Exchange Coupling Constants Research Articles

Chemical trend on the lanthanide-radical exchange coupling

From the high-frequency electron paramagnetic resonance spectra on [Ln(hfac)3(TMIO)2] (Ln=Tb, Dy; TMIO=1,1,3,3-tetramethylisoindolin-2-oxyl; hfac=1,1,1,5,5,5-hexafluoropentane-2,4-dionate) the level-crossing fields of the radical signal of the Tb and Dy complexes were determined to be 21.9(3) and 20(2)T, respectively. The observation of a single signal is consistent with the two-fold molecular symmetry. The coupling constants were evaluated, giving JTb-rad/kB=−4.47(4)K and JDy-rad/kB=−3.2(4)K. Since the exchange coupling constant in [Gd(hfac)3(TMIO)2] has already been determined to be JGd-rad/kB=−12.5(4)K from the magnetic susceptibility measurements, the lanthanide-dependence on |JLn-rad| was concluded as |JGd-rad|>|JTb-rad|>|JDy-rad| in this series.

Giant Exchange Coupling Evidenced with a Magnetization Jump at 52 T for a Gadolinium-Nitroxide Chelate.

The Gd-radical complex [GdIII(hfac)3(6bpyNO)] (6bpyNO = 2,2'-bipyridin-6-yl tert-butyl nitroxide; Hhfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dione) showed a magnetization jump at 52 T observed in a pulsed-field facility, corresponding to an exchange coupling constant of -17.4 K. Furthermore, hysteretic behavior due to a relatively slow magnetization reversal was recorded around 2 T. From the high-frequency EPR study, the exchange coupling between Gd and radical spins accompanies an anisotropic character, which is responsible for both the broad jump and the slow magnetization reversal.

MnGa-based fully perpendicular magnetic tunnel junctions with ultrathin Co2MnSi interlayers

Because tetragonal structured MnGa alloy has intrinsic (not interface induced) giant perpendicular magnetic anisotropy (PMA), ultra-low damping constant and high spin polarization, it is predicted to be a kind of suitable magnetic electrode candidate in the perpendicular magnetic tunnel junction (p-MTJ) for high density spin transfer torque magnetic random access memory (STT-MRAM) applications. However, p-MTJs with both bottom and top MnGa electrodes have not been achieved yet, since high quality perpendicular magnetic MnGa films can hardly be obtained on the MgO barrier due to large lattice mismatch and surface energy difference between them. Here, a MnGa-based fully p-MTJ with the structure of MnGa/Co2MnSi/MgO/Co2MnSi/MnGa is investigated. As a result, the multilayer is with high crystalline quality, and both the top and bottom MnGa electrodes show well PMA. Meanwhile, a distinct tunneling magnetoresistance (TMR) ratio of 65% at 10 K is achieved. Ultrathin Co2MnSi films are used to optimize the interface quality between MnGa and MgO barrier. A strong antiferromagnetic coupling in MnGa/Co2MnSi bilayer is confirmed with the interfacial exchange coupling constant of −5erg/cm2. This work proposes a novel p-MTJ structure for the future STT-MRAM progress.

Determination of exchange coupling constants in linear polyradicals by means of local spins

This work extends the previously reported studies (Oliva et al. in Theor Chem Acc 132:1329, 2013, Theor Chem Acc 134:9, 2015) on electronic structures of simple polyhedral polyradicals constructed from s = ½ closo-carborane CB11H12 • structural units. Linear polyradical structures obtained from these units connected by means of –CH2– bridges are described in terms of their energies and local spins. The resulting spin states of these chains have been mapped onto a phenomenological Heisenberg spin Hamiltonian, providing the evaluation of spin exchange coupling constants and performing an analysis of their transferability. The eigenvalues of this Hamiltonian allow one to determine the ground spin state and the suitable combinations of spin orientations of the magnetic sites. We prove that the minimal energy in all these systems corresponds to the highest-spin state.

