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Register a new userTheory of orbital magnetic quadrupole moment and magnetoelectric susceptibility
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We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room-temperature antiferromagnetic semiconductors BaMn$_2$As$_2$ and CeMn$_2$Ge$_{2 - x}$Si$_x$. We find that the orbital contribution to the ME susceptibility is comparable with or even dominant over the spin contribution.
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The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the one-particle band structure of the system and a part that contains the effects of exchange and correlations carried by the Green function. The derived formula provides a convenient means of including the effects of exchange and correlations beyond the commonly used local density approximation of density functional theory.
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 $mathbf{E}$.
We report electronic structure calculations of an iron impurity in gold host. The spin, orbital and dipole magnetic moments were investigated using the LDA+$U$ correlated band theory. We show that the {em around-mean-field}-LDA+$U$ reproduces the XMCD experimental data well and does not lead to formation of a large orbital moment on the Fe atom. Furthermore, exact diagonalization of the multi-orbital Anderson impurity model with the full Coulomb interaction matrix and the spin-orbit coupling is performed in order to estimate the spin Hall angle. The obtained value $gamma_S approx 0.025$ suggests that there is no giant extrinsic spin Hall effect due to scattering on iron impurities in gold.
Titanium disulfide TiS$_2$, which is a member of the layered transition-metal dichalcogenides with the 1T-CdI$_2$-type crystal structure, is known to exhibit a wide variety of magnetism through intercalating various kinds of transition-metal atoms of different concentrations. Among them, Fe-intercalated titanium disulfide Fe$_x$TiS$_2$ is known to be ferromagnetic with strong perpendicular magnetic anisotropy (PMA) and large coercive fields ($H_text{c}$). In order to study the microscopic origin of the magnetism of this compound, we have performed X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) measurements on single crystals of heavily intercalated Fe$_x$TiS$_2$ ($xsim0.5$). The grown single crystals showed a strong PMA with a large $H_text{c}$ of $mu_0H_text{c} simeq 1.0 text{T}$. XAS and XMCD spectra showed that Fe is fully in the valence states of 2+ and that Ti is in an itinerant electronic state, indicating electron transfer from the intercalated Fe atoms to the host TiS$_2$ bands. The Fe$^{2+}$ ions were shown to have a large orbital magnetic moment of $simeq 0.59 mu_text{B}text{/Fe}$, to which, combined with the spin-orbit interaction and the trigonal crystal field, we attribute the strong magnetic anisotropy of Fe$_x$TiS$_2$.
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