Orbital Magnetism Research Articles

Static magnetic and ESR spectroscopic properties of the dimer-chain antiferromagnet BiCoPO5

We report a comprehensive study of the static susceptibility, high-field magnetization and high-frequency/high-magnetic field electron spin resonance (HF-ESR) spectroscopy of polycrystalline samples of the bismuth cobalt oxy-phosphate BiCoPO$_5$. This compound features a peculiar spin system that can be considered as antiferromagnetic (AFM) chains built of pairs of ferromagnetically coupled Co spins and interconnected in all three spatial directions. It was previously shown that BiCoPO$_5$ orders antiferromagnetically at $T_{\rm N} \approx 10$ K and this order can be continuously suppressed by magnetic field towards the critical value $\mu_0H_{\rm c} \approx 15$ T. In our experiments we find strongly enhanced magnetic moments and spectroscopic $g$ factors as compared to the expected spin-only values, suggesting a strong contribution of orbital magnetism for the Co$^{2+}$ ions. This is quantitatively confirmed by ab initio quantum chemical calculations. Within the AFM ordered phase, we observe a distinct field-induced magnetic phase transition. Its critical field rises to $\sim 6$ T at $T \ll T_{\rm N}$. The HF-ESR spectra recorded at $T\ll T_{\rm N}$ are very rich comprising up to six resonance modes possibly of the multimagnonic nature that soften towards the critical region around 6 T. Interestingly, we find that the Co moments are not yet fully polarized at $H_{\rm c}$ which supports a theoretical proposal identifying $H_{\rm c}$ as the quantum critical point for the transition of the spin system in BiCoPO$_5$ to the quantum disordered state at stronger fields.

Effects of a far-infrared photon cavity field on the magnetization of a square quantum dot array

The orbital and spin magnetization of a cavity-embedded quantum dot array defined in a GaAs heterostructure are calculated within quantum-electrodynamical density-functional theory. To this end, a gradient-based exchange-correlation functional recently employed for atomic systems is adapted to the hosting two-dimensional electron gas submitted to an external perpendicular homogeneous magnetic field. Numerical results reveal the polarizing effects of the cavity photon field on the electron charge distribution and nontrivial changes of the orbital magnetization. We discuss its intertwined dependence on the electron number in each dot, and on the electron-photon coupling strength. In particular, the calculated dispersion of the photon-dressed electron states around the Fermi energy as a function of the electron-photon coupling strength indicates the formation of magnetoplasmon-polaritons in the dots.

Orbital Hall effect in crystals: Interatomic versus intra-atomic contributions

The orbital Hall effect (OHE) designates the generation of a charge-neutral flow of orbital angular momentum transverse to an initial charge current. Recent theoretical investigations suggest that transition metals display sizable OHE, encouraging experimental search along this direction. Nonetheless, most of these theories assume that the orbital moment originates from the region immediately surrounding the atom core, adopting the so-called {\it atomic center approximation}. In periodic crystals though, the contribution of the interstitial regions is crucial and can lead to a severe misestimation of the OHE. By applying the "modern theory" of orbital magnetization to the OHE, we assess the relative importance of intra-atomic and inter-atomic contributions in selected materials from first principles. We find that whereas the OHE is mostly of intra-atomic origin for wide band-gap semiconductors (e.g., MoS$_2$), the inter-atomic contribution becomes crucial in narrow band-gap semiconductors (SnTe, PbTe) and transition metals (Pt, V etc.). These predictions invalidate the atomic center approximation adopted in some of the previous works and open perspectives for the realization of efficient sources of orbital currents.

