Orbital Magnetism Research Articles

The particle flow oscillations of rotating non-interacting gases in a two-dimensional harmonic trap

The spatial distribution of particle flow and atomic density of the two-dimensional, harmonically trapped, ideal atomic gases in synthetic magnetic field and rotating frame are systematically investigated in various regimes of temperature. The magnetization and particle flow of rotating fermions exhibit a de Haas–van Alphen-like oscillation at relatively low temperature. This phenomenon is analogous to the quantum oscillation of orbital magnetism and current in confined electron system. An elaborate comparison with Bose system is also proposed.

Dirac fermions in a Fe ultrathin film

We show the existence of massive Dirac fermions in electronic band structures of a few Fe atomic layers with perpendicular magnetization. Based on a tight binding model fitted to ab-initio band structure, we observe four distinct massive Dirac fermions near the Fermi level, which result from atomic spin-orbit coupling of Fe and a band inversion between Fe $4s$-$3d_{x^2-y^2}$ hybrid orbital band and $3d_{xy}$ orbital band. These lead to a valence band with finite Chern integer (+2) and chiral edge modes near the Fermi level. When the chemical potential is set inside the Dirac gap by carrier doping, the Hall conductivity exhibits a plateau-like structure with quantized value $2\frac{e^2}{h}$, and orbital magnetization shows a prominent increase, latter of which is mostly due to chiral orbital motion of electrons along the edge modes. We discuss the stability of the Dirac fermions in Fe(001) monolayer on MgO(001) substrate and Fe(001) bilayer case.

Tunable Valley Polarization and Valley Orbital Magnetic Moment Hall Effect in Honeycomb Systems with Broken Inversion Symmetry.

In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. Compared to circular pumping, elliptical pumping is a more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous Hall effect (called valley orbital magnetic moment Hall effect) is predicted. Valley orbital magnetic moment Hall effect can generate an orbital magnetic moment current without the accompaniment of a charge current, which opens a new avenue for exploration of valleytronics and orbitronics. Valley orbital magnetic moment Hall effect is expected to overshadow spin Hall effect and is tunable under elliptical pumping.

Equilibrium surface current and role of U(1) symmetry: Sum rule and surface perturbations

We discuss effects of surface perturbations on equilibrium surface currents which contribute to orbital magnetization and orbital angular momentum in systems without time-reversal symmetry. We show that, in a U(1) particle-number-conserving system, disorder and other perturbations at a surface do not affect the equilibrium surface current and corresponding orbital magnetization, due to a sum rule which is analogous to Luttinger's theorem. On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.

Spin current generation and magnetic response in carbon nanotubes by the twisting phonon mode

We theoretically investigate spin current and magnetic response induced by the twisting phonon mode in carbon nanotubes via the spin-rotation coupling. An effective magnetic field due to the twisting mode induces both spin and orbital magnetizations. The induced spin and orbital magnetizations have both radial and axial components. We show that ac pure spin current is generated by the twisting phonon mode. The magnitude of the spin current and orbital magnetization for a (10,10) armchair nanotube is estimated as an example. We find that the ac pure spin current is detectable in magnitude when the frequency of the twisting mode is of the order of GHz, and that the orbital magnetization is found to be larger than the spin magnetization.

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles.

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure.

We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular to the applied current.

Topological orbital magnetization and emergent Hall effect of an atomic-scale spin lattice at a surface

We predict the occurrence of a novel type of atomic-scale spin lattice in an Fe monolayer on the Ir(001) surface. Based on density functional theory calculations we parametrize a spin Hamiltonian and solve it numerically using Monte Carlo simulations. We find the stabilization of a three-dimensional spin structure arranged on a $(3\ifmmode\times\else\texttimes\fi{}3)$ lattice. Despite an almost vanishing total spin magnetization we predict the emergence of orbital magnetization and large anomalous Hall effect, to which there is a significant topological contribution purely due to the real space spin texture at the surface.