Magnetic and HFEPR Studies of Exchange Coupling in a Series of μ-Cl Dicobalt Complexes.

We report three dinuclear cobalt(II) complexes, [Co(L)Cl2]2 (L = bpy, mbpy, and dmpbt), that are bridged solely by chloride ions. High-field electron paramagnetic resonance and magnetometric measurements were applied to investigate the magnetic intramolecular Co-Co interactions. Simulation results based on the multispin model reveal that the complexes are weakly ferromagnetically coupled and that the isotropic exchange coupling constants differ slightly for the three complexes. Moreover, the competing effects of zero-field splitting and magnetic coupling on the temperature-dependent magnetic susceptibility were analyzed.

What Controls the Magnetic Exchange and Anisotropy in a Family of Tetranuclear {Mn2IIMn2III} Single-Molecule Magnets?

Twelve heterovalent, tetranuclear manganese(II/III) planar diamond or "butterfly" complexes, 1-12, have been synthesized and structurally characterized, and their magnetic properties have been probed using experimental and theoretical techniques. The 12 structures are divided into two distinct "classes". Compounds 1-8 place the Mn(III), S = 2, ions in the body positions of the butterfly metallic core, while the Mn(II), S = 5/2, ions occupy the outer wing sites and are described as "Class 1". Compounds 9-12 display the reverse arrangement of ions and are described as "Class 2". Direct current susceptibility measurements for 1-12 reveal ground spin states ranging from S = 1 to S = 9, with each complex displaying unique magnetic exchange parameters (J). Alternating current susceptibility measurements found that that slow magnetic relaxation is observed for all complexes, except for 10 and 12, and display differing anisotropy barriers to magnetization reversal. First, we determined the magnitude of the magnetic exchange parameters for all complexes. Three exchange coupling constants (Jbb, Jwb, and Jww) were determined by DFT methods which are found to be in good agreement with the experimental fits. It was found that the orientation of the Jahn-Teller axes and the Mn-Mn distances play a pivotal role in determining the sign and strength of the Jbb parameter. Extensive magneto-structural correlations have been developed for the two classes of {MnII2MnIII2} butterfly complexes by varying the Mnb-O distance, Mnw-O distance, Mnb-O-Mnb angle (α), Mnb-O-Mnb-O dihedral angle (γ), and out-of-plane shift of the Mnw atoms (β). For the magnetic anisotropy the DFT calculations yielded larger negative D value for complexes 2, 3, 4, and 6 compared to the other complexes. This is found to be correlated to the electron-donating/withdrawing substituents attached to the ligand moiety and suggests a possible way to fine tune the magnetic anisotropy in polynuclear Mn ion complexes.

Magnetically ordered phase near transition to Bose-glass phase

We discuss magnetically ordered ("superfluid") phase near quantum transition to Bose-glass phase in a simple modeling system, Heisenberg antiferromagnet in spatial dimension $d>2$ in external magnetic field with disorder in exchange coupling constants. Our analytical consideration is based on hydrodynamic description of long-wavelength excitations. Results obtained are valid in the entire critical region near the quantum critical point (QCP) allowing to describe a possible crossover from one critical behavior to another. We demonstrate that the system behaves in full agreement with predictions by Fisher et al.\ (Phys.\ Rev.\ B {\bf 40}, 546 (1989)) in close vicinity of QCP. We find as an extension to that analysis that the anomalous dimension $\eta=2-d$ and $\beta=\nu d/2$, where $\beta$ and $\nu$ are critical exponents of the order parameter and the correlation length, respectively. The density of states per spin of low-energy localized excitations are found to be independent of $d$ ("superuniversal"). We show that many recent experimental and numerical results obtained in various 3D systems can be described by our formulas using percolation critical exponents. Then, it is a possibility that a percolation critical regime arises in the ordered phase in some 3D systems not very close to QCP.

