Space Berry Curvature Research Articles

Atomic disorder and intrinsic anomalous Hall effect in a half-metallic ferromagnet Co2VAl

Half-metallic ferromagnets, conducting for one spin channel while insulating for the other, are highly desirable for spintronic applications due to 100 % spin polarization around the Fermi level. Cobalt-based half-metallic Heusler compounds have attracted enormous attention due to their large spin polarization and a high magnetic transition temperature. In the present study, we report the experimental and theoretical investigation of crystal structure and anomalous Hall effect (AHE) in half-metallic ferromagnet Co2VAl. The structural investigation of high-resolution synchrotron x-ray diffraction data reveals 10 % antisite disorder between V and Al atoms within the L21 ordered crystal structure. The scaling analysis of anomalous Hall data shows that the AHE in our system is mainly driven by the Berry curvature in the momentum space. The magnitude of experimental intrinsic anomalous Hall conductivity (AHC) due to the momentum space Berry curvature is about 44.67 ± 0.02 S/cm at 5 K, which is less than the theoretically calculated AHC for the ordered structure. Our theoretical calculations suggest that the lower AHC obtained for the present system is due to the reduced Berry curvature in the disordered case with negligible impact on half-metallicity of the system.

Microscopic origin of local electric polarization in NiPS3

Recently, Zhang–Rice triplet to singlet excitations have been measured experimentally and verified numerically in a van der Waals antiferromagnet NiPS3, which reveals a collective local change of an electronic structure. In particular, such numerical simulations predicted that these electronic excitations occur simultaneously with local electric polarizations. In this study, we uncover the microscopic origin of this local electric polarization in the Zhang–Rice triplet to singlet excitation. Our lattice-model calculation predicts that the electric polarization can be controlled by applied magnetic fields, where the atomic spin–orbit coupling plays an important role. We speculate emergence of real space Berry curvature to describe the electric polarization in this strongly correlated system.

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.

Intrinsic anomalous Hall conductivity and real space Berry curvature induced topological Hall effect in Ni2MnGa magnetic shape memory alloy

Anomalous and topological Hall effect (THE) are the fascinating electronic transport properties in condensed matter physics and received tremendous interest in the field of spintronics. Here, we report the intrinsic anomalous Hall conductivity (AHC) and THE in the bulk Ni2MnGa magnetic shape memory alloy. The magnetization measurement reveals the premartensite, martensite and magnetic phase transitions. A detailed analysis of AHC reveals that the intrinsic Berry phase mechanism dominates over skew scattering and side jump in all the structural phases of Ni2MnGa. Further, an additional contribution in the Hall resistivity is observed as THE. The magnitude of the THE and its temperature independent behavior indicates that the THE arises due to the real space Berry curvature induced by topologically protected magnetic skyrmion textures in the martensite and premartensite phases of Ni2MnGa. The larger magnetic field is required to vanish the topological Hall resistivity in the martensite phase in comparison to the premartensite phase, which manifests the more stable skyrmion textures in the martensite phase. The present findings open a new direction in the field of functional materials, which hosts skyrmion, exhibits anomalous transport and magnetic shape memory effect.

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.

Ultrafast control of moiré pseudo‐electromagnetic field in homobilayer semiconductors

AbstractIn long‐wavelength moiré patterns of homobilayer semiconductors, the layer pseudospin of electrons is subject to a sizable Zeeman field that is spatially modulated from the interlayer coupling in moiré. By interference of this spatial modulation with a homogeneous but dynamically tunable component from an out‐of‐plane electric field, we show that the spatial‐temporal profile of the overall Zeeman field therefore features a topological texture that can be controlled in an ultrafast timescale by a terahertz field or an interlayer bias. Such dynamical modulation leads to the emergence of an in‐plane electric field for low‐energy carriers, which is related to their real space Berry curvature—the moiré magnetic field—through Faraday's law of induction. These emergent electromagnetic fields, having opposite signs at the time reversal pair of valleys, can be exploited to manipulate valley and spin in the moiré landscape under the control of a bias pulse or terahertz irradiation.Key Points Temporal control of topological texture through the interference of spatial and temporal modulations. Emergent electromagnetic fields in nanoscale that can be manipulated in picosecond timescale. Pulsed spin and valley pseudospin current controlled by electrical bias or terahertz irradiation.

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.

Absence of Hall effect due to Berry curvature in phase space

Transverse current due to Berry curvature in phase space is formulated based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet. It is shown that the Hall effect due to the phase space Berry curvature is absent because the contributions from “anomalous velocity” and “effective Lorentz force” are completely cancelled out.