Finite temperature orbital and spin magnetism of small Fe linear chains

The finite temperature spin and orbital magnetism of FeN linear chains is theoretically studied in the framework of a spin fluctuation theory based on a realistic d-band model Hamiltonian, which includes the spin–orbit coupling interaction in a non-perturbative way. Spin and orbital magnetic moments are calculated as a function of the temperature by using an exchange Monte Carlo method that takes into account in a full way the short-range magnetic order. The finite temperature anisotropy effects on the spin and orbital cluster moment values are analysed by considering magnetization directions perpendicular to and along the chain axis. The temperature dependence of the orbital cluster moment follows a general trend similar to that of the spin one and shows clear anisotropy effects at low and intermediate temperatures, before total thermal disorder appears. Interesting anisotropy effects driven by thermal spin fluctuations are also observed for the spin results in most of the systems.

Magnetization Signatures of Light-Induced Quantum Hall Edge States.

Circularly polarized light opens a gap in the Dirac spectrum of graphene and topological insulator (TI) surfaces, thereby inducing a quantum Hall-like phase. We propose to detect the accompanying edge states and their current by the magnetic field they produce. The topological nature of the edge states is reflected in the mean orbital magnetization of the sample, which shows a universal linear dependence as a function of a generalized chemical potential-independent of the driving details and the properties of the material. The proposed protocol overcomes several typically encountered problems in the realization and measurement of Floquet phases, including the destructive effects of phonons and coupled electron baths and provides a way to occupy the induced edge states selectively. We estimate practical experimental parameters and conclude that the magnetization signature of the Floquet topological phase may be detectable with current techniques.

Strain controlled orbital state and magnetization in insulating LaMnO3+δ films

LaMnO3+δ films with various thicknesses were grown on LaAlO3 (001) single crystal substrate to investigate the effect of in-plane compressive strain (∼−0.57%) on magnetic properties. All films exhibit a blocking temperature Tb at which the zero field cooled magnetization reaches a maximum, indicating the ferromagnetic (FM) nanoclusters are embedded in the background of antiferromagnetic (AFM) matrix. The onset temperature of FM transition Tc and Tb is increased by 24% and 89%, respectively, with the thickness decreasing from 82.4 nm to 9.2 nm. Simultaneously, the saturation magnetization greatly increases by 309%, which is ascribed to the strain-induced transition of AFM to FM phase due to the orbital order structure switching from x2− 1/y2−1 [A-type] to (x2− y2) + (z2− 1) [F-type].

Persistent current states in bilayer graphene

We argue that at finite carrier density and large displacement fields, bilayer graphene is prone to $\ell =0$ and $\ell = 1$ Pomeranchuk Fermi surface instabilities. The broken symmetries are driven by non-local exchange interactions which favor momentum space condensation. We find that electron-electron interactions lead first to spontaneous valley polarization, which breaks time-reversal invariance and is associated with spontaneous orbital magnetism, and then under some circumstances to a nematic phase with reduced rotational symmetry. When present, nematic order is signaled by reduced symmetry in the dependence of optical absorption on light polarization.

Relativistic first-principles study on spin and orbital magnetism of mattagamite (CoTe2)

We have demonstrated electronic and magnetic properties of CoTe2 compound in the framework of relativistic density functional theory using generalized gradient approximation (GGA). The spin and orbital magnetic moments of Co and Te atoms were obtained using full-potential local orbitals band structure scheme. We have found a partially quenched orbital moment of 0.096μB for Co atom in the local spin density approximation. In order to improve the intrinsic deficiency of local density approximation for describing orbital magnetism, an orbital polarization correction was applied to CoTe2 and a significant orbital moment of 0.153μB was found for Co atom in this compound.

Off-resonant polarized light-controlled thermoelectric transport in ultrathin topological insulators

We study thermoelectric transport in ultrathin topological insulators under the application of circularly polarized off-resonant light of frequency {\Omega} and amplitude A. We derive analytical expressions for the band structure, orbital magnetization Morb, and the thermal (\k{appa}xy) and Nernst ({\alpha}xy) conductivities. Reversing the light polarization from right to left leads to an exchange of the conduction and valence bands of the symmetric and antisymmetric surface states and to a sign change in Morb,{\alpha}xy, and \k{appa}xy. Varying the sample thickness or A/{\Omega} leads to a strong enhancement of Morb and {\alpha}xy. These effects, accessible to experiments, open the possibility for selective, state-exchanged excitations under light and the conversion of heat to electric energy.