Constrained DFT+U approach for understanding the magnetic behaviour of ACr2O4 (A = Zn, Mg, Cd and Hg) compounds

In this work, we try to understand the inconsistency reported by Yaresko (2008) [10] in the theoretically estimated sign of nearest neighbour exchange coupling constant (J1) and variation of its magnitude with increasing U in ACr2O4 (A=Zn, Cd, Mg and Hg) compounds by using density functional theory. In unconstrained calculations, the sign of J1 and variation of its magnitude as a function of U in the present study are not consistent with the experimental data and not according to the relation, J1∝t2U, respectively especially for CdCr2O4 for U>3 eV and HgCr2O4 for U=2–6 eV. Such an inconsistent behaviour of J1 is almost similar to that of Yaresko for these two compounds for U=2–4 eV. For ZnCr2O4 and MgCr2O4, the sign of J1 and variation of its magnitude in the present work are in accordance with the experimental data and above mentioned relation, respectively for U=2–6 eV and are similar to that of Yaresko for ZnCr2O4 for U=2–4 eV. However, in constrained calculations the sign of J1c and variation of its magnitude in the present work are according to experimental data and above mentioned relation, respectively for all four compounds. Hence, the present study shows the importance of constrained calculations in understanding the magnetic behaviour of these spinels. The values of magnitude of Curie–Weiss temperature (ΘCW)c for ZnCr2O4>MgCr2O4>CdCr2O4>HgCr2O4 for U=2–5 eV, which are according to the order of experimentally observed values for these spinels. The calculated values of (ΘCW)c for ZnCr2O4, MgCr2O4, CdCr2O4 and HgCr2O4 are −982 K, −721 K, −147 K and −122 K, respectively at U=5 eV.

Strong direct exchange coupling and single-molecule magnetism in indigo-bridged lanthanide dimers.

The synthesis, structure and magnetic properties of the indigo-bridged dilanthanide complexes [{(η5-Cp*)2Ln}2(μ-ind)]n- with Ln = Gd or Dy and n = 0, 1 or 2 are described. The gadolinium complexes with n = 0 and 2 show typically weak exchange coupling, whereas the complex bridged by the radical [ind]3- ligand shows an unusually large coupling constant of J = -11 cm-1 (-2J formalism). The dysprosium complexes with n = 0 and 1 are single-molecule magnets in zero applied field, whereas the complex with n = 2 does not show slow magnetic relaxation.

Structural, magnetic and electronic properties of Ni-Mn-Ga-Cr Heusler alloys: ab initio and Monte Carlo studies

A series of Ni2Mn1-xCrxGa (0.125≤x≤0.5) Heusler alloys have been theoretically investigated by density functional theory as well as finite-temperature Monte Carlo simulations to obtain Curie temperatures. By using ab initio calculations it was found that the most energetically favorable magnetic state for both austenite and martensite phases in Ni2Mn1-xCrxGa is a ferromagnetic state. Besides, an increase in energy difference between austenite and martensite with increasing Cr content was observed. With respect to the exchange coupling constants, it was shown that Ni-Mn(Cr) pairs show the strongest ferromagnetic exchange interaction between nearest neighbor atoms in austenite of all alloys considered. It was demonstrated that the most part of total spin up and spin down density of states is caused by Ni atoms. Estimated Curie temperatures were found to be less than experimental ones approximately by 80 K, but the TC(x) function repeats pattern of experimental one.

Complex investigation of structural and magnetic properties of the Ni-Mn-(Ga, Ge) alloys within ab initio approach

In this work we report results of ab initio calculations of structural and magnetic properties in a series of Heusler compositions Ni2+xMn1-x(Ga, Ge) (x = 0, 0.25, 0.50 and 0.75). It was found that, in contrast to the Ni-Mn-Ga, the martensitic transformation in Ni-Mn-Ge alloys occurs only in off-stoichiometric compositions. For both types of alloys studied in this work, the energy difference between austenite and martensite, were found to increase with increasing Ni excess, x, while the martensite is lower in energy compared with the austenite. By using optimized lattice parameters for the austenite, exchange coupling constants required for estimation of the Curie temperature by means of Monte Carlo simulations have been obtained. It was shown that the Curie temperature for the austenitic phase of Ni2+xMn1-x(Ga, Ge) decrease with increasing a Ni excess. In general, these theoretical results agree well with available experimental data and other theoretical results, and reveal a clear chemical trend.

