Large Orbital Moment Research Articles

Spin waves and orbital contribution to ferromagnetism in a topological metal

Honeycomb and kagome lattices can host propagating excitations with non-trivial topology as defined by their evolution along closed paths in momentum space. Excitations on such lattices can also be momentum-independent, and the associated flat bands are of interest due to strong interactions between heavy quasiparticles. Here, we report the discovery — using circularly polarized X-rays for the unambiguous isolation of magnetic signals — of a nearly flat spin-wave band and large (compared to elemental iron) orbital moment in the metallic ferromagnet Fe3Sn2 with compact AB-stacked kagome bilayers. As a function of out-of-plane momentum, the nearly flat optical mode and the global rotation symmetry-restoring acoustic mode are out of phase, consistent with a bilayer exchange coupling that is larger than the already large in-plane couplings. The defining units of this topological metal are therefore triangular lattices of octahedral iron clusters rather than weakly coupled kagome planes. The spin waves are strongly damped when compared to elemental iron, opening the topic of topological boson–fermion interactions for deeper exploration within this material platform.

Large Orbital Moment and Dynamical Jahn-Teller Effect of AlCl-Phthalocyanine on Cu(100).

Submonolayer amounts of chloroaluminum-phthalocyanine on Cu(100) were studied with scanning tunneling spectroscopy. The molecule can be prepared in a fourfold symmetric state whose conductance spectrum exhibits a zero-bias feature similar to a Kondo resonance. In magnetic fields, however, this resonance splits far more than expected from the spin of a single electron. Density functional theory calculations reveal a charge transfer of 1.3 electrons to the degenerate lowest unoccupied molecular orbitals. These orbitals are mixed by the orbital momentum operator L[over ^]_{z} with a large matrix element corresponding to m_{L}≈2.7. Dehydrogenation of a ligand lifts the degerenracy of the lowest unoccupied molecular orbital, reduces the splitting in magnetic fields, and induces a polarity dependence of the spectra. Using model calculations of the spin, orbital, and vibrational degrees of freedom we show that a dynamical Jahn-Teller effect reproduces the main experimental observations.

Intrinsic magnetism of an individual rare-earth atom on transition metal dichalcogenide semiconductors

Two-dimensional (2D) structures that exhibit intriguing magnetic phenomena such as perpendicular magnetocrystalline anisotropy (PMA) have become a focus of spintronic research due to their potentials in maximizing the information storage density. Herein we perform density-functional theory plus U (DFT+U) calculations to investigate the binding affinity and intrinsic magnetic properties of an individual rare-earth (RE) Sm atom on WSe2 monolayer. Our calculations show that Sm adatom energetically prefers to adsorb at the W-top site in WSe2 rather than the Se-top and hollow sites. We predict extremely large PMA values of ∼7–33 meV per Sm at the most stable W-top site, depending on U parameter in DFT+U calculations, while it is negligibly small for the Se-top and hollow sites. The underlying mechanism for large PMA is elucidated in terms of the strong spin–orbit coupled Sm 4f – W 5d orbital states and large 4f orbital magnetic moment in the high-spin crystal field. These results provide a viable route to achieving an atomic scale f-electron PMA in 2D structures, opening interesting prospects in two-dimensional semiconducting spintronics.

Evidence of Temperature-Dependent Interplay between Spin and Orbital Moment in van der Waals Ferromagnet VI3.

van der Waals materials provide a versatile toolbox for the emergence of new quantum phenomena and fabrication of functional heterostructures. Among them, the trihalide VI3 stands out for its unique magnetic and structural landscape. Here we investigate the spin and orbital magnetic degrees of freedom in the layered ferromagnet VI3 by means of temperature-dependent X-ray absorption spectroscopy and X-ray magnetic circular and linear dichroism. We detect localized electronic states and reduced magnetic dimensionality, due to electronic correlations. We furthermore provide experimental evidence of (a) an unquenched orbital magnetic moment (up to 0.66(7) μB/V atom) in the ferromagnetic state and (b) an instability of the orbital moment in the proximity of the spin reorientation transition. Our results support a coherent picture where electronic correlations give rise to a strong magnetic anisotropy and a large orbital moment and establish VI3 as a prime candidate for the study of orbital quantum effects.

