Berry Curvature In Momentum Space Research Articles

Large anomalous Hall effect and unusual domain switching in an orthorhombic antiferromagnetic material NbMnP

Specific antiferromagnetic (AF) spin configurations generate large anomalous Hall effects (AHEs) even at zero magnetic field through nonvanishing Berry curvature in momentum space. In addition to restrictions on AF structures, suitable control of AF domains is essential to observe this effect without cancellations among its domains; therefore, compatible materials remain limited. Here we show that an orthorhombic noncollinear AF material, NbMnP, acquired AF structure-based AHE and controllability of the AF domains. Theoretical calculations indicated that a large Hall conductivity of ~230 Ω−1cm−1 originated from the AF structure of NbMnP. Symmetry considerations explained the production of a small net magnetization, whose anisotropy enabled the generation and cancellation of the Hall responses using magnetic fields in different directions. Finally, asymmetric hysteresis in NbMnP shows potential for the development of controllability of responses in AF materials.

Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands.

Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.

Strain-tunable Berry curvature in quasi-two-dimensional chromium telluride

Magnetic transition metal chalcogenides form an emerging platform for exploring spin-orbit driven Berry phase phenomena owing to the nontrivial interplay between topology and magnetism. Here we show that the anomalous Hall effect in pristine Cr2Te3 thin films manifests a unique temperature-dependent sign reversal at nonzero magnetization, resulting from the momentum-space Berry curvature as established by first-principles simulations. The sign change is strain tunable, enabled by the sharp and well-defined substrate/film interface in the quasi-two-dimensional Cr2Te3 epitaxial films, revealed by scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. This Berry phase effect further introduces hump-shaped Hall peaks in pristine Cr2Te3 near the coercive field during the magnetization switching process, owing to the presence of strain-modulated magnetic layers/domains. The versatile interface tunability of Berry curvature in Cr2Te3 thin films offers new opportunities for topological electronics.

Collective Excitations in Chiral Stoner Magnets.

We argue that spin- and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The chiral edge behavior originates from the interplay between the momentum-space Berry curvature in Dirac bands and the geometric phase of a spin texture in position space. The edge modes are weakly confined to the edge, featuring dispersion that is robust and insensitive to the detailed profile of magnetization at the edge. This unique character of edge modes reduces their overlap with edge disorder and enhances the mode lifetime. The mode propagation direction reverses upon reversing valley polarization, an effect that provides a clear testable signature of geometric interactions in isospin-polarized Dirac bands.

Discovery of Topological Magnetic Textures near Room Temperature in Quantum Magnet TbMn6 Sn6.

The study of topology in quantum materials has fundamentally advanced the understanding in condensed matter physics and potential applications in next-generation quantum information technology. Recently, the discovery of a topological Chern phase in the spin-orbit-coupled Kagome lattice TbMn6 Sn6 has attracted considerable interest. Whereas these phenomena highlight the contribution of momentum space Berry curvature and Chern gap on the electronic transport properties, less is known about the intrinsic real space magnetic texture, which is crucial for understanding the electronic properties and further exploring the unique quantum behavior. Here, the stabilization of topological magnetic skyrmions in TbMn6 Sn6 using Lorentz transmission electron microscopy near room temperature, where the spins experience full spin reorientation transition between the a- and c-axes, is directly observed. An effective spin Hamiltonian based on the Ginzburg-Landau theory is constructed and micromagnetic simulation is performed to clarify the critical role of Ruderman-Kittel-Kasuya-Yosida interaction on the stabilization of skyrmion lattice. These results not only uncover nontrivial spin topological texture in TbMn6 Sn6 , but also provide a solid basis to study its interplay with electronic topology.

Field-linear anomalous Hall effect and Berry curvature induced by spin chirality in the kagome antiferromagnet Mn3Sn

During the past two decades, it has been established that a non-trivial electron wave-function topology generates an anomalous Hall effect (AHE), which shows itself as a Hall conductivity non-linear in magnetic field. Here, we report on an unprecedented case of field-linear AHE. In Mn3Sn, a kagome magnet, the out-of-plane Hall response, which shows an abrupt jump, was discovered to be a case of AHE. We find now that the in-plane Hall response, which is perfectly linear in magnetic field, is set by the Berry curvature of the wavefunction. The amplitude of the Hall response and its concomitant Nernst signal exceed by far what is expected in the semiclassical picture. We argue that magnetic field induces out-of-plane spin canting and thereafter gives rise to nontrivial spin chirality on the kagome lattice. In band structure, we find that the spin chirality modifies the topology by gapping out Weyl nodal lines unknown before, accounting for the AHE observed. Our work reveals intriguing unification of real-space Berry phase from spin chirality and momentum-space Berry curvature in a kagome material.

