Direct Exchange Interaction Research Articles

Cobalt doped rings and cages of ZnO clusters: Motifs for magnetic cluster-assembled materials

First principles electronic structure studies on pure and doped Zn n O n clusters have been carried out to identify elementary motifs with potential for cluster materials. In pure clusters Zn 12O 12 cages are shown to be particularly stable. When doped with a single Co or Fe atom, the doped units carry a magnetic moment of 3.0 μ B and 4.0 μ B, respectively. Doping of Zn 12O 12 with two Co sites leads to ferromagnetically coupled Co moments due to direct exchange interaction. It is proposed that the assemblies of such multiple doped units may lead to semiconductors with larger doping than attainable in bulk or films.

First-principles study on exchange force image of NiO(0 0 1) surface using a ferromagnetic Fe probe

Exchange force of a ferromagnetic Fe probe on antiferromagnetic NiO(0 0 1) surface has been investigated by means of a first-principles calculation. Calculated exchange force images show a clear spin image when the probe is located within 1 Å above the contact point. We can see antiferromagnetic pattern of the surface Ni atoms along the [1 1 0] direction, and asymmetric feature around surface O sites. The main contrast of Ni comes from the direct exchange interaction between the Fe probe and the surface Ni atom, while the asymmetric image possibly comes from the super exchange interaction between the Fe probe and the second layer Ni atom via the surface O. Such asymmetric feature is a key proof of the exchange force microscope image on observation.

Intramolecular energy transfer through charge transfer state in lanthanide compounds: A theoretical approach

A theoretical approach for the intramolecular energy transfer process involving the ligand-to-metal charge transfer (LMCT) state in lanthanide compounds is developed. Considering a two-electron interaction, both the direct Coulomb and exchange interactions are taken into account, leading to expressions from which selection rules may be derived and transfer rates may be calculated. These selection rules show that the direct Coulomb and exchange mechanisms are complementary, in the same way as obtained in previous works for the case of ligand-lanthanide ion energy transfer processes. An important result from numerical estimates is that the channel ligand-LMCT state is by far the dominant case, leading to transfer rates higher than for the channel lanthanide ion-LMCT state by several orders of magnitude. The analysis of the emission quantum yield as a function of the relative energy position of the LMCT state in a typical Eu(3+) compound allows the identification of two quenching regions, the most pronounced one occurring close to the lower ligand triplet level.

Dynamical Cluster Approximation in Disordered Systems with Magnetic Impurities

We present a theoretical method to study diluted magnetic semiconductors, beyond the single-site approximation, extending the dynamical cluster approximation (DCA). By the method, we can consider the nonlocal correlations due to disorder and discuss effects of the direct exchange interaction between magnetic impurities on the properties of the itinerant carriers. We apply the method to a three-dimensional cubic lattice system with random localized spins. We show that the strong antiferromagnetic superexchange interaction between nearest-neighbor sites suppresses the polarization of the carrier spins.

Ab initio Study of Electronic Structure and Magnetic Properties of a Novel Two-Dimensional Copper(II)-Radical Complex [Cu(NTTmPy)2(N3)2]n**The project supported by National Natural Science Foundation of China under Grant Nos. 90103034 and 10174023

The full-potential linearized augmented plane wave (FPLAPW) method with the generalized gradient approximations (GGA) is applied to study the compound [Cu(NTTmPy)2(N3)2]n (NITmPy = 2 - (3′ - Pyridy1) -4, 4, 5, 5 - tetramethylimidazolin - 1 - oxy1 - 3 - oxide). The total density of states (DOS) and the partial density of states (pDOS) are calculated to explain the electronic and the magnetic properties of [Cu(NTTmPy)2(N3)2]n. It is found that [Cu(NTTmPy)2(N3)2]n is stable in the ferromagnetic state and the magnetic moment of the molecule mainly comes from the Cu atoms (0.518 μB) with partial contribution from N, O atoms of nitronyl nitroxide radicals. There exist orbital hybridization between 3d orbital of Cu and p orbitals of N(1) (from pyridyl rings of the NITmPy ligands) and N(4) (from azido group) and the weak direct exchange interactions between Cu and O atoms of nitronyl nitroxides. In addition, the bridging carbon atom (C(6)) carries a significant negative spin density (-0.019 μB). The sign alternation of the magnetic moment along zthe pyridyl ring is obtained, which agrees with experiments.