Magnetic breakdown and spin-zero effect in quantum oscillations in kagome metal CsV3Sb5

In the recently discovered kagome metal CsV3Sb5, an intriguing proposal invoking a doped Chern insulator state suggests the presence of small Chern Fermi pockets hosting spontaneous orbital-currents and large orbital magnetic moments. While the net thermodynamic magnetization is nearly insensitive to these moments, due to their antiferromagnetic alignment, their presence can be revealed by the Zeeman effect, which shifts electron energies in magnetic fields with a proportionality given by the effective g−factor. Here, we determine the g-factor using the spin-zero effect in magnetic quantum oscillations. A large g-factor enhancement is visible only in magnetic breakdown orbits between conventional and concentrated Berry curvature Fermi pockets that host large orbital moments. Such Berry-curvature-generated large orbital moments are almost always concealed by other effects. In this system, however, magnetic breakdown orbits due to the proximity to a conventional Fermi-surface section allow them to be visibly manifested in magnetic quantum oscillations. Our results provide a remarkable example of the interplay between electronic correlations and more conventional electronic bands in quantum materials.

Symmetry and Electronic Properties of Metallic Nanoclusters

Spherical nanoclusters with countable member atoms and delocalized valence orbitals are superatoms with properties analogous to those of simple atoms. This is reflected, in particular, in their optical spectra and magnetic properties, in a similar sense to transition metal ions and complexes. Clusters can be of low-spin or high-spin with considerable contributions to magnetism by the large cluster orbital magnetic moment. Due to the large radius of the clusters, they can be diamagnetic with an unusually high diamagnetic susceptibility. Gold and platinum, which in the bulk are non-magnetic, show pronounced superparamagnetism associated with their high-spin nature, and the magnetic moment can be trapped in symmetry-breaking environments so that hysteresis pertains far beyond room temperature. A significant deviation from hydrogen-like orbitals results from the shape of the confining potential, which has the effect that the orbital quantum number ℓ is not limited to values less than the principal quantum number n.

Huge perpendicular magnetic anisotropy in a 12-fold planar hypercoordinate W@B12(NCCN)3 monolayer

Two-dimensional (2D) materials with planar hypercoordinate motifs are attractive in terms of both fundamental science and technological applications. Herein, we construct a stable hexagonal 2D W@B12(NCCN)3 monolayer using W@B12 cluster as a building block and –NCCN– as a bridge linker. Multi-center bonding analysis reveals that the abundant 3c–1e B–W–Β σ bonds are responsible for the stability of a 12-fold coordinated W@B12 wheel, which has the highest coordination number reported for a planar system. Moreover, 3c–1e Β−Ν−Β, 4c − 1e N–C–C–N, and 13c − 1e W–B12 π bonds together form big delocalized π bonds, endowing 2D W@B12(NCCN)3 with unusual stability. Remarkably, 2D W@B12(NCCN)3 is a robust ferromagnetic half-metal with a large orbital moment anisotropy of 1.3 μB, a high out-of-plane magnetic anisotropy energy of 199 meV/atom, and a high Curie temperature of 150 K, which provides a potential candidate for high-density memory devices. These findings provide vital guidance for the design of 2D magnets with planar hypercoordination and unusual functionality.

Large Orbital Moment of Two Coupled Spin-Half Co Ions in a Complex on Gold.

The magnetic properties of transition-metal ions are generally described by the atomic spins of the ions and their exchange coupling. The orbital moment, usually largely quenched due the ligand field, is then seen as a perturbation. In such a scheme, S = 1/2 ions are predicted to be isotropic. We investigate a Co(II) complex with two antiferromagnetically coupled 1/2 spins on Au(111) using low-temperature scanning tunneling microscopy, X-ray magnetic circular dichroism, and density functional theory. We find that each of the Co ions has an orbital moment comparable to that of the spin, leading to magnetic anisotropy, with the spins preferentially oriented along the Co-Co axis. The orbital moment and the associated magnetic anisotropy is tuned by varying the electronic coupling of the molecule to the substrate and the microscope tip. These findings show the need to consider the orbital moment even in systems with strong ligand fields. As a consequence, the description of S = 1/2 ions becomes strongly modified, which have important consequences for these prototypical systems for quantum operations.