Magnetic and transport properties of electron doped EuTiO3 thin films with La3+ (4f) or Gd3+ (4f7) donors grown by gas source molecular beam epitaxy

EuTiO3 (ETO) is a unique magnetic semiconductor with a large localized magnetic moment of Eu2+ (4f 7). By the doping of high-mobility electrons in the Ti 3d conduction band, peculiar magnetotransport properties such as the unconventional anomalous Hall effect (AHE) due to Berry curvature in momentum space, as well as the Shubnikov–de Haas oscillations of spin polarized electrons, have been observed. In this study, we have examined the physical properties of high quality ETO films with La3+ (4f0) or Gd3+ (4f7) donors (ELTO or EGTO) grown on nearly lattice matched SrTiO3 substrates with a gas source molecular beam epitaxy. We find that the anti-ferromagnetic ordering of ELTO is destabilized by the vacancy of the magnetic moment on the La-site for ELTO. The maximum electron mobility for ELTO (<3200 cm2 V−1 s−1) is larger than that of EGTO (<1500 cm2 V−1 s−1), keeping the metallic state at very diluted doping. The AHE changes its sign with shifting the Fermi level position across the Weyl nodes, as seen previously for compressively strained ELTO films, but the critical electron density is much lower, which can be explained by the absence of additional crystal-field splitting in the lattice matched system. These unveiled transport properties provide deeper understanding of the transport phenomena related to the topology of the band structure in high-mobility, magnetic oxide semiconductors.

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+ δ Te2.

Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Cr1+ δ Te2 is a self-intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real-space Berry curvature effects, similar considerations of momentum-space Berry curvatureare lacking. Here, the electronic structure and transport properties of epitaxial Cr1+ δ Te2 thin films are systematically investigated over a range of doping, δ (0.33 - 0.71). Spectroscopic experiments reveal the presence of a characteristic semi-metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi-metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum-space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

Observation of an anomalous Hall effect in single-crystal Mn3Pt

The Mn3X family of compounds was the first in which a large anomalous Hall effect (AHE) was predicted to arise from a purely antiferromagnetic structure, due to the Berry curvature in momentum space. Nearly simultaneously with this prediction, a large AHE was observed experimentally in one of the hexagonal members of this family, Mn3Sn. Aligning antiferromagnetic domains, a necessary step for observation of the AHE, is more challenging for the cubic members of the Mn3X family, due to a combination of smaller spontaneous ferromagnetic moments and much stronger magnetic anisotropy. Here, we use a combination of uniaxial stress and applied magnetic field to align domains of bulk single-crystal Mn3Pt, and demonstrate for the first time a substantial AHE in a bulk sample of a cubic member of the Mn3X family. The AHE remains locked in with essentially no quantitative variation when the stress is ramped back to zero, which shows that it is not a consequence of any stress-induced ferromagnetic moment.

Antisite disorder and Berry curvature driven anomalous Hall effect in the spin gapless semiconducting Mn2CoAl Heusler compound

Spin gapless semiconductors exhibit a finite band gap for one spin channel and a closed gap for another spin channel, and they have emerged as a new state of magnetic materials with a great potential for spintronic applications. The first experimental evidence for spin gapless semiconducting behavior was observed in an inverse Heusler compound ${\mathrm{Mn}}_{2}\mathrm{CoAl}$. Here, we report a detailed investigation of the crystal structure and anomalous Hall effect in ${\mathrm{Mn}}_{2}\mathrm{CoAl}$ using experimental and theoretical studies. The analysis of the high-resolution synchrotron x-ray diffraction data shows antisite disorder between Mn and Al atoms within the inverse Heusler structure. The temperature-dependent resistivity shows semiconducting behavior and follows Mooij's criteria for disordered metal. The scaling behavior of the anomalous Hall resistivity suggests that the anomalous Hall effect in ${\mathrm{Mn}}_{2}\mathrm{CoAl}$ is primarily governed by an intrinsic mechanism due to the Berry curvature in momentum space. The experimental intrinsic anomalous Hall conductivity (AHC) is found to be $\ensuremath{\sim}35$ S/cm, which is considerably larger than the theoretically predicted value for ordered ${\mathrm{Mn}}_{2}\mathrm{CoAl}$. Our first-principles calculations conclude that the antisite disorder between Mn and Al atoms enhances the Berry curvature and hence the value of intrinsic AHC, which is in very good agreement with the experiment.

