetic coupling remain rare. Herein, we present the synthesis and magnetic characterization of the series of radical-bridged dilanthanide complex salts [(Cp*2Ln)2(μ-5,5'-R2bpym)](BPh4) (Ln = Gd, Dy; R = NMe2 (1), OEt (2), Me (3), F (4); bpym = 2,2'-bipyrimidine). Modification of the substituent on the bridging 5,5'-R2bpym radical anion allows the magnetic exchange coupling constant, JGd-rad, for the gadolinium compounds in this series to be tuned over a range from -2.7 cm-1 (1) to -11.1 cm-1 (4), with electron-withdrawing or -donating substituents increasing or decreasing the strength of exchange coupling, respectively. Modulation of the exchange coupling interaction has a significant impact on the magnetic relaxation dynamics of the single-molecule magnets 1-Dy through 4-Dy, where stronger JGd-rad for the corresponding Gd3+ compounds is associated with larger thermal barriers to magnetic relaxation (Ueff), open magnetic hysteresis at higher temperatures, and slower magnetic relaxation rates for through-barrier processes. Further, we derive an empirical linear correlation between the experimental Ueff values for 1-Dy through 4-Dy and the magnitude of JGd-rad for the corresponding gadolinium derivatives that provides insight into the electronic structure of these complexes. This simple model applies to other organic radical-bridged dysprosium complexes in the literature, and it establishes clear design criteria for increasing magnetic operating temperatures in radical-bridged molecules.

Strongly two-dimensional exchange interactions in the in-plane metallic antiferromagnet Fe2As probed by inelastic neutron scattering

To understand spin interactions in materials of the Cu$_2$Sb structure type, inelastic neutron scattering of Fe$_2$As single crystals was examined at different temperatures and incident neutron energies. The experimental phonon spectra match well with the simulated phonon spectra obtained from density functional theory (DFT) calculations. The measured magnon spectra were compared to the simulated magnon spectra obtained via linear spin wave theory with the exchange coupling constants calculated using the spin polarized, relativistic Korringa-Kohn-Rostoker method in Zhang et al. (2013). The simulated magnon spectra broadly agree with the experimental data although, the energy values are underestimated along the $K$ direction. Exchange coupling constants between Fe atoms were refined by fits to the experimental magnon spectra, revealing stronger nearest neighbor Fe1-Fe1 exchange coupling than previously reported. The strength of this exchange coupling is almost an order of magnitude higher than other exchange interactions despite the three-dimensional nature of the phonon interactions. The lack of scattering intensity at energies above 60 meV makes unconstrained determination of the full set of exchange interactions difficult, which may be a fundamental challenge in metallic antiferromagnets.

Ising ferromagnetism and robust half-metallicity in two-dimensional honeycomb-kagome Cr2O3 layer

In contrast to the current research on two-dimensional (2D) materials, which is mainly focused on graphene and transition metal dichalcogenide-like structures, studies on 2D transition metal oxides are rare. By using ab initio calculations along with Monte Carlo simulations and nonequilibrium Green’s function method, we demonstrate that the transition metal oxide monolayer (ML) of Cr2O3 is an ideal candidate for next-generation spintronics applications. 2D Cr2O3 has honeycomb-kagome lattice, where the Dirac and strongly correlated fermions coexist around the Fermi level. Furthermore, the spin exchange coupling constant shows strong ferromagnetic (FM) interaction between Cr atoms. Cr2O3 ML has a robust half-metallic behavior with a large spin gap of ~3.9 eV and adequate Curie temperature. Interestingly, an intrinsic Ising FM characteristic is observed with a giant perpendicular magnetocrystalline anisotropy energy of ~0.9 meV. Most remarkably, nonequilibrium Green’s function calculations reveal that the Cr2O3 ML exhibits an excellent spin filtering effect.

Exchange coupling constants at finite temperature

An approach to account for the effect of thermal lattice vibrations when calculating exchange coupling parameters is presented on the basis of the Korringa-Kohn-Rostoker Green function method making use of the alloy analogy model. Using several representative systems, it is shown that depending on the material the effect of thermal lattice vibrations can have a significant impact on the isotropic exchange as well as the Dzyaloshinskii-Moriya interactions (DMI). This should lead in turn to an additional contribution to the temperature dependence of the magnetic properties of solids, which cannot be neglected in the general case. As an example, we discuss such an influence on the critical temperature of various magnetic phase transitions. In particular, in the case of skyrmion hosting materials, a strong impact of lattice vibrations on the DMI is an additional source for the temperature dependent skyrmion size and stability, which should be taken into consideration. The present approach gives also access to features of magnetic properties that are associated with static atomic displacements as, for example, in random high-entropy alloys.