Contrasting electronic states of RuI3 and RuCl3

The spin-orbital entangled states are of great interest as they hold exotic phases and intriguing properties. Here we use first-principles calculations to investigate the electronic and magnetic properties of ${\mathrm{RuI}}_{3}$ and ${\mathrm{RuCl}}_{3}$ in both bulk and monolayer cases. Our results show that ${\mathrm{RuI}}_{3}$ bulk is a paramagnetic metal, which is in agreement with recent experiments. We find that the ${\mathrm{Ru}}^{3+}$ ion of ${\mathrm{RuI}}_{3}$ is in the spin-orbital entangled ${j}_{\mathrm{eff}}=\frac{1}{2}$ state. More interestingly, a metal-insulator transition occurs from ${\mathrm{RuI}}_{3}$ bulk to monolayer, and this is mainly due to the band narrowing with the decreasing lattice dimensionality and to the Ru-I hybridization altered by the I $5p$ spin-orbit coupling. In contrast, ${\mathrm{RuCl}}_{3}$ bulk and monolayer both show Mott-insulating behavior, the ${\mathrm{Ru}}^{3+}$ ion is in the formal $S=\frac{1}{2}$ and $L=1$ state with a large in-plane orbital moment, and this result well explains the experimental large effective magnetic moment of ${\mathrm{RuCl}}_{3}$ and the strong in-plane magnetization. The present work demonstrates the contrasting spin-orbital states and the varying properties of ${\mathrm{RuI}}_{3}$ and ${\mathrm{RuCl}}_{3}$.

Elucidation of orbital moment, anisotropy, and magnetic damping in epitaxial Fe3O4 films

Fe${}_{3}$O${}_{4}$, the archetypal half metal, is one of the most studied magnetic materials to date, yet still the cause of intense debate regarding its physical characteristics. One particular property, the magnitude of the orbital moment, has been contested for over a decade with previous works measuring either a vanishingly small or a large orbital moment. Using complementary spectroscopic techniques, the authors demonstrate here that a finite orbital moment exists in Fe${}_{3}$O${}_{4}$, in addition to observing the interplay between defects, anisotropy, and magnetic damping.

Loop-current charge density wave driven by long-range Coulomb repulsion on the kagomé lattice

Recent experiments on vanadium-based nonmagnetic kagom\'e metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) revealed evidence for possible spontaneous time-reversal symmetry (TRS) breaking in the charge density wave (CDW) ordered state. The long-sought-after quantum order of loop currents has been suggested as a candidate for the TRS breaking state. However, a microscopic model for the emergence of the loop-current CDW due to electronic correlations is still lacking. Here, we calculate the susceptibility of the real and imaginary bond orders on the kagom\'e lattice near van Hove filling, and reveal the importance of next-nearest-neighbor Coulomb repulsion $V_2$ in triggering the instability toward imaginary bond ordered CDW. The concrete effective single-orbital $t$-$V_1$-$V_2$ model on the kagom\'e lattice is then studied, where $t$ and $V_1$ are the hopping and Coulomb repulsion on the nearest-neighbor bonds. We obtain the mean-field ground states, analyze their properties, and determine the phase diagram in the plane spanned by $V_1$ and $V_2$ at van Hove filling. The region dominated by $V_1$ is occupied by a $2a_0 \times 2a_0$ real CDW insulator with the inverse of Star-of-David (ISD) bond configuration. Increasing $V_2$ indeed drives a first-order transition from ISD to stabilized loop-current insulators that exhibit four possible current patterns of different topological properties, leading to orbital Chern insulators. We then extend these results away from van Hove filling and show that electron doping helps the stabilization of loop currents, and gives rise to doped orbital Chern insulators with emergent Chern Fermi pockets carrying large Berry curvature and orbital magnetic moment. Our findings provide a concrete model realization of the loop-current Chern metal at the mean-field level for the TRS breaking normal state of the kagom\'e superconductors.

On-Surface Design of a 2D Cobalt-Organic Network Preserving Large Orbital Magnetic Moment.

The design of antiferromagnetic nanomaterials preserving large orbital magnetic moments is important to protect their functionalities against magnetic perturbations. Here, we exploit an archetype H6HOTP species for conductive metal-organic frameworks to design a Co-HOTP one-atom-thick metal-organic architecture on a Au(111) surface. Our multidisciplinary scanning probe microscopy, X-ray absorption spectroscopy, X-ray linear dichroism, and X-ray magnetic circular dichroism study, combined with density functional theory simulations, reveals the formation of a unique network design based on threefold Co+2 coordination with deprotonated ligands, which displays a large orbital magnetic moment with an orbital to effective spin moment ratio of 0.8, an in-plane easy axis of magnetization, and large magnetic anisotropy. Our simulations suggest an antiferromagnetic ground state, which is compatible with the experimental findings. Such a Co-HOTP metal-organic network exemplifies how on-surface chemistry can enable the design of field-robust antiferromagnetic materials.