Sign Structure of Thermal Hall Conductivity and Topological Magnons for In-Plane Field Polarized Kitaev Magnets.

The appearance of half-quantized thermal Hall conductivity in α-RuCl_{3} in the presence of in-plane magnetic fields has been taken as a strong evidence for the Kitaev spin liquid. Apart from the quantization, the observed sign structure of the thermal Hall conductivity is also consistent with predictions from the exact solution of the Kitaev honeycomb model. Namely, the thermal Hall conductivity changes sign when the field direction is reversed with respect to the heat current, which is perpendicular to one of the three nearest neighbor bonds on the honeycomb lattice. On the other hand, the thermal Hall conductivity is almost zero when the field is applied along the bond direction. Here, we theoretically demonstrate that such a peculiar sign structure of the thermal Hall conductivity is a generic property of the polarized state in the presence of in-plane magnetic fields. In this case, the thermal Hall effect arises from topological magnons with finite Chern numbers, and the sign structure follows from the symmetries of the momentum space Berry curvature. Using a realistic spin model with bond-dependent interactions, we show that the thermal Hall conductivity can have a magnitude comparable to that observed in the experiments. Hence, the sign structure alone cannot make a strong case for the Kitaev spin liquid. The quantization at very low temperatures, however, will be a decisive test as the magnon contribution vanishes in the zero temperature limit.

THz-range Faraday rotation in the Weyl semimetal candidate Co2TiGe

The Co2 family of ferromagnetic Heusler alloys has attracted interest due to their fully spin-polarized nature, making them ideal for applications in spintronic devices. More recently, the existence of room temperature time-reversal-breaking Weyl nodes near the Fermi level was predicted and confirmed in these systems. As a result of the presence of these Weyl nodes, these systems possess a non-zero momentum space Berry curvature that can dramatically influence transport properties such as the anomalous Hall effect. One of these candidate compounds is Co2TiGe. Recently, high-quality molecular beam epitaxy-grown thin films of Co2TiGe have become available. In this work, we present a THz-range measurement of MBE-grown Co2TiGe films. We measure the THz-range Faraday rotation, which can be understood as a measure of the anomalous Hall effect. We supplement this work with electronic band-structure calculations showing that the principal contribution to the anomalous Hall effect in this material stems from the Berry curvature of the material. Our work shows that this class of Heusler materials shows promise for Weyl semimetal based spintronics.

Anomalous Hall effect in the half-metallic Heusler compound Co2TiX ( X=Si , Ge)

Though Weyl fermions have recently been observed in several materials with broken inversion symmetry, there are very few examples of such systems with broken time reversal symmetry. Various Co$_{2}$-based half-metallic ferromagnetic Heusler compounds are lately predicted to host Weyl type excitations in their band structure. These magnetic Heusler compounds with broken time reversal symmetry are expected to show a large momentum space Berry curvature, which introduces several exotic magneto-transport properties. In this report, we present systematic analysis of experimental results on anomalous Hall effect (AHE) in Co$_2$Ti$X$ ($X$=Si and Ge). This study is an attempt to understand the role of Berry curvature on AHE in Co$_2$Ti$X$ family of materials. The anomalous Hall resistivity is observed to scale quadratically with the longitudinal resistivity for both the compounds. The detailed analysis indicates that in anomalous Hall conductivity, the intrinsic Karplus-Luttinger Berry phase mechanism dominates over the extrinsic skew scattering and side-jump mechanism.

Robust topological Hall effect driven by tunable noncoplanar magnetic state in Mn-Pt-In inverse tetragonal Heusler alloys

Manipulation of magnetic ground states by effective control of competing magnetic interactions has led to the finding of many exotic magnetic states. In this direction, the tetragonal Heusler compounds consisting of multiple magnetic sublattices and crystal symmetry favoring chiral Dzyaloshinskii-Moriya interaction (DMI) provide an ideal base to realize non-trivial magnetic structures. Here, we present the observation of a large robust topological Hall effect (THE) in the multi-sublattice Mn$_{2-x}$PtIn Heusler magnets. The topological Hall resistivity, which originates from the non-vanishing real space Berry curvature in the presence of non-zero scalar spin chirality, systematically decreases with decreasing the magnitude of the canting angle of the magnetic moments at different sublattices. With help of first principle calculations, magnetic and neutron diffraction measurements, we establish that the presence of a tunable non-coplanar magnetic structure arising from the competing Heisenberg exchanges and chiral DMI from the D$_{2d}$ symmetry structure is responsible for the observed THE. The robustness of the THE with respect to the degree of non-collinearity adds up a new degree of freedom for designing THE based spintronic devices.

