Topological Hall Effect Research Articles

Growth and characterization of the dynamical axion insulator candidateMn2Bi2Te5with intrinsic antiferromagnetism

Intrinsic antiferromagnetic ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ crystals, a candidate of dynamical axion insulator proposed theoretically recently, were successfully grown by the self-flux method. The crystal structure and chemical composition of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ crystals were experimentally substantiated. Temperature-dependent resistivity of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ shows a metallic behavior $(d\ensuremath{\rho}/dT>0)$ when temperature $T>25\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and a subsequently semiconductorlike feature $(d\ensuremath{\rho}/dT<0)$. Magnetic measurement verifies that ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ is ferromagnetic at $ab$ plane but antiferromagnetic along the $c$ axis, whose N\'eel temperature is around 20 K. Analysis of magnetic hysteresis loops measured at different temperatures substantiates that critical indices of magnetic-paramagnetic phase transition in ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ are satisfied to the prediction of Landau mean-field theory. When $T<20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, there are unconventional Hall effects, including both anomalous Hall effect and topological Hall effect, when magnetic field $B<3.4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. Based on theoretical electronic-band structure of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$, the anomalous Hall effect of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ can be described by the Karplus-Luttinger (Berry curvature) mechanism, while the topological Hall effect of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$, under $B<3.4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, is attributed to noncollinear spin structure. Our results strongly suggest that ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ is an axion insulator.

Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet

The long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition. Here, we report that for a highly conducting ferromagnet with a two-dimensional array of spin trimers, the thermally generated SSC can give rise to a gigantic geometrical Hall conductivity even larger than the intrinsic anomalous Hall conductivity of the ground state. We also demonstrate that the SSC induced by thermal fluctuations leads to a strong response in the Nernst effect. A comparison of the sign and magnitude of fluctuation-Nernst and Hall responses in fundamental units indicates the need for a momentum-space picture to model these thermally induced signals.

Topological Hall effect in frustrated B2-ordered Mn0.74Co0.57Al0.69 films

Exploring materials with topological magnetic structures has always been the subject of intense research due to fundamental and technological interests. Here we report the topological Hall effect in the frustrated B2-ordered ${\mathrm{Mn}}_{0.74}{\mathrm{Co}}_{0.57}{\mathrm{Al}}_{0.69}$ thin films. A large topological Hall resistivity of $58.3\phantom{\rule{0.28em}{0ex}}\mathrm{n}\mathrm{\ensuremath{\Omega}}$ cm is found at 300 K. It is shown that a spin reorientation transition occurs around 200 K through the temperature-dependent magnetization and angular-dependent ferromagnetic resonance measurements. Using the obtained magnetic anisotropy parameters, we perform the micromagnetic simulations to simulate the formation and evolution of topological magnetic structures with temperature, demonstrating the influence of the higher-order magnetic anisotropies. This work enriches the variety of materials exhibiting topological Hall effect and helps to clarify the mechanism of new emergent topological features in magnetic materials.

Electronic scattering off a magnetic hopfion

We study scattering of itinerant electrons off a magnetic hopfion in a three-dimensional metallic magnet described by a magnetization vector $\mathbf S(\mathbf r)$. A hopfion is a confined topological soliton of $\mathbf S(\mathbf r)$ characterized by an {\it emergent} magnetic field $B_\gamma(\mathbf r) \equiv \epsilon_{\alpha\beta\gamma} \,\mathbf S\cdot(\nabla_\alpha \mathbf S\times \nabla_\beta \mathbf S)/4 \neq 0$ with vanishing average value $\langle \mathbf B(\mathbf r)\rangle = 0$. We evaluate the scattering amplitude in the opposite limits of large and small hopfion radius $R$ using the eikonal and Born approximations, respectively. In both limits, we find that the scattering cross-section contains a skew-scattering component giving rise to the Hall effect within a hopfion plane. That conclusion contests the popular notion that the topological Hall effect in non-collinear magnetic structures necessarily implies $\langle \mathbf B(\mathbf r)\rangle \neq 0$. In the limit of small hopfion radius $pR \ll 1$, we expand the Born series in powers of momentum $p$ and identify different expansion terms corresponding to the hopfion anisotropy, toroidal moment, and skew-scattering.

Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals.

Recently, higher-order topological matter and 3D quantum Hall effects have attracted a great amount of attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed to exist in Weyl semimetals is characterized by the one-sided hinge states, which do not exist in all the previous quantum Hall systems, and more importantly, pose a realistic example of the higher-order topological matter. The experimental effort so far is in the Dirac semimetal Cd_{3}As_{2}, where, however, time-reversal symmetry leads to hinge states on both sides of the top and bottom surfaces, instead of the aspired one-sided hinge states. We propose that under a tilted magnetic field, the hinge states in Cd_{3}As_{2}-like Dirac semimetals can be one sided, highly tunable by field direction and Fermi energy, and robust against weak disorder. Furthermore, we propose a scanning tunneling Hall measurement to detect the one-sided hinge states. Our results will be insightful for exploring not only the quantum Hall effects beyond two dimensions, but also other higher-order topological insulators in the future.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators (Adv. Mater. 33/2021)

Inducing long-range magnetic order in three-dimensional topological insulators can gap the Diraclike metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. In this review, we focus on one strategy, inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. We discuss the unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators. We also highlight some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, and we conclude with an outlook on remaining challenges and opportunities in the field.

