Direct Exchange Interaction Research Articles

Effects of Coulomb interactions on spin states in vertical semiconductor quantum dots

The effects of direct Coulomb and exchange interactions on spin states are studied for quantum dots contained in circular and rectangular mesas. For a circular mesa a spin-triplet favored by these interactions is observed at zero and nonzero magnetic fields. We tune and measure the relative strengths of these interactions as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states. For a rectangular mesa we observe no signatures of the spin-triplet at zero magnetic field. Due to the anisotropy in the lateral confinement single-particle state degeneracy present in the circular mesa is lifted, and Coulomb interactions become weak. We evaluate the degree of the anisotropy by measuring the magnetic field dependence of the energy spectrum for the ground and excited states, and find that at zero magnetic field the spin-singlet is more significantly favored by the lifting of level degeneracy than by the reduction in the Coulomb interaction. We also find that the spin-triplet is recovered by adjusting the level degeneracy with magnetic field.

Small-angle neutron scattering investigations of magnetic nanostructures using polarized neutrons

Crystalline and magnetic nanostructures have been studied by means of small angle neutron scattering. Using polarised neutrons, the relative contrasts are strongly modified which allowed magnetisation, density and composition profiles at surfaces and interfaces to be evaluated. In nanocrystalline Fe3O4 embedded in a glass ceramics matrix the magnetic order is strongly disturbed at the surface of the particles, leading to a magnetically inactive layer. In partially crystallised metallic Fe-Si-B-(Nb,Cu) alloys the presence of a non-magnetic interface between Fe3Si nanocrystals and the amorphous matrix has been demonstrated which breaks the direct ferromagnetic exchange interactions. In Co-ferrofluids the superparamagnetic core is encapsulated by a shell of surfactant molecules which was found to be impenetrable for the solvent.

Structure and magnetism of a phenazinium cyclopentadienide salt

Electron spin resonance (esr) study of the salt of the stable organic cation radical, N, N′-dimethylphenazinium (M 2P +) with the symmetric diamagnetic anion, penta(methoxycarbonyl)cyclopentadienide (PMC −), reveals weak antiferromagnetic interactions in this material. Analysis of the crystal structure shows dimerized stacks of the cation radical with electrostatic stabilization offered by the surrounding anion lattice. The antiferromagnetic coupling of the spins can be explained as arising from the direct exchange interaction between the radicals in the stack. The anions do not appear to have any specific influence on the magnetic property of this material.

Theoretical Studies on Magnetic Interactions of Dichromium Tetraacetate by Using Hybrid Density Functional Method

The hybrid parameters of the density functional theory (DFT) for the open shell system in terms of the effective exchange integrals (Jab ). By using the parameters, Jab value for Cr2(O2CCH3)4(H2O)2 are calculated and Cr-Cr direct exchange interaction are estimated by using DFT natural orbital (DNO) CAS CI method.

Direct coulomb and exchange interaction in artificial atoms

We determine contributions from the direct Coulomb and exchange interactions to the total interaction in artificial semiconductor atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. The electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle-state degeneracy, and find that the spin configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.

Microscopic conditions favoring itinerant ferromagnetism

A systematic investigation of the microscopic conditions stabilizing itinerant ferromagnetism of correlated electrons in a single-band model is presented. Quantitative results are obtained by quantum Monte Carlo simulations for a model with Hubbard interaction U and direct Heisenberg exchange interaction F within the dynamical mean-field theory. Special emphasis is placed on the investigation of (i) the distribution of spectral weight in the density of states, (ii) the importance of genuine correlations, and (iii) the significance of the direct exchange, for the stability of itinerant ferromagnetism at finite temperatures. We find that already a moderately strong peak in the density of states near the band edge suffices to stabilize ferromagnetism at intermediate U values in a broad range of electron densities n. Correlation effects prove to be essential: Slater--Hartree-Fock results for the transition temperature are both qualitatively and quantitatively incorrect. The nearest-neighbor Heisenberg exchange does not, in general, play a decisive role. Detailed results for the magnetic phase diagram as a function of U, F, n, temperature T, and the asymmetry of the density of states are presented and discussed.

Ferromagnetic and Antiferromagnetic Phases of 4-(4-Iodobenzylideneamino)-2,2,6,6-tetramethylpiperidin-1-yloxyl

Abstract Temperature dependences of d.c. magnetic susceptibilities and magnetizations were measured for two different crystallographic phases of 4-(4-iodobenzylideneamino)-2,2,6,6-tetramethylpiperidin-1-yloxyl. Intermolecular ferromagnetic (Weiss temperature θ = +0.71 K) and antiferromagnetic (θ = −0.23 K) interactions were found for α- and β-phases, respectively, in the magnetic measurements above 1.8 K; the former phase showed a bulk ferromagnetic transition at 0.28 K. Based on the X-ray crystallographic data, intermolecular magnetic interactions are discussed. In the α-phase crystal, NO-radical sites form two-dimensional zigzag sheets. The ferromagnetic interaction within the sheet can be interpreted in terms of a β-hydrogen mechanism, ON(↑)–Cα(↓)–Cβ(↑)–Hβ(↓)···(↑)ON<, in which the magnetic interaction is transmitted by β-hydrogens. A dimer structure was found in the β-phase crystal, and direct exchange and/or dipole interactions between N–O radicals seem to be the main origin of the antiferromagnetic interaction.

