Kinetic Exchange Interaction Research Articles

Collective spin and charge excitations in the t-J-U model of high-[formula omitted] cuprates

The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.

Momentum-resolved spin splitting in Mn-doped trivial CdTe and topological HgTe semiconductors

Exchange coupling between localized spins and band or topological states accounts for giant magnetotransport and magnetooptical effects as well as determines spin-spin interactions in magnetic insulators and semiconductors. However, even in archetypical dilute magnetic semiconductors such as Cd$_{1-x}$Mn$_x$Te and Hg$_{1-x}$Mn$_x$Te the evolution of this coupling with the wave vector is not understood. A series of experiments have demonstrated that exchange-induced splitting of magnetooptical spectra of Cd$_{1-x}$Mn$_x$Te and Zn$_{1-x}$Mn$_x$Te at the L points of the Brillouin zone is, in contradiction to the existing theories, more than one order of magnitude smaller compared to its value at the zone center and can show an unexpected sign of the effective Land\'e factors. The origin of these findings we elucidate quantitatively by combining: (i) relativistic first-principles density functional calculations; (ii) a tight-binding approach that takes carefully into account k-dependence of the potential and kinetic sp-d exchange interactions; (iii) a theory of magnetic circular dichroism (MCD) for $E_1$ and $E_1$ + $\Delta_1$ optical transitions, developed here within the envelope function $kp$ formalism for the L point of the Brillouin zone in zinc-blende crystals. This combination of methods leads to the conclusion that the physics of MCD at the boundary of the Brillouin zone is strongly affected by the strength of two relativistic effects in particular compounds: (i) the mass-velocity term that controls the distance of the conduction band at the L point to the upper Hubbard band of Mn ions and, thus, a relative magnitude and sign of the exchange splittings in the conduction and valence bands; (ii) the spin-momentum locking by spin-orbit coupling that reduces exchange splitting depending on the orientation of particular L valleys with respect to the magnetization direction.

Ferromagnetic kinetic exchange interaction in magnetic insulators

The superexchange theory predicts dominant antiferromagnetic kinetic interaction when the orbitals accommodating magnetic electrons are covalently bonded through diamagnetic bridging atoms/groups. Here we show that explicit consideration of magnetic and (leading) bridging orbitals, together with the electron transfer between the former, reveals a strong ferromagnetic kinetic exchange contribution. First principle calculations show that it is comparable in strength with antiferromagnetic superexchange in a number of magnetic materials with diamagnetic metal bridges. In particular, it is responsible for a very large ferromagnetic coupling ($-10$ meV) between the iron ions in a Fe$^{3+}$-Co$^{3+}$-Fe$^{3+}$ complex.

Nonlocal exchange interactions in strongly correlated electron systems

We study the influence of ferromagnetic nonlocal exchange on correlated electrons in terms of a $SU(2)$-Hubbard-Heisenberg model and address the interplay of on-site interaction induced local moment formation and the competition of ferromagnetic direct and antiferromagnetic kinetic exchange interactions. In order to simulate thermodynamic properties of the system in a way that largely accounts for the on-site interaction driven correlations in the system, we advance the correlated variational scheme introduced in [M. Sch\"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for explicitily symmetry broken electronic phases by introducing an auxiliary magnetic field. After benchmarking the method against exact solutions of a finite system, we study the $SU(2)$-Hubbard-Heisenberg model on a square lattice. We obtain the $U$-$J$ finite temperature phase diagram of a $SU(2)$-Hubbard-Heisenberg model within the correlated variational approach and compare to static mean field theory. While the generalized variational principle and static mean field theory yield transitions from dominant ferromagnetic to antiferromagnetic correlations in similar regions of the phase diagram, we find that the nature of the associated phase tranistions differs between the two approaches. The fluctuations accounted for in the generalized variational approach render the transitions continuous, while static mean field theory predicts discontinuous transitions between ferro- and antiferromagnetically ordered states.

Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory

Computing momentum-dependent susceptibilities in the dynamical mean-field theory (DMFT) requires solving the Bethe-Salpeter equation, which demands large computational cost. Exploiting the strong-coupling feature of local fluctuations, we derive a simplified formula that can be solved at a considerably lower cost. The validity and the physical meaning of the formula are confirmed by deriving the effective intersite interactions in the strong-coupling limit, such as the kinetic exchange and RKKY interactions. Furthermore, numerical calculations for single-orbital and multiorbital models demonstrate surprisingly wider applicability including weak-coupling region. Based on this formula, we propose three levels of practical approximations that can be chosen depending on complexity of problems. Simpler evaluations of spin and orbital susceptibilities in multiorbital systems thus become possible within DMFT.