Possible crossover to percolation scenario near superfluid-Bose-glass transition

We discuss magnetically ordered (“superfluid”) phase near quantum transition to Bose-glass phase in a simple modeling system, Heisenberg antiferromagnet in spatial dimension d>2 in external magnetic field with disorder in exchange coupling constants. Our analytical consideration is based on hydrodynamic description of long-wavelength excitations and it is valid in the entire critical region near the quantum critical point (QCP). We demonstrate that the system behaves in full agreement with predictions by Fisher et al. (Phys. Rev. B 40, 546 (1989)) in close vicinity of QCP. On the other hand, we show that many recent experimental and numerical results obtained in various 3D systems can be described by our formulas using percolation critical exponents. Then, it is a possibility that a percolation critical regime arises in the ordered phase in some 3D systems not very close to QCP.

Structural transitions in iron-based Ba3NbFe3Si2O14 langasite at high pressures

Synchrotron X-ray diffraction studies of the structural characteristics of Ba3NbFe3Si2O14 langasite were performed at high hydrostatic pressures (up to 60 GPa) created in a diamond anvil cell. The Mössbauer absorption spectra of 57Fe nuclei and optical absorption spectra were recorded at pressures up to 10 and 54 GPa, respectively. The cascade of structural phase transitions at pressures of about ∼ 3, ∼ 20, and ∼ 41 GPa was discovered. The first transition corresponds to the displacements of light oxygen atoms and associated with an increase in the local symmetry of oxygen 3f tetrahedra surrounding iron ions. The volume drop at the first transition is about 1.5%. The second transition at ∼ 20 GPa is accompanied by a pronounced change in the lattice parameters a and c, while the unit cell volume undergoes a stepwise drop by 7%. Significant decrease in the parameter c at the structural transition should result in a strong increase of the exchange coupling constants between iron ions in neighboring ab planes, which may lead to a giant increase in the Néel temperature in this crystal at pressures above ∼ 20 GPa. At the third transition at about 38–44 GPa, only a small anomaly in the relation is observed, but this anomaly is accompanied by substantial changes in the optical gap and in the quadruple splitting parameter.

The role of non-covalent interaction in the hexadentate coordination environment on the magnetic behavior of binuclear helical complex [Ni2(L)2]4+: A broken-symmetry approach

The nature of bonds in coordination environments of a homobimetallic supramolecular helicate complex has been studied using Quantum Theory of Atom in Molecule (QTAIM) and the electron localization function (ELF) analysis. The topological parameters at critical points (CPs) indicate that all bonds between nickel ions and ligand donors have non-covalent nature. The lack of any disynaptic basins in coordination environments confirms the QTAIM results. The broken-symmetry (BS) approach has been employed to predict properties of the complex using B3LYP functional and different basis sets for metal ions. The calculated magnetic exchange coupling constants (J) are 2683.34 and 2897.87cm−1 for different metal basis sets. The NBO analysis has been performed to explain the role of coordination bonds nature in strong ferromagnetic behavior of the complex.