Intrinsic anomalous Hall effect and Lifshitz transition in a ferromagnetic kagome-lattice metal

Magnetic topological materials with broken time-reversal symmetry have demonstrated colossal intrinsic anomalous Hall effects, originating from large Berry curvature in momentum space. Here, we report the electrical transport study of a ferromagnetic kagome-lattice material Nd3Al, which is predicted to be a magnetic topological high symmetry line metal candidate. We observed a polarity reversal of ordinary Hall resistivity across 40 K, plainly indicating a perceptible shift in chemical potential and change of the Fermi surface, i.e., temperature-induced Lifshitz transition. More strikingly, as the shifting of Fermi level around the band (anti-)crossing points contributes to a considerable Berry curvature, the anomalous Hall conductivity ultimately stabilizes to a constant of approximately ∼427 Ω−1 cm−1 below 40 K, accompanied by a maximum anomalous Hall angle reaching 1.4%, conforming to the intrinsic dissipationless topological Berry-phase mechanism. The similar scaling behavior of anomalous Hall conductivity in Nd3Al to that of magnetic Weyl semimetal Co3Sn2S2 further signals the possible presence of nontrivial topological bands in kagome Nd3Al. In view of the kagome-lattice structure and predicted topological nature, our work unveils the significant potential of the large intrinsic anomalous Hall effect in Nd3Al for investing the interaction between ferromagnetism and topology.

Spin chirality induced large topological Hall effect in magnetic Weyl semimetallic Eu2Ir2O7 (111) thin films

Antiferromagnetic (AFM) pyrochlore iridates are a fertile ground to hunt for a Weyl semimetallic state characterized by a linear crossing of two nondegenerate bands near the Fermi level ${E}_{F}$. Here, we demonstrate evidence of low-temperature anomalous and topological Hall effects in an antiferromagnetic ${\mathrm{Eu}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$(111) epitaxial thin film. The observed anomalous Hall effect is explained in terms of the momentum space Berry curvature associated with the Weyl nodes in the electronic band structure. The topological Hall effect reaches a large value ${\ensuremath{\rho}}_{xy}^{\text{THE}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\text{cm}$ at 2 K. The topological nature of the Hall effect is attributed to the nonzero scalar spin chirality of the all-in-all-out/all-out-all-in (AIAO/AOAI) type noncoplanar AFM spin structure. The magnetoresistance (MR) shows a prominent negative variation ($\mathrm{MR}\ensuremath{\sim}10%$ at 2 K) below 10 K. The field dependence of MR below 5 K varies quadratically in the low-field regime, and above 40 kOe it shows a linear trend. The quadratic to linear crossover of the MR is explained by the field-induced ($H$) spin canting (spin chirality) of the static spins in the AIAO/AOAI spin structure. In the intermediate-temperature region MR of $15\ensuremath{-}25$ K exhibits a hysteretic response which is associated with field-induced domain switching of the AIAO/AOAI spin structure. This work highlights the interplay of magnetism and topology in a spin-orbit-coupled correlated electron system and unravels the possibility for realizing the Weyl phase in antiferromagnetic ${\mathrm{Eu}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$(111) thin films.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators.

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Conserved current of nonconserved quantities

We provide a unified semiclassical theory for the conserved current of nonconserved quantities, and manifest it in two physical contexts: the spin current of Bloch electrons and the charge current of mean-field Bogoliubov quasiparticles. We reveal that the previously overlooked torque quadrupole density and Berry phase correction to the torque dipole density are essential to assure a circulating spin current with null net flow at equilibrium. The band geometric origin of spin transport is ascertained to be the momentum space Berry curvature instead of the spin Berry curvature, paving the way for material related studies. In superconductors the attained conserved charge current corresponds to the quasiparticle charge current renormalized by the condensate backflow. Its circulation at equilibrium gives an orbital magnetization, which involves the characteristics of superconductivity, such as the Berry curvature arising from unconventional pairing and an orbital magnetic moment induced by the charge dipole of moving quasiparticles.