New mechanism of kinetic exchange interaction induced by strong magnetic anisotropy

It is well known that the kinetic exchange interaction between single-occupied magnetic orbitals (s-s) is always antiferromagnetic, while between single- and double-occupied orbitals (s-d) is always ferromagnetic and much weaker. Here we show that the exchange interaction between strongly anisotropic doublets of lanthanides, actinides and transition metal ions with unquenched orbital momentum contains a new s-d kinetic contribution equal in strength with the s-s one. In non-collinear magnetic systems, this s-d kinetic mechanism can cause an overall ferromagnetic exchange interaction which can become very strong for transition metal ions. These findings are fully confirmed by DFT based analysis of exchange interaction in several Ln3+ complexes.

Fifty years of Hubbard and Anderson lattice models: from magnetism to unconventional superconductivity - A brief overview

We briefly overview the importance of the Hubbard- and Anderson-lattice models as applied to the explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus essentially extended their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. We also present some of the new results concerning the unconventional superconductivity obtained very recently in our group. A comparison with experiment is also discussed, but the main emphasis is put on rationalization of the superconducting properties of those materials within the real-space pairing mechanism based on either kinetic exchange and/or Kondo-type interaction combined with the electron correlation effects.

Theoretical Model on the Interplay of Disorder and Electron Correlations

In the present review paper we discuss a general theoretical treatment to investigate the interplay between the effects of disorder and electron-electron interaction in the Anderson-localized regime. In constructing the model Hamiltonian, the behaviour of Anderson-localized states with envelope function is explicitly taken into account. It is shown that, in the approximation of neglecting the interstate interactions, the rival effects of disorder and electron correlation can be described by two fundamental quantities: the average intrastate interaction energy and the distribution width of one-electron energies. On the basis of this model the spin susceptibility and electronic specific heat as well as density of states are calculated. It is shown that the intrastate interaction gives rise to the occurrence of singly-occupied states below the Fermi energy and that this results in a Curie-type spin susceptibility at low temperatures. It is shown that the configuration interaction which is one of the effects of interstate interactions gives rise to a kinetic type exchange interaction between singly-occupied states which favours spin-singlet states and that the competition between direct and kinetic exchanges leads to the spin pair model in which each localized spin of singly occupied state forms a ferromagnetic or antiferromagnetic pair with its nearest neighbour. Specific heat anomaly, in particular its magnetic field dependence, and magnetic susceptibility at very low temperatures are calculated by taking into account the coexistence of ferromagnetic and antiferromagnetic interactions within a spin pair model. It is shown that the experimental results on Si:P can be well explained by the present treatment. Finally the effects of electron-electron interactions on the magnetoresistance of the variable range hopping conduction are investigated. It is shown that magnetoresistance is positive as far as the change of localization length due to a magnetic field is neglected Taking into account the latter effect which is responsible for negative magneto-resistance, the total magnetoresistance is calculated for the systems of 1T-TaS2 and their observed peculiar features of magnetoresistance can be explained well by the present theory.

Magnetocrystalline anisotropies in (Ga,Mn)As: Systematic theoretical study and comparison with experiment

We present a theoretical survey of magnetocrystalline anisotropies in (Ga,Mn)As epilayers and compare the calculations to available experimental data. Our model is based on an envelope function description of the valence band holes and a spin representation for their kinetic-exchange interaction with localised electrons on Mn ions, treated in the mean-field approximation. For epilayers with growth induced lattice-matching strains we study in-plane to out-of-plane easy-axis reorientations as a function of Mn local-moment concentration, hole concentration, and temperature. Next we focus on the competition of in-plane cubic and uniaxial anisotropies. We add an in-plane shear strain to the effective Hamiltonian in order to capture measured data in bare, unpatterned epilayers, and we provide microscopic justification for this approach. The model is then extended by an in-plane uniaxial strain and used to directly describe experiments with strains controlled by postgrowth lithography or attaching a piezo stressor. The calculated easy-axis directions and anisotropy fields are in semiquantitative agreement with experiment in a wide parameter range.

Theory of weak localization in ferromagnetic (Ga,Mn)As

We study quantum interference corrections to the conductivity in (Ga,Mn)As ferromagnetic semiconductors using a model with disordered valence band holes coupled to localized Mn moments through a p-d kinetic-exchange interaction. We find that at Mn concentrations above 1% quantum interference corrections lead to negative magnetoresistance, i.e. to weak localization (WL) rather than weak antilocalization (WAL). Our work highlights key qualitative differences between (Ga,Mn)As and previously studied toy model systems, and pinpoints the mechanism by which exchange splitting in the ferromagnetic state converts valence band WAL into WL. We comment on recent experimental studies and theoretical analyses of low-temperature magnetoresistance in (Ga,Mn)As which have been variously interpreted as implying both WL and WAL and as requiring an impurity-band interpretation of transport in metallic (Ga,Mn)As.