Boundary effects on orbital magnetization for a bilayer system with different Chern numbers

The real space formalism of orbital magnetization (OM) is an average of the local OM over some appropriate region of the system. Previous studies prefer a bulk average (i.e., without including boundaries). Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the effects of boundaries on the real space expressions of OM. The size convergence processes of its three constituent terms ${M}_{\mathrm{LC}}$, ${M}_{\mathrm{IC}}$, and ${M}_{\mathrm{BC}}$ are analyzed. The topological term ${M}_{\mathrm{BC}}$ makes a nonnegligible contribution from boundaries as a manifestation of edge states, especially in the case of nonzero Chern numbers. However, we show that the influence of the boundary on ${M}_{\mathrm{LC}}$ and ${M}_{\mathrm{IC}}$ exactly compensates that on ${M}_{\mathrm{BC}}$. This compensation effect leads to the conclusion that the whole sample average is also a correct algorithm in the thermodynamic limit, which gives the same value as those from the bulk average and the $k$-space formula. This clarification will be beneficial to further studies on orbitronics, as well as the orbital magnetoelectric effects in higher dimensions.

Anomalous Hall effect at half filling in twisted bilayer graphene

Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($\nu=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($\nu=2$) owing to competing intervalley coherent states, as well as spin-polarized and valley Hall states that are favored by an intervalley Hund's coupling. Here, we present measurements of two tBLG devices with twist angles slightly away from the magic angle (0.96$^{\circ}$ and 1.20$^{\circ}$), in which we report the surprising observation of the AHE at $\nu=+2$ and $-2$, respectively. These findings imply that a valley-polarized phase can become the ground state at half filling in tBLG rotated slightly away from the magic angle. Our results reveal the emergence of an unexpected ground state in the intermediately-coupled regime ($U/W \sim 1$, where $U$ is the strength of Coulomb repulsion and $W$ is the bandwidth), in between the strongly-correlated insulator and weakly-correlated metal, highlighting the need to develop a more complete understanding of tBLG away from the strongly-coupled limit.

Quantum cascade of correlated phases in trigonally warped bilayer graphene.

Divergent density of states offersan opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene1-5, the band touching points of few-layer rhombohedral graphite6-8 and the lightly doped rhombohedral trilayer graphene9-11. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality7 leading to layer antiferromagnetic states12 or quantum anomalous Hallstates13. Here we report the observation of a cascade of correlated phases in the vicinity of electric-field-controlled Lifshitz transitions14,15 and van Hove singularities16 in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals10,11. Furthermore, we identify signatures consistent with a topologically non-trivial Wigner-Hall crystal17 at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behaviour deviates from that of standard Fermi liquids. Our results in this reproducible, tunable, simple systemopen up new horizons for studying strongly correlated electrons.

Spin and orbital magnetism of exohedral fullerene doped with single transition metal atom (Sc-Ni): A relativistic density functional theory study

Relativistic density functional theory calculations have been implemented to study the structural configurations, electronic and magnetic properties of exohedral 3d transition metal atoms doping on C60 fullerene (TM-C60) by a full potential local orbital method. The calculated binding energies revealed that the TM-C60 molecules are energetically stable in all adsorption sites. We also found that the TM-doped exohedral C60 complexes are more reactive than pure C60 fullerene. The spin and orbital magnetic moments were also determined. We have indicated that in all of the five adsorption sites, exohedral TM-C60 molecules (except for Ni-C60) are magnetized. Our magnetic calculations show that the total spin magnetic moments of TM-C60 molecules mainly come from the TM atoms. We found that the spin magnetic moments of adsorbed TM atoms in exohedral doping C60 fullerene from Sc to Mn (HH adsorption site) and for Sc to Cr (HP and P adsorption sites) are greater than their free states. Our calculations suggest that exohedral doping 3d TM-C60 complexes can almost maintain spin magnetic moments. We have indicated that the magnetic properties of exohedral TM-C60 molecules change in the presence of spin–orbit coupling. Significant orbital contributions to magnetic moments are recognized in these configurations while the spin moments are unaffected. We found that Co in exohedral doping of C60 fullerene shows a robust orbital moment in all the five adsorption sites.

Antisymmetric Seebeck Effect in a Tilted Weyl Semimetal.

Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co_{3}Sn_{2}S_{2}. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.