Kondo lattice model with a direct exchange interaction between localized moments

We study the Kondo lattice model with a direct antiferromagnetic exchange interaction between localized moments. Ferromagnetically long-range ordered state coexisting with the Kondo screening shows a continuous quantum phase transition to the Kondo singlet state. We obtain the value of the critical point where the magnetizations of the localized moments and the conduction electrons vanish. The magnetization curves yield a universal critical exponent independent of the filling factors and the strength of the interaction between localized moments. It is shown that the direct exchange interaction between localized moments introduces another phase transition from an antiferromagnetic ordering to a ferromagnetic ordering for small Kondo exchange interaction. We also explain the local minimum of the Kondo temperature in recent experiments.

Electronic structure and magnetic interactions in MnN andMn3N2

Electronic structure calculations were performed for MnN and ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ using a full-potential linearized muffin-tin orbital method in the local spin density approximation. Structural relaxation by energy minimization and calculations for various different magnetic configurations were performed. Antiferromagnetic ordering along the [001] direction was found to have the lowest energy in both materials in agreement with experimental neutron diffraction data. The magnetic moments were found to be about $3{\ensuremath{\mu}}_{B}$ in good agreement with experiment. Analysis of the partial densities of states reveals that the magnetic moments arise primarily from the ${t}_{2g}$ orbitals. In ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2},$ the magnetic moment was found to be slightly larger on the ${\mathrm{Mn}}_{1}$ atoms, i.e., the Mn atoms in planes without N than on ${\mathrm{Mn}}_{2}$ atoms. Band structures and densities of states are presented. The energy differences between different magnetic configurations were analyzed in terms of a Heisenberg Hamiltonian. We find strong second-nearest-neighbor ferromagnetic interactions for Mn connected collinearly with N, indicative of a double exchange mechanism and about four times weaker nearest-neighbor antiferromagnetic interactions in MnN. In a perfect rocksalt structure, this situation would lead to a multiply degenerate ground state. However, we find that the $c/a$ reduction of about 2% is due to the AFM coupling (it is absent in FM and nonmagnetic MnN) and leads to stronger inter-(001)-plane exchange interactions than intraplane exchange interaction. In ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2},$ the Mn connected via a vacancy lack the strong ferromagnetic interaction. This would suggest a lower N\'eel temperature for MnN with increasing concentration of N vacancies. However, the nearest-neighbor direct exchange interaction in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ is found to be about two times as large in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ than in MnN which partially compensates for the lack of fewer indirect second-nearest exchange interactions. These changes in the exchange interactions are related to the structural relaxations. Nevertheless, the mean field approximation predicts a slightly lower N\'eel temperature in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ than in MnN in contrast with experiment. Effects beyond mean field are discussed and are deemed not to be able to provide an explanation for this discrepancy. We suggest that the observed phase transition in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ previously interpreted as the AFM-paramagnetic phase transition may in reality be an order-disorder transition of the N vacancies.

Ab-Initio Study ofElectronic Structure and Magnetic Properties ofPipz-H2[MnF4(HF2)

The full-potential linearized augmented plane wave method wasapplied to study the electronic and the magnetic properties ofthe compound pipz-H2[MnF4(HF2)](pipz=piperazine). The band structure,the total density of states, the partial density of states andthe electron density were calculated to explain the electronic and themagnetic properties of pipz-H2[MnF4(HF2)] in the ferromagneticstate. It is found that the magnetic moment of the molecule mainly comesfrom the Mn atoms with partial contribution from the F atoms. Thesymmetrical σ/σ bonds via H atoms along Mn-F-H-F-Mnchains and the weak direct-exchange interaction between F(2), F(3) andMn atoms have effect on the electronic structure and the magnetism ofpipz-H2[MnF4(HF2)].