Effective t-J model of pairing: singlet versus triplet

The tnJ model is regarded as a canonical model of spin-singlet pairing induced by the kinetic exchange interaction also responsible for an antiferromagnetic ordering in the strongly correlated narrow-band systems. In the orbitally degenerate systems both ferromagnetic and antiferromagnetic kinetic exchange interactions occur. I briey review the analogy between the singlet and triplet types of pairing, as well as draw some general conclusions about the pairing induced by these exchange interactions. The general discussion is also illustrated with a concrete case of a two-dimensional lattice with the spin triplet pairing.

A-Type Antiferrospin Ordering under the Antiferroorbital Order in Perovskite-Type Compounds

The appearance of the A -type antiferrospin ( A -AFS) order under the antiferroorbital (AFO) order observed in some perovskite-like compounds is studied theoretically to resolve discrepancies between existing theories and to clarify its mechanism in an open way. The various kinetic exchange interactions (KEI) between degenerate d γ orbitals of neighboring magnetic ions are derived not to violate the crystal symmetry with making no assumption on the transfer integrals. The KEI constants which are affected by the Hund coupling under the AFO order due to the joint effect of the cooperative Jahn–Teller effect (CJTE) and the orbital exchange interaction can explain successfully the appearance of the A -AFS ordering. The close relation between the AFO and A -AFS orders, the role of the CJTE, and the effect of the presence of the unfilled d e orbitals are clarified. The obtained results are consistent with the properties of the A -AFS order observed in LaMnO 3 , MnF 3 and KCuF 3 .

Orbitally dependent kinetic exchange in a heterobimetallic pair: Ferromagnetic spin alignment and magnetic anisotropy in the cyano-bridged Cr(III)Fe(II) dimer

The problem of the kinetic exchange interaction in the cyanide-bridged heterobinuclear dimers involving orbitally degenerate transition metal ions is considered. The developed approach is based on the concept of the effective Hamiltonian of the orbitally dependent kinetic exchange. We deduce this many-electron Hamiltonian on the microscopic background so that all relevant biorbital transfer processes are taken into account as well as the properties of the many-electron states. The bioctahedral cyanide-bridged Cr(III)Fe(II) dimer is considered in detail as an example distinctly exhibiting new quantitative and qualitative features of the orbitally dependent exchange and as a structural unit of three-dimensional ferromagnetic crystals {Fe(II)3[Cr(III)(CN)6]2}⋅13H2O. The proposed mechanism of the kinetic exchange involves the electron transfer from the double occupied t2 orbitals of Fe(II) [ground state T52(t24e2)] to the half occupied t2 orbitals of Cr(III) [ground state A42(t23)] resulting in the charge transfer state T31(t24)Cr(II)−6A1(t23e2)Fe(III) and the transfer between the half-occupied t2 orbitals of the metal ions resulting in the charge transfer state T31(t24)Cr(II)−4T2(t23e2)Fe(III). The effective Hamiltonian of the orbitally dependent exchange for the Cr(III)Fe(II) pair deduced within this theoretical framework describes competitive ferro- and antiferromagnetic contributions arising from these two charge transfer states. This Hamiltonian leads to a complex energy pattern, consisting of two interpenetrating Heisenberg-like schemes, one exhibiting ferromagnetic and another one antiferromagnetic splitting. The condition for the ferromagnetic spin alignment in the ground state is deduced. The orbitally dependent terms of the Hamiltonian are shown to give rise to a strong magnetic anisotropy of the system, this result as well as the condition for the spin alignment in the ground term are shown to be out of the scope of the Goodenough–Kanamori rules. Along with the full spin S the energy levels are labeled by the orbital quantum numbers providing thus the direct information about the magnetic anisotropy of the system. Under a reasonable estimation of the excitation energies based on the optical absorption data we conclude that the kinetic exchange in the cyanide-bridged Cr(III)Fe(II) pair leads to the ferromagnetic spin alignment exhibiting at the same time strong axial magnetic anisotropy with C4 easy axis of magnetization.

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.

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.

