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Register a new userOrbital Magnetism of Bloch Electrons I. General Formula
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We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Greens functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time.
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The orbital susceptibility for graphene is calculated exactly up to the first order with respect to the overlap integrals between neighboring atomic orbitals. The general and rigorous theory of orbital susceptibility developed in the preceding paper is applied to a model for graphene as a typical two-band model. It is found that there are contributions from interband, Fermi surface, and occupied states in addition to the Landau--Peierls orbital susceptibility. The relative phase between the atomic orbitals on the two sublattices related to the chirality of Dirac cones plays an important role. It is shown that there are some additional contributions to the orbital susceptibility that are not included in the previous calculations using the Peierls phase in the tight-binding model for graphene. The physical origin of this difference is clarified in terms of the corrections to the Peierls phase.
Orbital susceptibility for Bloch electrons is calculated for the first time up to the first order with respect to overlap integrals between the neighboring atomic orbitals, assuming single-band models. A general and rigorous theory of orbital susceptibility developed in the preceding paper is applied to single-band models in two-dimensional square and triangular lattices. In addition to the Landau-Peierls orbital susceptibility, it is found that there are comparable contributions from the Fermi surface and from the occupied states in the partially filled band called intraband atomic diamagnetism. This result means that the Peierls phase used in tight-binding models is insufficient as the effect of magnetic field.
We derive the Landau-Lifshitz-Bloch (LLB) equation for a two-component magnetic system valid up to the Curie temperature. As an example, we consider disordered GdFeCo ferrimagnet where the ultrafast optically induced magnetization switching under the action of heat alone has been recently reported. The two-component LLB equation contains the longitudinal relaxation terms responding to the exchange fields from the proper and the neighboring sublattices. We show that the sign of the longitudinal relaxation rate at high temperatures can change depending on the dynamical magnetization value and a dynamical polarisation of one material by another can occur. We discuss the differences between the LLB and the Baryakhtar equation, recently used to explain the ultrafast switching in ferrimagnets. The two-component LLB equation forms basis for the largescale micromagnetic modeling of nanostructures at high temperatures and ultrashort timescales.
Iron telluride (FeTe), a relative of the iron based high temperature superconductors, displays unusual magnetic order and structural transitions. Here we explore the idea that strong correlations may play an important role in these materials. We argue that the unusual orders observed in FeTe can be understood from a picture of correlated local moments with orbital degeneracy, coupled to a small density of itinerant electrons. A component of the structural transition is attributed to orbital, rather than magnetic ordering, introducing a strongly anisotropic character to the system along the diagonal directions of the iron lattice. Double exchange interactions couple the diagonal chains leading to the observed ordering wavevector. The incommensurate order in samples with excess iron arises from electron doping in this scenario. The strong anisotropy of physical properties in the ordered phase should be detectable by transport in single domains. Predictions for ARPES, inelastic neutron scattering and hole/electron doping studies are also made.
We use symmetry analysis and first principles calculations to show that the linear magnetoelectric effect can originate from the response of orbital magnetic moments to the polar distortions induced by an applied electric field. Using LiFePO4 as a model compound we show that spin-orbit coupling partially lifts the quenching of the 3d orbitals and causes small orbital magnetic moments ($mu_{(L)}approx 0.3 mu_B$) parallel to the spins of the Fe$^{2+}$ ions. An applied electric field $mathbf{E}$ modifies the size of these orbital magnetic moments inducing a net magnetization linear in $mathbf{E}$.
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