Josephson current in the presence of a precessing spin

The Josephson current in the presence of a precessing spin between various types of superconductors is studied. It is shown that the Josephson current flowing between two spin-singlet pairing superconductors is not modulated by the precession of the spin. When both superconductors have equal-spin-triplet pairing state, the flowing Josephson current is modulated with twice of the Larmor frequency by the precessing spin. It was also found that up to the second tunneling matrix elements, no Josephson current can occur with only a direct exchange interaction between the localized spin and the conduction electrons, if the two superconductors have different spin-parity pairing states.

Theory of covalent heterodinuclear magnetic exchange interaction and its application to Mn IIIFe III and Fe IIFe II spin clusters in complex molecules

A covalent heterodinuclear magnetic exchange interaction formula has been established and the antiferromagnetic coupling phenomena of both heterodinuclear Mn IIIFe III and homodinuclear Fe IIFe II spin-clusters in complex molecules have been studied. It is demonstrated that the antiferromagnetic phenomenon of transition-metal ion-pairs in molecules should be attributed to the combined effect of the direct-exchange interaction, the kinetic exchange interaction and the covalent effect; the strong antiferromagnetic characteristic of Mn IIIFe III cluster in [L ′Mn III(μ-O)(μ-CH 3CO 2) 2Fe IIIL ′] is mainly due to the d xz –d xz and d yz –d yz orbital exchange interactions, while the weak antiferromagnetic coupling in deoxyhemerythrin should be attributed to a μ-OH −–Fe IIFe II cluster with a long Fe–O bond length in its active site. The theoretical results agree well with the experimental findings.

Magnetic phase transitions in amorphous systems with competing exchange interactions

A method is proposed for analyzing magnetic phase transitions within the Ising model under the conditions of competing direct and indirect exchange interactions. It is demonstrated that the competition of exchange interactions leads to a reentrant phase transition between the ferromagnet and spin glass near the percolation threshold below the Curie temperature.

Theory of magnetic exchange interaction for heterodinuclear Fe III( a3)Cu II(B) in cytochrome c oxidase

As a development of our recent works about the magnetic study for heterodinuclear clusters, a covalent effect has been introduced in the magnetic exchange interaction formula and a more general magnetic expression for heterodinuclear transition-metal ion pairs in covalent complexes has been derived. By means of this expression and our double-Slater function (DSF) calculation procedure, the relationship between the magnetic exchange coupling parameter J and the covalent factors N A and N B for a heterodinuclear system AB has been studied. For the heterodinuclear Fe III( a 3)Cu II(B) pair in beef heart cytochrome c oxidase, it is demonstrated that the stronger the covalent effect the stronger the antiferromagnetic coupling. The theoretical curve of the magnetic exchange interaction J vs. the values of the Fe III( a 3)Cu II(B) separation R and the covalent factors N A (for Fe III) and N B (for Cu II) has been obtained. It is shown that the strong antiferromagnetic phenomenon for the heterodinuclear Fe III( a 3)Cu II(B) pairs in cytochrome c oxidase can be attributed to the combined effect of the direct-exchange interaction, the kinetic exchange interaction and the covalent effect. It is also shown that in order to reproduce the very strong antiferromagnetic exchange interaction J (− J⩾200 cm −1) in cytochrome c oxidase the theoretical range of the Fe III( a 3)Cu II(B) separation R should be smaller than 4.0 A. This result is obviously smaller than the value R expt=4.5 A reported by Tsukihara et al. and Iwata et al., but it is in good agreement with the value R expt⩽4 A obtained by Scott et al. and Powers et al. from their EXAFS experiments.