A Giant Spin Molecule with Ninety-Six Parallel Unpaired Electrons

Unpaired electrons which are essential for organic radicals and magnetic materials are hardly to align parallel, especially upon the increasing of spin numbers. Here we show the antiferromagnetic interaction in the largest Cr(III)-RE (RE = rare earth) cluster {Cr10RE18} leads to 96 parallel electrons, forming a ground spins state ST of 48 for RE = Gd. This is so far the third largest ground spin state achieved in one molecule. Moreover, by using the classical Monte Calo simulation the exchange-coupling constants J_ij can be determined. Spin dynamics simulation reveals that the strong Zeeman effects of 18 Gd(III) ions stabilize the ground ferrimagnetic state and hinder the magnetization reversals of these spins. In addition, the dysprosium(III) analogue is an exchange-biasing single-molecule magnet. We believe the ferrimagnetic approach and analytical protocol established in this work can be applied generally in constructing and analysing giant spin molecules.

Influence of Nanosize Effect and Non-Magnetic Dilution on Interlayer Exchange Coupling in Fe–Cr/Cr Nanostructures

Magnetic properties of multilayered [Fe–Cr/Cr]×8 nanostructures with the interlayer exchange coupling of the antiferromagnetic type and without the interlayer coupling have been studied. The values of the saturation magnetization and the interlayer exchange coupling constant are shown to strongly depend on the thickness and non-magnetic dilution of the Fe–Cr layers. It is found that those parameters differently affect the interlayer exchange coupling, which is explained by an interplay between the size effect (the thickness of the Fe–Cr layers) and the magnetic polarization of the Fe–Cr/Cr interfaces depending on the Fe concentration.

Magnetocaloric effect in MnCoGe alloys studied by first-principles calculations and Monte-Carlo simulation

The magnetocaloric effect in orthorhombic MnCoGe1−xCux (x = 0.0–0.35) alloys are investigated by combining density functional theory (DFT) and Monte-Carlo simulation. The long-range interactions of the magnetic exchange coupling constants evaluated by the DFT calculations are considered for the Monte-Carlo simulation. The magnetic phase transition temperature is estimated by the divergence of the specific heat, and the isothermal entropy change is computed by integrating the isothermal magnetization curves with the Maxwell relation. The magnetic exchange coupling constants of the Mn-Mn pairs is decreased significantly with increasing of the concentration of Cu from 0.0 to 0.35, resulting in the rapid decrease of the Curie temperature from 618 K to 28 K. Not only the Curie temperature of the MnCoGe alloy is controllable by changing the concentration of Cu at Ge site, but also the magnetocaloric properties such as isothermal magnetic entropy change and relative cooling power are strongly dependent on the concentration of Cu.

Joining of Trinuclear Heterometallic CuII2-MII (M = Mn, Cd) Nodes by Nicotinate to Form 1D Chains: Magnetic Properties and Catalytic Activities.

In the present work, four new heterometallic coordination complexes, {[(CuL)2Mn(nic)(H2O)2](ClO4)(0.5H2O)}n (1), {[(CuL)2Cd(nic)(H2O)2](ClO4)(H2O)}n (2), [(CuL)2Mn(nic)2]·2CH3OH (3), and [(CuL)2Cd(nic)2]·2CH3OH (4) (where H2L = N,N'-bis(α-methylsalicylidene)-1,3-propanediamine and nic = nicotinate ion), have been synthesized and characterized by single-crystal X-ray crystallography. In complexes 1 and 2, the nicotinate ion acts as a bifunctional linker (N,O donor) and joins the linear trinuclear nodes to form 1D polymeric chains. However, in complexes 3 and 4, the nicotinate ion uses only the oxygen atoms of the carboxylic acid (O donor) to bind to the metal centers, forming discrete linear trinuclear units, while the pyridyl nitrogen (N donor atom) remains free. The dc magnetic susceptibility measurements show that the CuII and MnII ions are antiferromagnetically coupled in both 1 and 3, with exchange coupling constants (JMn-Cu) of -20.57 ± 0.08 and -9.38 ± 0.08 cm-1, respectively. Among the four complexes, 1 and 3 show catechol oxidase and phenoxazinone synthase like catalytic activities. The turnover numbers (kcat) of complexes 1 and 3 for catecholase activity are 1121 and 720 h-1, respectively, at an optimum pH of 8.0 and for phenoxazinone synthase activity are 429 and 398 h-1, respectively, at an optimum pH of 9.7. The higher kcat values of 1 for both reactions are attributable to a water molecule coordinated to the central MnII atom that facilitates the substrate-catalyst binding. An ESI-mass spectral analysis indicates that trinuclear heterometallic species, e.g., [(CuL)2Mn(nic)(H2O)]+ for 1 and [(CuL)2Mn(nic)]+ for 3, are the active species that bind to the substrate, and on that basis, probable mechanisms through the formation of radical intermediates have been proposed.