Pseudodipole interaction of ions with nonzero orbital angular momenta

It is shown that the direct exchange interaction of ions possessing electrons (holes) with orbital angular momenta L and l always contains a contribution $$V_0 L \cdot \ell + V_1 (L \cdot \hat B)(\hat B \cdot \ell )$$ , where $$\hat B$$ is a unit vector along the bond connecting the ions. As a result, taking the spin-orbit interaction into account gives rise to a pseudodipole interaction of the spins (total angular momenta) of the ions under study and to uniaxial anisotropy. The possibility of using this pseudodipole interaction to explain the magnetic properties of cuprates is discussed.

To the theoretical analysis of the work function changes of platinum group metals adsorbed on (110) W

The simple theoretical model based on the Anderson-Newns Hamiltonian is proposed for the description of work function changes for different surface structures of adatoms. The direct exchange interaction of adjacent adatoms is taken into account. The model permits one to calculate values of the adatom dipole moment as a function of the nearest-neighbor adatom's number. This give some key to the understanding of the variations of adatom structures with temperature and concentration. The numerical calculations are performed for Rh, Ir, and Pt adsorbed on (110)W.

Theoretical Studies on Magnetic Interactions in Prussian Blue Analogs and Active Controls of Spin States by External Fields

The symmetry rules for the d-orbital interactions are considered for simple prediction of the sign of effective exchange integrals between transition metal ions in Prussian blue analogs. Ab initio UHF and DFT calculations were carried out for binuclear transition-metal cyanides in order to elucidate variations of the through-bond exchange integrals with combinations of transition metal ions having different d-electron configurations. It was shown that the sign of effective exchange integrals predicted from the symmetry rules and the ab initio calculations are consistent with the experiments but their magnitudes calculated for tetracentric systems MCNM' (M=Cr(III), M'=V(II), Mn(II), etc.) by the use of triple zeta basis sets are larger than the observed values for Prussian blue analogs. The calculated results clearly indicated that the direct exchange interactions between M and M' are negligible, whereas the through-bond superexchange and spin polarization interactions are crucial for the high-Tc ferri (or ferro) magnetism in Prussian blue analogs. The modifications of electronic states in antiferromagnetic or paramagnetic precursors are also discussed in relation to our previous theoretical proposals for molecular spinics and recent experiments to obtain the switching type molecular magnets controlled by photochemical, electrochemical and other techniques.

Ferromagnetism of Anderson localized electrons: Application to cluster compounds

A study of the electrical transport and magnetic properties of a series of cluster compounds with the generic formula ${A}_{0.5}{M}_{2}{X}_{4}$ suggests that the electrons at the Fermi surface are localized, and the ferromagnetism seen in these compounds arises from these electrons. The magnetism of these compounds shows some features characteristic of itinerant models and others which are characteristic of localized models. We construct a model which has a nondegenerate band of localized states with on-site repulsion. Further, the singly occupied states interact via direct exchange interaction which is ferromagnetic. Using a mean-field approximation we calculate the various magnetic properties, which are in qualitative accord with the observed behavior. In particular, we find that the single-particle excitations play a dominant role in the magnetism of these compounds, even though the electrons are localized. We also analyze the spin-wave excitations in this model and discuss their effect on low-temperature thermodynamics.

Theoretical Approaches to Direct Exchange Couplings between Divalent Chromium Ions in Naked Dimers, Tetramers, and Clusters

Direct exchange interactions between divalent chromium ions in naked dimers, tetramers, and clusters were investigated theoretically. The orbital energy gaps, occupation numbers, and bond orders for the naked Cr(II)−Cr(II) dimer (1) were calculated by ab initio UHF MO and density functional (DFT) methods. All these calculations indicated that the orbital energy gaps are very small for 1, and therefore the occupation numbers of the bonding σ, π, and δ molecular orbitals and formal quadruple bond orders were largely reduced because of strong electron correlation effects. The UHF and DFT MO calculations were also performed for the linear naked Cr(II) tetramer to elucidate possible electronic structures of the d−d conjugated systems. The energy differences among singlet, triplet, and quintet states for 1 were calculated from the total energies obtained by the CASCI and CASSCF methods based on the UHF and DFT natural orbitals (UNO). The reliability of the Heisenberg model Hamiltonian was elucidated from variations of these calculated effective exchange integrals with the interatomic distance. The calculated Jab values are compared with the experimental results for several binuclear Cr(II) complexes with different interatomic distances. The Heisenberg spin Hamiltonian was used to discuss the spin alignments in large d−d conjugated Cr(II) clusters and a possibility of the macroscopic quantum spin tunneling in mesoscopic magnetic systems.