Bound magnetic polaron interactions in insulating doped diluted magnetic semiconductors

The magnetic behavior of insulating doped diluted magnetic semiconductors (DMS) is characterized by the interaction of large collective spins known as bound magnetic polarons. Experimental measurements of the susceptibility of these materials have suggested that the polaron-polaron interaction is ferromagnetic, in contrast to the antiferromagnetic carrier-carrier interactions that are characteristic of nonmagnetic semiconductors. To explain this behavior, a model has been developed in which polarons interact via both the standard direct carrier-carrier exchange interaction (due to virtual carrier hopping) and an indirect carrier-ion-carrier exchange interaction (due to the interactions of polarons with magnetic ions in an interstitial region). Using a variational procedure, the optimal values of the model parameters were determined as a function of temperature. At temperatures of interest, the parameters describing polaron-polaron interactions were found to be nearly temperature-independent. For reasonable values of these constant parameters, we find that indirect ferromagnetic interactions can dominate the direct antiferromagnetic interactions and cause the polarons to align. This result supports the experimental evidence for ferromagnetism in insulating doped DMS.

Exchange interaction in binuclear complexes with rare-earth and copper ions: A many-body model study

We have used a many-body model Hamiltonian to study the nature of the magnetic ground state of hetero-binuclear complexes involving rare-earth and copper ions. We have taken into account all diagonal repulsions involving the rare-earth 4f and 5d orbitals and the copper 3d orbital. Besides, we have included direct exchange interaction, crystal field splitting of the rare-earth atomic levels and spin-orbit interaction in the 4f orbitals. We have identified the inter-orbital $4f$ repulsion, U$_{ff}$ and crystal field parameter, $\Delta_f$ as the key parameters involved in controlling the type of exchange interaction between the rare earth $4f$ and copper 3d spins. We have explored the nature of the ground state in the parameter space of U$_{ff}$, $\Delta_f$, spin-orbit interaction strength $\lambda$ and the $4f$ filling n$_f$. We find that these systems show low-spin or high-spin ground state depending on the filling of the $4f$ levels of the rare-earth ion and ground state spin is critically dependent on U$_{ff}$ and $\Delta_f$. In case of half-filling (Gd(III)) we find a reentrant low-spin state as U$_{ff}$ is increased, for small values of $\Delta_f$, which explains the recently reported apparent anomalous anti-ferromagnetic behaviour of Gd(III)-radical complexes. By varying U$_{ff}$ we also observe a switch over in the ground state spin for other fillings . We have introduced a spin-orbit coupling scheme which goes beyond L-S or j-j coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.

The origin of frustration of magnetic coupling in the NiFeCrO4 ferrite

The magnetostriction of the NiFeCrO4 ferrite is investigated for the first time. It is found that the frustration of magnetic coupling occurs only in the B sublattice of the NiFeCrO4 ferrite, whereas the A sublattice has a usual magnetic structure. The inference is made that the frustration of magnetic coupling in the B sublattice is caused not only by the negative direct BB exchange interaction Cr B 3+ -Cr B 3+ but also by the positive indirect AB exchange interaction Fe A 3+ -O2−-Cr B 3+ . Reasoning from the experimental data and an analysis of the exchange interactions in the NiFeCrO4 ferrite sample, it is demonstrated for the first time that the magnetic moments of Fe A 3+ ions in this ferrite deviate from collinearity. It is established that, at low temperatures, the B sublattice of the NiFeCrO4 ferrite is responsible for the total magnetic moment n 0exp.