Topological magnetoelectric response in ferromagnetic axion insulators.

The topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all surface states. Here, we theoretically propose that axion insulators with a simple ferromagnetic configuration, such as the MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize the TME. In the designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical electric field, the surface Hall currents give rise to a nearly half-quantized orbital moment, accompanied by a gapless chiral hinge mode circulating in parallel. Thus, the orbital magnetization from the two topological origins can be easily distinguished by reversing the electric field. Our work paves the way for direct observation of the TME in realistic axion-insulator materials.

Tunable Spin and Orbital Edelstein Effect at (111) LaAlO3/SrTiO3 Interface.

Converting charge current into spin current is one of the main mechanisms exploited in spintronics. One prominent example is the Edelstein effect, namely, the generation of a magnetization in response to an external electric field, which can be realized in systems with lack of inversion symmetry. If a system has electrons with an orbital angular momentum character, an orbital magnetization can be generated by the applied electric field, giving rise to the so-called orbital Edelstein effect. Oxide heterostructures are the ideal platform for these effects due to the strong spin–orbit coupling and the lack of inversion symmetries. Beyond a gate-tunable spin Edelstein effect, we predict an orbital Edelstein effect an order of magnitude larger then the spin one at the (111) LaAlO/SrTiO interface for very low and high fillings. We model the material as a bilayer of orbitals using a tight-binding approach, whereas transport properties are obtained in the Boltzmann approach. We give an effective model at low filling, which explains the non-trivial behaviour of the Edelstein response, showing that the hybridization between the electronic bands crucially impacts the Edelstein susceptibility.

Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $\nu$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $\nu=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices.

Anomalous Response in the Orbital Magnetic Susceptibility of 2D Topological Systems

2D compounds with nonzero Berry curvature are ideal systems to study exotic and technologically favorable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and nontrivial regimes have to present very different behaviors, which are encoded for the orbital susceptibility and magnetization. To try to reveal them, it is found that it was necessary to introduce a k‐dependent mass term in the relativistic formalism of these materials. Thus, while a topologically trivial insulator is predicted to have a very limited response, in the nontrivial regime, a singular contribution to the orbital magnetic susceptibility, which is inversely proportional to the square of the quantum magnetic flux is unveiled. In this scenario, besides determining the measurement conditions a new route for enhancing the intrinsic orbital magnetism of topological materials widening the range of temperatures and magnetic fields without involving tiny bandgaps is found.

Floquet topological systems with flat bands: Edge modes, Berry curvature, and orbital magnetization

Results are presented for Floquet systems in two spatial dimensions where the Floquet driving breaks an effective time-reversal symmetry. The driving protocol also induces flat bands that correspond to anomalous Floquet phases where the Chern number is zero and yet chiral edge modes exist. Analytic expressions for the edge modes, Berry curvature, and orbital magnetization are derived for the flat bands. Results are also presented for the static Haldane model for parameters when the bands are flat. Floquet driving of the same model is shown to give rise to Chern insulators as well as anomalous Floquet phases. The orbital magnetization for these different topological phases are presented and are found to be enhanced at half filling by the broken particle-hole symmetry of the Haldane model.

Excitonic fractional quantum Hall hierarchy in moiré heterostructures

We consider fractional quantum Hall states in systems where two flat Chern number $C=\ifmmode\pm\else\textpm\fi{}1$ bands are labeled by an approximately conserved valley index and interchanged by time reversal symmetry. At filling factor $\ensuremath{\nu}=1$ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized orbital ferromagnet parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for moir\'e heterostructures of bilayer graphene on a hexagonal boron nitride substrate.

Evidence of Magnon-Mediated Orbital Magnetism in a Quasi-2D Topological Magnon Insulator.