Detailed ferromagnetic resonance study of amorphous Fe-rich alloys. I: re-entrant behaviour and low-lying magnetic excitations

Results of exhaustive ferromagnetic resonance (FMR) measurements performed on amorphous (a-) alloys at temperatures ranging from 10 to 500 K are presented and discussed in the light of existing theoretical models. The peak-to peak FMR linewidth consists of two contributions: one originating from two-magnon and multiple-magnon scattering processes and the other arising from the Laundau - Lifshitz - Gilbert damping mechanism. for the alloys with , as in other re-entrant (RE) systems, increases exponentially as the temperature is lowered through the RE transition temperature . The Landé splitting factor is independent of both temperature and Co concentration, whereas the Gilbert damping parameter is temperature-independent but decreases with increasing x. For all the alloys in question, thermal demagnetization is mainly due to spin-wave (SW) excitations and the SW stiffness coefficient D renormalizes with temperature in accordance with the predictions of the itinerant-electron model. SW modes in the alloys with soften at and D possesses a reduced but finite value in the RE state. Competing interactions present in the parent alloy a- confine the direct exchange interactions (DEIs) to the nearest neighbours only and partial replacement of Fe with Co progressively tilts the balance in favour of ferromagnetic interactions between Fe spins with the result that DEIs now involve next-nearest neighbours too and the divergence in at low temperatures is completely suppressed for x > 4.

The magnetic state of diamagnetically diluted antiferromagnetic cobalt monoxide

Magnetic neutron diffraction measurements have been performed on (Co 1− x Mg x )O solid solutions with x = 0.1, 0.2, 0.3, 0.43, 0.53, 0.63 and 0.7 at T = 4.2 –300 K. It is shown that the concentration dependence of the average magnetic moment per atom does not obey the condition of simple dilution. The diamagnetic atom results in a local canting of the moments and an additional reduction of the average magnetic moment. One can consider this atom as a source of random magnetic field due to the appearance of a new superexchange interaction between magnetic atoms through the diamagnetic impurity. The sign of this interaction is opposite to the sign of the direct exchange interaction in the magnetic sublattice.

Non-perturbative approaches to magnetism in strongly correlated electron systems

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough U. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of U above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.

Theoretical Studies of the Ferromagnetic Inter-Molecular Interaction of P-Carboxylate Phenyl Nitronyl Nitroxide

Abstract Ab initio and semiempirical MO calculations were carried out for dimers of p-carboxylate phenyl nitronyl nitroxide, whose geometries were extracted from the X-ray diffraction results. It was shown that the effective exchange integrals for the nearest neighbor dimer are largely positive (ferromagnetic), in accord with the experimental results. The direct potential exchange interactions between SOMOs are operative, giving the large Jab values, but the spin polarization plus other higher-order terms reduce their magnitudes. Implications of these results are discussed in relation to molecular design of high Tc crystalline organic ferromagnets.

Monte Carlo study of magnetic properties of a Cu1 − cNic(pc) I spin chain

The magnetic properties of transition-metal based quasi-one-dimensional molecular metals show unusual concentration and temperature dependence. The ion magnetization in the chain formed by the metal spine of Cu1-cNIc(pc)I phthalocyanine iodide was modeled by Monte Carlo methods, using dipolar, direct, and indirect exchange interaction potentials of variable range. The effects of dilution of Cu spin moments by diamagnetic Ni ions and impurity scattering effects on the electron gas polarization are determined. The results are compared with magnetic susceptibility measurements for this molecular metal.

Theory of magnetism in low symmetry crystals: cuprates and nickelates

The effective spin Hamiltonians for the distorted NiO 2 and CuO 2 planes with low-temperature orthorhombic (LTO) and low-temperature tetragonal (LTT) structures are derived by taking into account the spin-orbit coupling and structural distortion as perturbations. We explain why the weak ferromagnetism occurs in both LTO and LTT phases for cuprates whereas it does only in the LTT phase for nickelates. The spin-wave gaps observed by neutron scattering experiments are analyzed. We find that the gaps of the in-plane and out-of-plane modes in La 1.65Nd 0.35CuO 4 are caused, respectively, by anisotropic superexchange and direct-exchange interactions.

Detailed magnetization study of quenched random ferromagnets. I. Low-lying magnetic excitations.