Analysis of the magnetic coupling in binuclear complexes. II. Derivation of valence effective Hamiltonians from ab initio CI and DFT calculations

Most interpretations of the magnetic coupling J between two unpaired electrons rest upon simple valence models that involve essentially the ferromagnetic direct exchange contribution, Kab, and the antiferromagnetic effect of the delocalization resulting from the interaction between neutral and ionic determinants, tab, whose energy difference is U. Ab initio valence-only calculations give very poor estimates of J, whatever the definition of the magnetic orbitals, and large CI expansions are required to evaluate it properly. It is, however, possible to define valence effective Hamiltonians from the knowledge of the eigenenergies and the eigenvectors of these accurate CI calculations. When applied to four different complexes, this strategy shows that spin polarization may change the sign of the direct exchange interaction, Kab, and that dynamical correlation results in a dramatic reduction of the effective repulsion U. The present article also shows how Kab, tab, and U effective parameters can be extracted from density functional theory (DFT) calculations and that the typical overestimation of J in DFT can be attributed to an excessive lowering of the effective on-site repulsion.

On the direct exchange energy in Co2 and Co2+ doped lattices

In efforts to try to study the interactions in materials doped with magnetic Co ions, we first calculated the nearest neighbor numbers via simulation procedure, in which the ions were randomly distributed at various concentrations in a 100×100×100 crystalline lattice. Secondly, in order to attempt to understand the direct exchange interactions between Co ions we calculated the exchange energy as a function of Co–Co distance by the B3PW91/LanL2MB hybrid density functional theory method.

Theory of exchange interaction for heterodinuclear Mn–Ni in KZnF 3:Mn 2+–Ni 2+ system

As a development of our recent works about homodinuclear clusters, a theoretical formula for describing the exchange interaction of heterodinuclear system has been derived in terms of the natural magnetic orbital method. By means of this formula and the Double-Slater-Function (DSF) calculation procedure, the various integrals in the magnetic expression have been calculated. The theoretical curve of the magnetic exchange interaction of the Mn–F–Ni cluster in KZnF 3:Mn 2+–Ni 2+ vs the Mn 2+–Ni 2+ separation R have been obtained and the antiferromagnetic phenomenon of the heterodinuclear Mn 2+–Ni 2+ pair has been reasonably explained. It is shown that the contribution of kinetic exchange interaction is considerably important and that the mainly physical mechanism of the antiferromagnetic phenomenon in KZnF 3:Mn 2+–Ni 2+ should be attributed to the combined effect of the direct exchange and kinetic exchange interactions.

Spin effects in semiconductor quantum dot structures

The spin effects on the electronic properties are studied for two different quantum dots: a quantum dot well isolated from the leads and that strongly coupled to the leads. For the first quantum dot, we use a magnetic field to adjust the single-particle state degeneracy, and observe a singlet–triplet transition at zero and non-zero magnetic fields, favored by direct Coulomb and exchange interactions. The spin configurations in an arbitrary magnetic field are well explained in terms of two-interacting electron model. For the second quantum dot we adjust the single-particle state degeneracy as a function of magnetic field and observe a novel Kondo effect associated with the singlet–triplet degeneracy. This Kondo anomaly appears when the quantum dot holds an even number of electrons, and the characteristic energy scale is much larger than in the ordinary half-spin case.

Theoretical studies of strong direct magnetic interactions of 5-methyl-1,2,4-triazole nitronylnitroxide

Theoretical calculations were carried out for dimers of 5-methyl-1,2,4-triazole nitronylnitroxide, whose geometry was extracted from the X-ray diffraction results of Kahn and co-workers. It was shown that the effective exchange integrals for the molecular pair are largely positive (ferromagnetic), in accord with the experimental results. The origin of a large ferromagnetic intermolecular interaction in the linear chain structure is successfully identified as SOMO–SOMO direct interaction. Namely, the direct potential exchange interaction between SOMOs is operative, giving a large J ab value. On the other hand, the intermolecular hydrogen bond is not crucial for the ferromagnetic interaction but it contributes to structural stabilization. In addition to semiempirical, ab initio and DFT methods, we developed two types of hybrid DFT methods and successfully applied these methods in order to evaluate the intermolecular magnetic interaction.