Skyrmion-size dependence of the topological Hall effect: A real-space calculation

Motivated by the recent discoveries of magnets harboring short-pitch skyrmion lattices, we investigate the skyrmion-size dependence of the topological Hall effect. By means of large-scale real-space calculations, we find that the Hall conductivity takes its extreme value in the crossover region where both the real-space and momentum-space Berry curvature play a crucial role. We also investigate how the optimum skyrmion size ($\lambda_{\rm sk}^*$) depends on the lifetime of itinerant electrons ($\tau$) and coupling constant between electrons and localized spins ($J$). For the former, we show that $\lambda_{\rm sk}^{*}$ is proportional to $\sqrt{\tau}$, which indicates that $\lambda_{\rm sk}^{*}$ is much less sensitive to $\tau$ than the conventional expectation that $\lambda_{\rm sk}^{*}$ is proportional to the mean-free path $\propto \tau$. For the latter, we show that the non-adiabaticity considerably suppresses the topological Hall effect when the time scale determined by the skyrmion size and Fermi velocity is shorter than $1/J$. However, its effect on $\lambda_{\rm sk}^{*}$ is not so siginificant and $\lambda_{\rm sk}^{*}$ is about ten times the lattice constant in a wide range of $J$ and $\tau$.

Phonon Magnetic Moment from Electronic Topological Magnetization.

The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by the lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a k resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yang's monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gapped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where nontopological contribution is also important. Our results agree with recent observations in experiments.

Coupling Charge and Topological Reconstructions at Polar Oxide Interfaces.

In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion symmetry across the heterointerfaces. A notable example is the interface between polar and nonpolar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way for the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wave functions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO_{3}, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and LaAlO_{3}, a polar wide-band-gap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO_{2}/SrO interface configuration, leading to excess charge being pinned near the LaAlO_{3}/SrRuO_{3} interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction drives a reorganization of the topological charges in the band structure, thereby modifying the momentum-space Berry curvature in SrRuO_{3}. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.

Topological characteristic of Weyl degeneracies in a reciprocal chiral metamaterials system

Being a research hotspot in the field of topological semimetals, Weyl points (WPs) are monopoles of Berry curvature in momentum space. In this paper, we report the existence of photonic Weyl degeneracies in a reciprocal chiral metamaterials system. Due to the flat dispersion relation of the bulk plasmon modes, Weyl degeneracies here lie right on the critical transition between the type-I and type-II WPs. The photonic ‘Fermi arc’ connects the projection of pairs of WPs at the interface between the metamaterials and vacuum. Despite the bulk equi-frequency surfaces have changed dramatically, the ‘Fermi arc’ always exists. In addition, numerical simulations of topologically protected ‘Fermi arc’ surface states show that the surface waves are not scattered or reflected by the presence of sharp corners. Notably, such metamaterials host either type-I, type-II WPs or triple degenerate points (TDPs) depending on the nonlocal response. Our work provides an ideal photonic platform for studying the closely relation between WPs and other exotic states.

Weyl Nodes Close to the Fermi Energy in NbAs

The noncentrosymmetric transition‐metal monopnictides NbP, TaP, NbAs, and TaAs are a family of Weyl semimetals in which pairs of protected linear crossings of spin‐resolved bands occur. These so‐called Weyl nodes are characterized by integer topological charges of opposite sign associated with singular points of Berry curvature in momentum space. In such a system, anomalous magnetoelectric responses are predicted, which should only occur if the crossing points are close to the Fermi level and enclosed by Fermi surface pockets penetrated by an integer flux of Berry curvature, dubbed Weyl pockets. TaAs is shown to possess Weyl pockets, whereas TaP and NbP have trivial pockets enclosing zero net flux of Berry curvature. Herein, via measurements of the magnetic torque, resistivity, and magnetization, a comprehensive quantum‐oscillation study of NbAs is presented, the last member of this family where the precise shape and nature of the Fermi surface pockets is still unknown. Seven distinct frequency branches, three of which have not been observed before, are detected. A comparison with density functional theory calculations suggests that the two largest pockets are topologically trivial, whereas the low frequencies might stem from tiny Weyl pockets. The enclosed Weyl nodes are within a few meV of the Fermi energy.

Mapping the phase diagram of the quantum anomalous Hall and topological Hall effects in a dual-gated magnetic topological insulator heterostructure

The authors use a dual-gated device to map out the phase diagram created by the interplay between Berry curvature in real space and Berry curvature in momentum space in a magnetic topological insulator heterostructure