Ground-state magnetization for interacting fermions in a disordered potential: Kinetic energy, exchange interaction, and off-diagonal fluctuations

We study a model of n interacting fermions in a disordered potential, which is assumed to generate uniformly fluctuating interaction matrix elements. We show that the ground-state magnetization is systematically decreased by off-diagonal fluctuations of the interaction matrix elements. This effect is neglected in the Stoner picture of itinerant ferromagnetism in which the ground-state magnetization is simply determined by the balance between ferromagnetic exchange and kinetic energy, and increasing the interaction strength always favors ferromagnetism. The physical origin of the demagnetizing effect of interaction fluctuations is the larger number K of final states available for interaction-induced scattering in the lower-spin sectors of the Hilbert space. We analyze the energetic role played by these fluctuations in the limits of small and large interactions U. In the small-$U$ limit we use second-order perturbation theory and identify explicitly transitions which are allowed for minimal spin and forbidden for higher spin. These transitions then on average lower the energy of the minimal spin ground state with respect to higher spin; we analytically evaluate the size of this reduction and find it to give a contribution ${\ensuremath{\Delta}}^{s}\ensuremath{\propto}{\mathrm{nU}}^{2}/\ensuremath{\Delta}$ to the spin gap between the two lowest-spin ground states. In terms of an average effective Hamiltonian, these contributions induce a ${\mathrm{nU}}^{2}{S}^{2}/\ensuremath{\Delta}$ term which decreases the strength of the ferromagnetic exchange, thereby delaying the onset of Stoner ferromagnetism, and generate a second, larger S term $\ensuremath{\propto}{S}^{3},$ which results in a saturation of the ground-state spin before full polarization is achieved, in contrast to the Stoner scenario. For large interactions U we amplify on our earlier work [Ph. Jacquod and A. D. Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that the broadening of the many-body density of states is proportional to $\sqrt{K}U$ and hence favors minimal spin. Numerical results are presented in both limits. After evaluating the effect of fluctuations, we discuss the competition between fluctuations plus kinetic energy and the exchange energy. We finally present numerical results for specific microscopic models and relate them to our generic model of fluctuations. We discuss the different physical situations to which such models may correspond, the importance of interaction fluctuations, and hence the relevance of our results to these situations and recall an experimental setup which we proposed in an earlier work to measure the importance of interaction fluctuations on the ground-state spin of lateral quantum dots in the Coulomb blockade regime.

Study of exchange interaction of Ni 2+ pairs in MgO : Ni 2+, KMgF 3 : Ni 2+ and KNiF 3 crystals

The exchange interactions of the Ni 2+ pairs in MgO : Ni 2+, KMgF 3 : Ni 2+ and KNiF 3 systems have been studied based on the Girerd–Journaux–Kahn (GJK) model and the Heitler–London (HL) model, respectively, and by use of a double Slater-type radial wave function and an effective potential, which are constructed in terms of the spectral calculation. For the Ni–Ni distance R in the range 3.2 Å< R<4.8 Å, the values of the exchange interaction parameter J calculated based on the GJK model are greater by a factor 2 than those based on the HL model. The calculated results give a reasonable explanation for the magnetic structure of the three systems and show that:(i) the kinetic exchange interaction is notably important, (ii) the antiferromagnetic effect is governed by both the direct exchange and the superexchange mechanisms, and (iii) the GJK model is suitable for describing the Ni–Ni exchange interactions in the three systems.

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.

Organic polymers with indirect magnetic interaction caused by the molecular topology of the elementary units

The magnetic properties of two classes of open-shell π-systems, namely diradicals and one-dimensional polymers, having frontier non-overlapping non-bonding MOs (NBMOs) localized within the monoradical units have been studied theoretically. The non-overlap and localization of the NBMOs is determined by the topology of the π-systems, and can be explained by means of the extended Coulson–Rushbrooke–Longuet-Higgins theorem. The localization and non-overlapping of the NBMOs results in vanishing of the direct (Hund) and the kinetic exchange interaction between the unpaired electrons. The indirect exchange of the unpaired electrons (spin polarization exchange) is the only contribution to the effective exchange integral and occurs via the delocalized π-electrons in the filled energy bands. A comparison of our models is accomplished with the indirect exchange in rare earth compounds (f–s model) and with the superexchange of the Kramers–Anderson model.

Organic Open-Shell Systems with Indirect Magnetic Interaction Caused by the Topology of the Elementary Units

The magnetic properties of a class of 1-D π-systems having a frontier half-filled band (HFB) of degenerate non-bonding MOs (NBMOs) localized within the elementary units (EU) have been studied theoretically. The localization of the MOs, determined by the topology of the π-fragments which form the EUs is explained by means of the extended Coulson-Rush-brooke-Longuet-Higgins theorem. The perfect localization and non-overlapping of the NBMOs results in vanishing of the direct (Hund-) and the kinetic exchange interaction between the unpaired electrons. The indirect exchange of the unpaired electrons (spin polarization exchange) occurs via the delocalized π-electrons in the filled energy bands.