Magnetization as a function of temperature has been measured for amorphous (a-) (${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$${\mathrm{B}}_{19}$${\mathrm{Si}}_{1}$ (0.0625\ensuremath{\le}p\ensuremath{\le}0.2), (${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$${\mathrm{B}}_{20}$ (0.25\ensuremath{\le}p\ensuremath{\le}1.0), and (${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$${\mathrm{P}}_{14}$${\mathrm{B}}_{6}$ (0.1125\ensuremath{\le}p\ensuremath{\le}1.0) alloys in the temperature range 3.8--300 K at various constant applied magnetic-field values in the interval 5\ensuremath{\le}H\ensuremath{\le}15 kOe. An elaborate data analysis reveals the following. (i) For all p in the a-(${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$(B,Si${)}_{20}$ alloy series, the contribution to the thermal demagnetization due to single-particle (SP) excitations of the weak itinerant type, though present at all temperatures, is completely dominated by that arising from spin-wave (SW) excitations in the temperature range 0\ensuremath{\lesssim}t (=T/${\mathit{T}}_{\mathit{C}}$)\ensuremath{\lesssim}${\mathit{t}}^{\mathrm{*}}$(p) but the reverse is true for t>${\mathit{t}}^{\mathrm{*}}$(p). However, in a-(${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$${\mathrm{P}}_{14}$${\mathrm{B}}_{6}$ alloys, SP excitations of the weak itinerant type give a feeble contribution, which is masked by the SW contribution, for temperatures up to 0.9${\mathit{T}}_{\mathit{C}}$ (300 K) in the concentration range 0.1125\ensuremath{\le}p\ensuremath{\le}0.25 (0.375\ensuremath{\le}p\ensuremath{\le}0.625) but for T\ensuremath{\lesssim}300 K and p\ensuremath{\gtrsim}0.75, a significant SP contribution of the strong itinerant type accompanies a dominant SW contribution.(ii) The spin-wave stiffness coefficient D in both the alloy series, as in fcc ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Ni}}_{100\mathrm{\ensuremath{-}}\mathit{x}}$ alloys, varies with temperature as D(T)\ensuremath{\sim}${\mathit{T}}^{5/2}$ and D(T)\ensuremath{\sim}${\mathit{T}}^{2}$ for Fe concentrations below and above x=80p=60 at. %, respectively. (iii) The direct exchange interactions extend beyond the second nearest-neighbor distance for compositions close to, but above, the critical concentration for the appearance of long-range ferromagnetic order whereas the competing interactions in the alloy with p>0.75 confine the direct exchange to the nearest neighbors only. The observation (i) above is shown to imply that all the compositions in the a-(${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$ (B,Si${)}_{20}$ alloy series behave as weak itinerant ferromagnets while a transition from weak itinerant to strong itinerant ferromagnetism occurs at p\ensuremath{\simeq}0.75 in the a-(${\mathrm{Fe}}_{\mathit{p}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${)}_{80}$${\mathrm{P}}_{14}$${\mathrm{B}}_{6}$ alloy series. Arguments are presented to show that the property ${\mathit{D}}_{\mathit{n}}$ (inelastic neutron scattering) \ensuremath{\gg}${\mathit{D}}_{\mathit{m}}$ (magnetization) of the alloys with p>0.75 in both the alloy series studied is a consequence of the fact that the longitudinal spin fluctuations make as significant a contribution to the ${\mathit{T}}^{3/2}$ decrease of magnetization as the transverse spin fluctuations (spin waves) do, but leave ${\mathit{D}}_{\mathit{n}}$ unaltered from its ``spin-wave-only'' value.

Coulomb and exchange interactions in C60n-

Semiempirical modified-neglect-of-differential-overlap (MNDO) quantum chemistry calculations are performed for the negative ions of an isolated ${\mathrm{C}}_{60}$. The value computed for the first electron affinity is in excellent agreement with experiment. MNDO predictions of the energies of the low-lying states of ${\mathrm{C}}_{60}^{2\mathrm{\ensuremath{-}}}$ and ${\mathrm{C}}_{60}^{3\mathrm{\ensuremath{-}}}$ allow us to extract an effective on-site repulsion ${\mathit{U}}_{0}$\ensuremath{\sim}3 eV, and a direct exchange interaction K\ensuremath{\sim}50 meV for ${\mathrm{C}}_{60}$. These values are used to estimate the effective on-site repulsion and dielectric constant of solid ${\mathrm{C}}_{60}$, with results in good agreement with experiment. A similar approach is used to determine ``partially'' screened parameters appropriate to a model of ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$. We find that both the on-site (${\mathit{U}}_{0}$\ensuremath{\sim}1.3 eV) and near-neighbor (V\ensuremath{\sim}0.3 eV) Coulomb terms are significant relative to the bandwidth (W\ensuremath{\sim}0.6 eV).