Controlling magnetic interfaces using ordered surface alloys

We have investigated the growth and magnetic properties of Fe thin films on the clean W(100) surface and W(100)-M c(2 \ifmmode\times\else\texttimes\fi{} 2) ($M=\mathrm{Cu}$, Ag, Au) surface alloy substrates. The influence of the interface on magnetism is assessed experimentally by studying sensitive threshold behavior in magnetic ordering using spin-polarized low-energy electron microscopy. The onset of ferromagnetic order that occurs with increasing film thickness at room temperature due to finite-sized scaling of the Curie temperature varies reproducibly among films on W(100) and the surface alloys. Magnetic moments and exchange coupling constants of the magnetic ground states are also determined theoretically for films with ideal interfaces by first-principles density functional theory calculations. These microscopic quantities are consistently enhanced in Fe films on the noble metal-induced surface alloys compared to their values in films on the clean W(100) surface. We attribute the systematic variation of magnetic onset observed experimentally to the competition between the intrinsically enhanced magnetic coupling and moments on the surface alloy substrates and several extrinsic factors that could suppress magnetic ordering, including intermixing, substrate and film roughness, and surface alloy disorder. Tendencies for intermixing are explored theoretically by determining the energy barrier for noble metal segregation. Despite these possible extrinsic effects, the results suggest that the use of the broad class of ordered surface alloys as alternative substrates may offer greater opportunities for manipulating thin film magnetism.

Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels

The inconsistency about the degree of geometrical frustration has been a long issue in AV2O4 (A≡Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using ab initio electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behavior of these compounds. The magnitude of the maximum calculated values of orbital magnetic moment per formula unit for ZnV2O4, MgV2O4 and CdV2O4 compounds are found to be ∼1.54 μB, ∼0.92 μB and ∼1.74 μB, respectively. The inclusion of the orbital and spin angular momenta for calculating the frustration indices improves the understanding about the degree of geometrical frustration in these compounds. The calculated values of the frustration indices (fJ) are largest for MgV2O4 and smallest for CdV2O4 for 3.3⩽U⩽5.3eV. In this range of U, the calculated values of ΔM2=Mtotal-Mexp (where, Mtotal=Mspin-|Morbital|) are also found to be largest for MgV2O4 and smallest for CdV2O4. Hence, the consistency about the degree of geometrical frustration, which arises from the fJ as well as from the ΔM2 is achieved and improves the understanding about the degree of geometrical frustration in these compounds. Calculated values of band gap in this range of U are found to be closer to that of experimentally observed values for all three compounds. The absolute values of the nearest neighbor exchange coupling constant (Jnn) between V spins are found to be largest for MgV2O4 and smallest for CdV2O4, which indicate that the calculated absolute values of the Curie-Weiss temperature (ΘCW)J are highest for MgV2O4 and smallest for CdV2O4 for 3.3⩽U⩽5.3eV. In this range of U, the magnetic transition temperature(TN)J is found to be ∼150K, ∼60K and ∼22K for MgV2O4, ZnV2O4 and CdV2O4, respectively, which shows that the order of (TN)J is similar to that of (TN)exp for these compounds. Hence, all the magnetic properties studied in the present work are well explained in these spinels for 3.3⩽U⩽5.3eV. This work is expected to provide a valuable input in understanding the geometrically frustrated magnetic behavior for those systems for which the orbital part of the angular momenta are not quenched.

Exchange interaction in pyrochlore vanadates Lu2V2O7 and Y2V2O7: Ab initio approach

The exchange interaction in vanadates with the pyrochlore structure, namely, Lu2V2O7 and Y2V2O7, has been investigated using the first-principles approach. The isotropic exchange coupling constants have been determined. The calculations have been performed within the unrestricted Hartree–Fock (UHF) approximation, as well as in the framework of the density functional theory (DFT), using hybrid functionals. It has been shown that, in the description of the exchange interaction in the compounds under investigation, the nonlocal Hartree–Fock exchange should be taken into account. The splitting patterns of the 3d1 level of the V4+ ion in the crystal field have been obtained within the model approach. The calculation has been carried out in the approximation of point charges taking into account the spin–orbit interaction. It has been revealed that the “orbital liquid” state cannot be observed in the compounds under investigation, because the exchange interaction energy is significantly less than the energy spacing between the ground state and the first excited state. The orbital ordering has been analyzed, and the spin density maps have been constructed.

