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Register a new userOrbital Magnetism of Bloch Electrons II. Application to Single-Band Models and Corrections to Landau-Peierls susceptibility
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Authors
Masao Ogata
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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.
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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.
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.
Using the Landau-Lifshitz-Bloch (LLB) equation for ferromagnetic materials, we derive analytic expressions for temperature dependent absorption spectra as probed by ferromagnetic resonance (FMR). By analysing the resulting expressions, we can predict the variation of the resonance frequency and damping with temperature and coupling to the thermal bath. We base our calculations on the technologically relevant L1$_0$ FePt, parameterised from atomistic spin dynamics simulations, with the Hamiltonian mapped from ab-initio parameters. By constructing a multi-macrospin model based on the LLB equation and exploiting GPU acceleration we extend the study to investigate the effects on the damping and resonance frequency in ${mu}$m sized structures.
Sigma-phase intermetallic compound of Fe54Cr46 was investigated using DC and AC magnetic susceptibility techniques. A clear-cut evidence was found that the sample orders magnetically at Tc=23.5 K and its ground magnetic state is constituted by a spin glass. The temperature at which the zero-field cooled magnetization has its maximum decreases with an external magnetic field in line with the Gabay-Toulouse prediction. The temperature at which the AC magnetic susceptibility has its maximum does not depend on frequency which, in the light of the mean-field theory, testifies to very long magnetic interactions.
Based on the Phase Hamiltonian, two types of solitons are found to exist in the crossover region between band insulator and Mott insulator in one-dimension. Both of these solitons have fractional charges but with different spins, zero and 1/2, respectively. The results are in accord with the experimental results by Kanoda et al. for TTF-Chloranil under pressure.
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