Tuning structural-transformation temperature toward giant magnetocaloric effect in MnCoGe alloy: A theoretical study

We propose a new model and scheme to consider the effect of structural transformation on magnetocaloric properties of Mn1-xCuxCoGe. The magnetic exchange coupling constants are estimated from first-principles calculations based on density functional theory. The magnetic phase diagram is semi-quantitatively reproduced by using mean-field approximation. The giant isothermal magnetic entropy change with the magnetostructural coupling of Mn0.89Cu0.11CoGe alloy is well reproduced by using the modified Potts model. The enhancement of magnetostructural coupling on the isothermal magnetic entropy change strongly depends on the condition of the magnetic phase transition temperature of orthorhombic and hexagonal phases.

Model Dimeric Manganese(IV) Complexes Featuring Terminal Tris-hydroxotetraazaadamantane and Various Bridging Ligands.

A series of model dinuclear manganese(IV) complexes of the general formula [(H3COH)(L')MnIV(μ-L)2MnIV(L')(HOCH3)] is presented. These compounds feature capping 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands derived from a polydentate oxime compound (L'). The bridging ligands L include azide (1), methoxide (2), and oxalate (3) anions. The magnetic properties and high-field (HF) EPR spectra of 1-3 were studied in detail and revealed varying weak antiferromagnetic coupling and modest zero-field splitting (ZFS) of the local quartet spin sites. Our HF EPR studies provide insight into the dimer ZFS, including determination of the corresponding parameters by giant spin approach for methoxido-bridged complex 2. Furthermore, the physicochemical properties of 1-3 were studied using IR, UV-vis, and electrochemical (cyclic voltammetry) methods. Theoretical exchange coupling constants were obtained using broken-symmetry (BS) density functional theory (DFT). Computational estimates of the local quartet ground spins state ZFSs of 1-3 were obtained using coupled-perturbed (CP) DFT and complete active space self-consistent field (CASSCF) calculations with n-electron valence state perturbation theory (NEVPT2) corrections. We found that the CP DFT calculations which used the B3LYP functional and models derived experimental structures performed best in reproducing both the magnitude and the sign of the experimental D values. Moreover, our computational investigation of 1-3 suggests that we observe metals sites which have an increased +3 character and are supported by redox noninnocent 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands. The latter conclusion is further corroborated by the observation that the free ligand can be readily oxidized to yield a NO-based radical.

Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations.

Exchange coupling constants (J) are fundamental to the understanding of spin spectra of magnetic systems. Here, we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. J values calculated from CC in this fashion converge smoothly toward the full configuration interaction result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary equation-of-motion CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

Strain-induced magnetic moment enhancement in frustrated antiferromagnet Cs2CuBr4

The structure and magnetic properties are studied in co-doped Cs2−xKxCuBr4−xClx and pressurized Cs2CuBr4 samples. No structural phase transition is found with doping concentration x ⩽ 0.1 and pre-compression pressure up to 4.5 GPa. The maximum susceptibility temperature Tmax of the zero-field-cooling (ZFC) susceptibility curves decreases slightly with increasing doping concentration and pre-compression pressure, indicating only small changes in the exchange coupling constants. However, an unusual enhancement of the magnetic moment deduced from the ZFC susceptibility is observed in both series samples. A maximum increase of 40% is obtained in Cs1.9K0.1CuBr3.9Cl0.1 sample. The magnetic moment increases almost linearly with decreasing Δ, i.e., defined as the wavenumber difference between the short- and long-bond stretching modes of the CuBr42− tetrahedra in the Raman spectra. The effect is likely due to the recovery of the Cu-3d orbital magnetic moments by strain-induced suppression of Jahn–Teller distortion in CuBr42− tetrahedra.

Analysis of Exchange Interactions in Dimers of Mn3 Single-Molecule Magnets, and Their Sensitivity to External Pressure

In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$\mathrm{Mn}_{3}$]$_{2}$ dimers of $\mathrm{Mn}_3$ SMMs, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $\mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $\mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.

Antiferromagnetism of Double Molybdate LiFe(MoO4)2.

The magnetic properties of the spin-5/2 double molybdate LiFe(MoO4)2 have been characterized by heat capacity, magnetic susceptibility, and neutron powder diffraction techniques. Unlike the multiferroic system LiFe(WO4)2 which exhibits two successive magnetic transitions, LiFe(MoO4)2 undergoes only one antiferromagnetic transition at TN ∼ 23.8 K. Its antiferromagnetic magnetic structure with the commensurate propagation vector k = (0, 0.5, 0) has been determined. Density functional theory calculations confirm the antiferromagnetic ground state and provide a numerical estimate of the relevant exchange coupling constants.