Real-space Berry curvature of itinerant electron systems with spin-orbit interaction

By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, $\gamma=\Omega/2$, where $\Omega$ is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of $\gamma$ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or $\pi$, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials.

Anisotropic topological Hall effect with real and momentum space Berry curvature in the antiskrymion-hosting Heusler compound Mn1.4PtSn

The topological Hall effect (THE) is one of the key signatures of topologically non-trivial magnetic spin textures, wherein electrons feel an additional transverse voltage to the applied current. The magnitude of THE is often small compared to the anomalous Hall effect. Here, we find a large THE of 0.9 $\mu\Omega$cm that is of the same order of the anomalous Hall effect in the single crystalline antiskyrmion hosting Heusler compound Mn$_{1.4}$PtSn, a non-centrosymmetric tetragonal compound. The THE is highly anisotropic and survives in the whole temperature range where the spin structure is noncoplanar (<170 K). The THE is zero above the spin reorientation transition temperature of 170 K, where the magnetization will have a collinear and ferromagnetic alignment. The large value of the THE entails a significant contribution from the momentum space Berry curvature along with real space Berry curvature, which has never been observed earlier.

Field-induced topological Hall effect in the noncoplanar triangular antiferromagnetic geometry of Mn3Sn

Non-collinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their non-vanishing momentum space Berry curvature. Here we show the existence of a large field induced topological Hall effect in the non-coplanar triangular antiferromagnetic geometry of Mn3Sn. A detailed magnetic and Hall effect measurements demonstrate the presence of three distinct Hall contributions; a high temperature anomalous Hall effect, a low temperature topological Hall effect and an intermediate temperature region with coexistence of both the effects. The origin of the observed topological Hall effect is attributed to the scalar spin chirality induced real space Berry curvature that appears when the system undergoes from a trivial non-coplanar triangular spin alignment to a topologically protected non-trivial spin texture like skyrmions by application of magnetic field at low temperatures.

Weyl magnons in noncoplanar stacked kagome antiferromagnets

Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological (anomalous) thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other magnetic systems, the current Weyl nodes do not rely on time-reversal symmetry breaking by the magnetic order. Rather, they result from explicit macroscopically broken time reversal symmetry by the scalar spin chirality of noncoplanar spin textures, and can be generalized to chiral spin liquid states. Moreover, the scalar spin chirality gives a real space Berry curvature which is not available in previously studied magnetic Weyl systems. We show the existence of magnon arc surface states connecting projected Weyl magnon nodes on the surface Brillouin zone. We also uncover the first realization of triply-degenerate nodal magnon point in the non-collinear regime with zero scalar spin chirality.

Valley Hall effect in disordered monolayerMoS2from first principles

Electrons in certain two-dimensional crystals possess a pseudospin degree of freedom associated with the existence of two inequivalent valleys in the Brillouin zone. If, as in monolayer ${\mathrm{MoS}}_{2}$, inversion symmetry is broken and time-reversal symmetry is present, equal and opposite amounts of $k$-space Berry curvature accumulate in each of the two valleys. This is conveniently quantified by the integral of the Berry curvature over a single valley---the valley Hall conductivity. We generalize this definition to include contributions from disorder described with the supercell approach, by mapping (``unfolding'') the Berry curvature from the folded Brillouin zone of the disordered supercell onto the normal Brillouin zone of the pristine crystal, and then averaging over several realizations of disorder. We use this scheme to study from first principles the effect of sulfur vacancies on the valley Hall conductivity of monolayer ${\mathrm{MoS}}_{2}$. In dirty samples the intrinsic valley Hall conductivity receives gating-dependent corrections that are only weakly dependent on the impurity concentration, consistent with side-jump scattering and the unfolded Berry curvature can be interpreted as a $k$-space resolved side jump. At low impurity concentrations skew scattering dominates, leading to a divergent valley Hall conductivity in the clean limit. The implications for the recently observed photoinduced anomalous Hall effect are discussed.

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non-relativistic limit of a generally covariant Dirac equation with an electromagnetic field present, where the methodology of the Foldy–Wouthuysen transformation is applied to achieve the non-relativistic limit. Spin currents appear due to the combined action of the external electric field, the crystal field and the induced inertial electric field via the total effective spin–orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.

A novel “magnetic” field and its dual non-commutative phase space

In this Letter we have studied a new form of non-commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an “ internal ” magnetic field, that is singular at a specific position θ −1 . By “internal” we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here θ is the NC parameter and induces the coupling between the particle and the “internal” magnetic field. The magnetic moment of the particle is computed. Interaction with an external physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) real space Berry curvature in material systems.