Orbital magnetism in coupled-bands models

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called {\it modern theory of orbital magnetization} and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band -- either gapless or gapped -- systems. We point out some surprising features in the orbital susceptibility -- such as in-gap diamagnetism or parabolic band edge paramagnetism -- coming from interband coupling. From that we draw general conclusions on the orbital magnetism of itinerant electrons in multi-band tight-binding models.

Numerical optimization algorithm for rotationally invariant multi-orbital slave-boson method

We develop a generalized numerical optimization algorithm for the rotationally invariant multi-orbital slave boson approach, which is applicable for arbitrary boundary constraints of high-dimensional objective function by combining several classical optimization techniques. After constructing the calculation architecture of rotationally invariant multi-orbital slave boson model, we apply this optimization algorithm to find the stable ground state and magnetic configuration of two-orbital Hubbard models. The numerical results are consistent with available solutions, confirming the correctness and accuracy of our present algorithm. Furthermore, we utilize it to explore the effects of the transverse Hund’s coupling terms on metal–insulator transition, orbital selective Mott phase and magnetism. These results show the quick convergency and robust stable character of our algorithm in searching the optimized solution of strongly correlated electron systems.

Temperature dependent spin and orbital magnetization in TbCo2: Magnetic Compton scattering and first-principles investigations

Spin-polarized Compton profiles of TbCo2 have been measured to elucidate the interesting behavior of spin and orbital moments at different temperatures. The magnetic Compton profiles (MCPs) have been analyzed in terms of site specific spin moments due to Tb-4f electrons, Co and itinerant electrons. The temperature dependence of the orbital moment has been deduced using Compton and magnetometry data ranging between 6 and 300K. The present data exhibit a decrease in the ratio of orbital to spin moments from 43.9% to 35.0% (while going from 6 to 300K). First-principles calculations within DFT+U scheme have also been performed to confirm the spin-, orbital- and site specific-magnetic moments in TbCo2. An antiparallel exchange coupling between the Tb-4f and Co spin moments is found. The orbital moment is found to have a parallel coupling with the Tb spin moment, as evident from the experimental MCPs. From first-principles data it is seen that the orbital moments of Tb and Co sites are antiparallel to each other, as in the case of their spin magnetic moments. The present experimental study also shows an existence of an itinerant moment which is coupled ferromagnetically with the Tb-4f spin moment.

Pair breaking due to orbital magnetism in iron-based superconductors

We consider superconductivity in the presence of impurities in a two-band model suited for the description of iron-based superconductors. We analyze the effect of interband scattering processes on superconductivity, allowing for orbital, i.e., nonspin-magnetic but time-reversal symmetry-breaking impurities. Pair breaking in such systems is described by a nontrivial phase in an interband-scattering matrix element. We find that the transition temperature of conventional superconductors can be suppressed due to interband scattering, whereas unconventional superconductors may be unaffected. We also discuss the stability of density wave phases in the presence of impurities. As an example, we consider impurities associated with imaginary charge density waves that are of interest for iron-based superconductors.

Spin and orbital magnetic response on the surface of a topological insulator

Coupling of the spin and orbital degrees of freedom on the surface of a strong three-dimensional insulator, on the one hand, and textured magnetic configuration in an adjacent ferromagnetic film, on the other, is studied using a combination of transport and thermodynamic considerations. Expressing exchange coupling between the localized magnetic moments and Dirac electrons in terms of the electrons' out-of-plane orbital and spin magnetizations, we relate the thermodynamic properties of a general ferromagnetic spin texture to the physics in the zeroth Landau level. Persistent currents carried by Dirac electrons endow the magnetic texture with a Dzyaloshinski-Moriya interaction, which exhibits a universal scaling form as a function of electron temperature, chemical potential, and the time-reversal symmetry breaking gap. In addition, the orbital motion of electrons establishes a direct magnetoelectric coupling between the unscreened electric field and local magnetic order, which furnishes complex long-ranged interactions within the magnetic film.

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.