We explore spin dynamics in Cu(1,3-bdc), a quasi-2D topological magnon insulator. The results show that the thermal evolution of the Landé g factor (g) is anisotropic: gin-plane decreases while gout-of-plane increases with increasing temperature T. Moreover, the anisotropy of the g factor (Δg) and the anisotropy of saturation magnetization (ΔMs) are correlated below 4 K, but they diverge above 4 K. We show that the electronic orbital moment contributes to the g anisotropy at lower T, while the topological orbital moment induced by thermally excited spin chirality dictates the g anisotropy at higher T. Our work suggests an interplay among topology, spin chirality, and orbital magnetism in Cu(1,3-bdc).

Anomalous random multipolar driven insulators

It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry, nonequilibrium topological phases of matter can exist in aperiodically driven systems for tunably parametrically long prethermal lifetimes. As a prerequisite, we first demonstrate the existence of longlived prethermal Anderson localization in two dimensions under random multipolar driving. We then show that the localization may be topologically nontrivial with a quantized bulk orbital magnetization even though there are no well-defined Floquet operators. We further confirm the existence of this anomalous random multipolar driven insulator by detecting quantized charge pumping at the boundaries, which renders it experimentally observable.

Colossal Orbital Edelstein Effect in Noncentrosymmetric Superconductors.

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a nonvanishing magnetization, a phenomenon which is at the heart of nondissipative magnetoelectric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments, a question of fundamental relevance deals with the orbital nature of magnetoelectric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than 1 order of magnitude greater than that due to the spin, giving rise to a colossal magnetoelectric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone. In the presence of superconducting phase inhomogeneities, a modulation of the Edelstein signal on the scale of the superconducting coherence length appears, leading to domains with opposite orbital moment orientations. These hallmarks are robust to real-space self-consistent treatment of the superconducting order parameter. The orbital-dominated magnetoelectric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multiorbital superconductors with inversion symmetry breaking.

Orbital magnetization of Floquet topological systems

A general expression for the orbital magnetization of a Floquet system is derived. The expression holds for a clean system and is valid for any driving protocol and arbitrary occupation of the bands. The orbital magnetization is shown to be large not only for Chern insulators, but also for anomalous phases where the Chern number does not fully account for the topology. In addition, the orbital magnetization is shown to take significant values both for a thermal equilibrium occupation of the Floquet bands and for occupations determined by a quantum quench from an initial state with zero orbital magnetization. For the latter case, the orbital magnetization is shown to be highly sensitive to van Hove singularities of the Floquet bands.

Alternating twisted multilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

Recently the alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, which motivates us to study the electronic structures and possible correlation effects for this class of alternating twisted multilayer graphene (ATMG) systems. In this work we consider generic ATMG systems with M-L-N stacking configurations, in which the M (L) graphene layers and the L (N) layers are twisted by an angle θ (−θ). Based on analysis from a simplified k⋅p model approach, we derive generic partition rules for the low-energy electronic structures, which exhibit various band dispersions including two pairs of flat bands and flat bands co-existing with various gapless Fermionic excitations. For a mirror-symmetric ATMG system with doubled flat bands, we further find that Coulomb interactions may drive the system into a state with intertwined electric polarization and orbital magnetization orders, which can exhibit an interaction-driven orbital magnetoelectric effect.

A semiclassical approach to surface Fermi arcs in Weyl semimetals

We present a semiclassical explanation for the morphology of the surface Fermi arcs of Weyl semimetals. Viewing the surface states as a two-dimensional Fermi gas subject to band bending and Berry curvatures, we show that it is the non-parallelism between the velocity and the momentum that gives rise to the spiral structure of Fermi arcs. We map out the Fermi arcs from the velocity field for a single Weyl point and a lattice with two Weyl points. We also investigate the surface magnetoplasma of Dirac semimetals in a magnetic field, and find that the drift motion, the chiral magnetic effect and the Imbert-Fedorov shift are all involved in the formation of surface Fermi arcs. Our work not only provides an insightful perspective on the surface Fermi arcs and a practical way to find the surface dispersion, but also paves the way for the study of other physical properties of the surface states of topological semimetals, such as transport properties and orbital magnetization, using semiclassical methods.