Origin of perpendicular magnetic anisotropy in CoxFe3−xO4+δ thin films studied by x-ray magnetic circular and linear dichroisms

We investigate the element-specific spin and orbital states and their roles on magnetic anisotropy in the Co-ferrite (Co$_x$Fe$_{3-x}$O$_{4+\delta}$ (001)) thin films which exhibit perpendicular magnetic anisotropy (PMA). The origin of PMA in the low $x$ region ($x$ $<$ 1) can be mainly explained by the large perpendicular orbital magnetic moments in the Co$^{2+}$ (3$d^7$) states detected by X-ray magnetic circular and linear dichroisms (XMCD/XMLD). The XMLD for a PMA film ($x=0.2$) with square hysteresis curve shows the oblate charge distribution in the Co$^{2+}$ site, which is consistent with the change in local nearest neighbor distance in Co detected by extended X-ray absorption fine structure analysis. Our finding reveals that the microscopic origin of PMA in Co-ferrite comes from the enhanced orbital magnetic moments along out-of-plane [001] direction through in-plane charge distribution by tensile strain, which adds the material functionalities in spinel ferrite thin films from the viewpoint of strain and orbital magnetic moments.

First-principles study on the structure, magnetic and electronic properties of cobalt-based double perovskite Sr2CoTeO6

The Co-based double perovskite oxides have been attracting great attention for their unique physical properties. Herein, we perform first-principles calculations on the structure, magnetic and electronic properties of fully ordered Sr2CoTeO6. The tolerance factor (τ) of ∼0.99 approves the stability of the perovskite structure. Studying the magnetic and electronic structure demonstrates that Sr2CoTeO6 is a semiconducting antiferromagnet. The effective magnetic interactions generate from B-site Co(↑)-Co(↓) antiferromagnetic spins and the chemical composition is Sr2+2Co2+Te6+O2-6. Detailed analysis of Co 3d orbitals indicates the B-site Co2+ with 3d7 (t2g5eg2) electronic configuration is in the high-spin state. The spin-orbital coupling effects of the Co cations do not alter the semiconducting performance of Sr2CoTeO6 but produce a large orbital magnetic moment of −1.07 μB/atom. This work is a useful complement for understanding the inextricable effects of Co on the physical properties, paving a credible way for the investigation of Co-based double perovskite oxides.

Single-domain perpendicular magnetization induced by the coherent O 2p -Ru 4d hybridized state in an ultra-high-quality SrRuO3 film

We investigated the Ru $4d$ and O $2p$ electronic structure and magnetic properties of an ultrahigh-quality $\mathrm{SrRu}{\mathrm{O}}_{3}$ film on $\mathrm{SrTi}{\mathrm{O}}_{3}$ grown by machine-learning assisted molecular-beam epitaxy. The high itinerancy and long quantum lifetimes of the quasiparticles in the Ru $4d$ ${t}_{2g}$-O $2p$ hybridized valence band are confirmed by observing the prominent well-screened peak in the Ru $3d$ core-level photoemission spectrum, the coherent peak near the Fermi energy in the valence-band spectrum, and quantum oscillations in the resistivity. The element-specific magnetic properties and the hybridization between the Ru $4d$ and O $2p$ orbitals were characterized by Ru ${M}_{2,3}$-edge and O $K$-edge soft x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements. The ultrahigh-quality $\mathrm{SrRu}{\mathrm{O}}_{3}$ film with the residual resistivity ratio of 86 shows the large orbital magnetic moment of oxygen ions induced by the strong orbital hybridization of the O $2p$ states with the spin-polarized Ru $4d$ ${t}_{2g}$ states. The film also shows single-domain perpendicular magnetization with an almost ideal remanent magnetization ratio of 0.97. These results provide detailed insights into the relevance between orbital hybridization and the perpendicular magnetic anisotropy in $\mathrm{SrRu}{\mathrm{O}}_{3}/\mathrm{SrTi}{\mathrm{O}}_{3}$ systems.

Distorted 3Q state driven by topological-chiral magnetic interactions

We demonstrate that topological-chiral magnetic interactions can play a key role for magnetic ground states in ultrathin films at surfaces. Based on density functional theory we show that significant chiral-chiral interactions occur in hexagonal Mn monolayers due to large topological orbital moments which interact with the emergent magnetic field. Due to the competition with higher-order exchange interactions superposition states of spin spirals such as the 2Q state or a distorted 3Q state arise. Simulations of spin-polarized scanning tunneling microscopy images suggest that the distorted 3Q state could be the magnetic ground state of a Mn monolayer on Re(0001).

Valence fluctuations and Kondo resonance in Co adatom on Cu2N/Cu(100) surface: DFT + ED study

We report density functional theory plus exact diagonalization of the multi-orbital Anderson impurity model calculations including the spin–orbit coupling for the Co adatom on the top of Cu2N/Cu(001) surface. It is found that experimentally observed zero-bias peak in differential conductance can occur for quasi-degenerate many-body solution representing a mixed valence state of the Co adatom with the non-integer d manifold occupation of 7.4. Estimated 5 meV inelastic step energy is in a quantitative agreement with the experimental scanning tunnelling spectroscopy value of 6 meV. We find the non-zero spin and orbital magnetic moments in the applied magnetic field, in a reasonable agreement with the x-ray magnetic circular dichroism data. The presence of large orbital magnetic moment was not considered in previous spin-only theoretical interpretations, and can unravel complexity of the physics behind the experimental spectra for Co and other adatoms on Cu2N/Cu(001) surface.

Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multilayer graphene

We study the electronic structure and band topology of fully relaxed twisted multi-layer graphene (TMLG). Isolated flat bands emerge in TMLG with the number of layers [$M+N$ with $M$ the layer number of the bottom few-layer graphene (FLG)] up to 10 and with various stacking orders, and most of them are on the hole side. The touched bands of FLGs around the Fermi level are split by the moir\'{e} coupling through the electron-hole asymmetry in low-energy bands of FLGs and by the vertical hopping between next-nearest layers. The full structural relaxation leads to global gaps that completely isolate a flat band. For TMLG with given $M$ and $N$, the highest magnitude of Chern numbers ($|C|$) of the separable flat bands reaches $M+N-1$ and can be hosted by certain isolated bands. The $|C|=9$ occurs in the isolated flat valence band of several configurations with 10 layers. Such high $|C|$ originates from the lifting of the band-state degeneracy in the weak regime of moir\'{e} coupling or from the topological phase transitions induced by the strong moir\'{e} coupling. Moreover, large orbital magnetic moments arise in isolated flat bands with high $|C|$ and depend on the structural configurations of TMLG.

5f states in UGa2 probed by x-ray spectroscopies

The $5f$-based ferromagnet $\mathrm{U}{\mathrm{Ga}}_{2}$ with the Curie temperature ${T}_{\mathrm{C}}=125\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ was investigated by x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) experiments at the $\mathrm{U}--{M}_{4,5}$ and Ga--K edges. The position of the $\mathrm{U}--{M}_{4}$ white line, determined in the high-energy resolution fluorescence detection XAS, suggests that $\mathrm{U}{\mathrm{Ga}}_{2}$ is neither a localized $5{f}^{2}$ nor an itinerant system with $5f$ occupancy close to ${n}_{5f}=3$. The analysis of the acquired ${M}_{4,5}$ XANES and XMCD spectra indicates the $5f$ occupancy close to 2.5 and a large orbital magnetic moment of the uranium $5f$ states (3.18 ${\ensuremath{\mu}}_{\mathrm{B}}$) that is partly compensated by the antiparallel spin moment (1.31 ${\ensuremath{\mu}}_{\mathrm{B}}$). Thus, the total $5f$ magnetic moment of 1.87 ${\ensuremath{\mu}}_{\mathrm{B}}$ is obtained, which is smaller than the known bulk magnetization of 3.0 ${\ensuremath{\mu}}_{\mathrm{B}}$ per formula unit, while the magnetic moments of the Ga atoms are negligible. Several methods based on density-functional theory were applied and the obtained results were compared with XAS spectral features, the Sommerfeld coefficient of the electronic specific heat, and the size of the U moments and $5f$ occupancies. A clear correlation is revealed between the $\mathrm{U}--{M}_{4}$ white-line position of three metallic uranium compounds and the calculated uranium ionicity. It is demonstrated that only electronic structure methods taking appropriate care of orbital magnetism and related atomic multiplet effects can successfully describe all considered properties.

Superconducting orbital magnetoelectric effect and its evolution across the superconductor-normal metal phase transition

Superconducting magnetoelectric effect, which is the current-induced magnetization in a superconductor, mainly focused on the spin magnetization in previous studies, but ignore the effect of the orbital magnetic moments carried by the paired Bloch electrons. In this work, we show that orbital magnetic moments in superconductors can induce large orbital magnetization in the presence of a current. We constructed a unified description for the current-induced spin and orbital magnetization across the superconductivity normal metal phase transition. We find that in a superconductor with uniform pairing, the current-induced magnetization at a given current density is the same as that in its normal metal state, while with the nonuniform superconducting pairing, the current-induced magnetization exhibits an abrupt change in magnitude near the superconductivity normal metal phase transition. Importantly, our theory predicts the orbital magnetoelectric effect in superconducting twisted bilayer graphene which has paired Bloch electrons with large orbital magnetic moments and negligible spin-orbit coupling. We propose that the measurement of the current-induced orbital magnetoelectric effect can be used to detect the possible nonuniform pairings in twisted bilayer graphene and other newly discovered superconductors with non-trivial Berry curvatures.