Spin structure factors of Heisenberg spin chain in the presence of anisotropy and magnetic field

We have theoretically studied the spin structure factors of spin chain in the presence of longitudinal field and transverse anisotropy. The possible effects of easy axis magnetization are investigated in terms of anisotropy in the Heisenberg interactions. This anisotropy is considered for exchange coupling constants perpendicular to magnetic field direction. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the longitudinal structure factor at fixed value for anisotropy moves to higher frequency with magnetic field. Also the intensity of dynamical structure factor decreases with magnetic field. A small dependence of longitudinal dynamical spin structure factor on the anisotropy is observed for fixed value of magnetic field. Our results show longitudinal static structure factor is found to be monotonically increasing with magnetic field due to increase of spins aligning along magnetic field. Furthermore the dispersion behaviors of static longitudinal and transverse structure factors for different magnetic fields and anisotropy parameters are addressed.

Modeling and calculation of RKKY exchange coupling to explain Ti-vacancy-induced ferromagnetism in Ta-doped TiO2

We present a theoretical study on Ti-vacancy-induced ferromagnetism in anatase TiO2. A recent experimental study has revealed room temperature ferromagnetism in Ta-doped anatase TiO2thin films (Rusydi et al., 2012) [7]. Ta doping assists the formation of Ti vacancies which then induce the formation of localized magnetic moments around the Ti vacancies. As neighboring Ti vacancies are a few unit cells apart, the ferromagnetic order is suspected to be mediated by itinerant electrons. We propose that such an electron-mediated ferromagnetism is driven by Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction. To examine our hypothesis, we construct a tight-binding based model Hamiltonian for the anatase TiO2 system. We calculate the RKKY exchange coupling constant of TiO2 as a function of distance between local magnetic moments at various temperatures. We model the system by taking only the layer containing a unit of TiO2, at which the Ti vacancy is believed to form, as our effective two-dimensional unit cell. Our model incorporates the Hubbard repulsive interactions between electrons occupying Ti d orbitals treated within mean-field approximation. The density of states profile resulting from the model captures the relevant electronic properties of TiO2, such as the energy gap of ~3.4eV and the n-type character, which may be a measure of the adequacy of the model. The calculated RKKY coupling constant shows that the ferromagnetic coupling extends up to 3–4 unit cells and enhances slightly as temperature is increased from 0 to 400K. These results support our hypothesis that the ferromagnetism of this system is driven by RKKY mechanism.

Understanding Thermodynamic and Spectroscopic Properties of Tetragonal Mn12 Single-Molecule Magnets from Combined Density Functional Theory/Spin-Hamiltonian Calculations.

We apply broken-symmetry density functional theory to determine isotropic exchange-coupling constants and local zero-field splitting (ZFS) tensors for the tetragonal Mn12(t)BuAc single-molecule magnet. The obtained parametrization of the many-spin Hamiltonian (MSH), taking into account all 12 spin centers, is assessed by comparing theoretical predictions for thermodynamic and spectroscopic properties with available experimental data. The magnetic susceptibility (calculated by the finite-temperature Lanczos method) is well approximated, and the intermultiplet excitation spectrum from inelastic neutron scattering (INS) experiments is correctly reproduced. In these respects, the present parametrization of the 12-spin model represents a significant improvement over previous theoretical estimates of exchange-coupling constants in Mn12, and additionally offers a refined interpretation of INS spectra. Treating anisotropic interactions at the third order of perturbation theory, the MSH is mapped onto the giant-spin Hamiltonian describing the S = 10 ground multiplet. Although the agreement with high-field EPR experiments is not perfect, the results clearly point in the right direction and for the first time rationalize the angular dependence of the transverse-field spectra from a fully microscopic viewpoint. Importantly, transverse anisotropy of the effective S = 10 manifold is explicitly shown to arise largely from the ZFS-induced mixing of exchange multiplets. This effect is given a thorough analysis in the approximate D2d spin-permutational symmetry group of the exchange Hamiltonian.