Probing exchange bias at the surface of a doped ferrimagnetic insulator

With the realization of stress-induced perpendicular magnetic anisotropy, efficient spin-orbit torque switching, and room temperature topological Hall effect, interest in rare earth iron garnets has been revived in recent years for their potential in spintronic applications. In this study, we investigate the magnetic properties of micrometer-thick Bi and Ga substituted thulium iron garnets (BiGa:TmIG) grown by the liquid-phase epitaxy method. Above the magnetization compensation (MC) temperature, anomalous triple hysteresis is observed in BiGa:TmIG/Pt heterostructures by anomalous Hall effect measurements. X-ray magnetic circular dichroism and energy dispersive spectroscopy measurements reveal its origin as an internal exchange bias (EB) effect arising from inhomogeneities localized at the surface of the film. Possibly depending on the difference in thickness and defect realization of the EB layer, two types of magnetization reversal mechanisms, namely, the Stoner-Wohlfarth type and the reversible domain-wall motion type, are observed. Our results show that rich meta-magnetic phases exist in garnets close to MC, which can be robustly tuned by chemical composition engineering and conveniently probed by electrical transport measurements.

Spacer-Layer-Tunable Magnetism and High-Field Topological Hall Effect in Topological Insulator Heterostructures

Controlling magnetic order in magnetic topological insulators (MTIs) is a key to developing spintronic applications with MTIs and is commonly achieved by changing the magnetic doping concentration, which inevitably affects the spin-orbit coupling strength and the topological properties. Here, we demonstrate tunable magnetic properties in topological heterostructures over a wide range, from a ferromagnetic phase with a Curie temperature of around 100 K all the way to a paramagnetic phase, while keeping the overall chemical composition the same, by controlling the thickness of nonmagnetic spacer layers between two atomically thin magnetic layers. This work showcases that spacer-layer control is a powerful tool to manipulate magneto-topological functionalities in MTI heterostructures. Furthermore, the interaction between the MTI and the Cr2O3 buffer layers also leads to a robust topological Hall effect surviving up to a record-high 6 T of magnetic field, shedding light on the critical role of interfacial layers in thin-film topological materials.

Magnetic frustration and paramagnetic state transport anomalies in Ho4RhAl and Er4RhAl: Possible test cases for newly identified roles of itinerant electrons

We report the results of magnetic, heat-capacity, electrical and magnetoresistance measurements on Ho4RhAl and Er4RhAl, characterized by 3 sites for rare-earths (R). The main conclusions are: (i) Antiferromagnetic ordering sets in at (TN = ) ~ 8.8 and ~ 4.0 K respectively. While Ho compound appears to enter into a complex spin-glass phase at T < TN (at nearly 5 K), spin-glass component appears to set in essentially almost at TN for the Er case. (ii) The loss of the spin-disorder contribution in the magnetically ordered state is not pronounced, mimicking that in Gd2PdSi3, a compound which now attracts interest in the area of topological Hall effect and magnetic skyrmions, indicating complex Fermi surface. (iii) There is a minimum in the temperature dependence of electrical resistivity in the case of only Ho above TN, but significant negative magnetoresistance is observed over a wide temperature range in the paramagnetic state increasing with decreasing temperature for both the cases. This finding establishes that these compounds belong to a select group of intermetallics in which spin-disorder contribution apparently increases gradually as one approaches respective TN with decreasing temperature. This could be an experimental signature for the effect due to classical spin-liquid above TN. In view of these properties analogous to those of Gd2PdSi3, it is of interest to investigate these 4:1:1 compounds further to understand possible unconventional roles of itinerant electrons, not only in the magnetically ordered state but also in the paramagnetic state, predicted by some theories in recent years for which this Gd compound is considered to be a classic example. Besides, magnetoresistance and isothermal entropy change (magnetocaloric effect) track each other. Isothermal entropy change at the peak in its plot versus temperature is large in comparison with that of the Gd analogue, possible implication of which is pointed out.

Magnetic phase transition, magnetoresistance, and anomalous Hall effect in Ga-substituted YMn6Sn6 with a ferromagnetic kagome lattice

The $\mathrm{Hf}{\mathrm{Fe}}_{6}{\mathrm{Ge}}_{6}$-type $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$, a metallic system consisting of ferromagnetic kagome planes of Mn, has been recently shown to be a candidate hosting topological electronic properties. In this paper, we report magnetic and electronic properties in $\mathrm{Y}{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6\ensuremath{-}x}{\mathrm{Ga}}_{x}$ single crystals via magnetic susceptibility, electrical transport, and single-crystal neutron diffraction measurements. We show that the magnetic ground state of $\mathrm{Y}{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6\ensuremath{-}x}{\mathrm{Ga}}_{x}$ ($0\ensuremath{\le}x\ensuremath{\le}0.61$) evolves from incommensurate antiferromagnet to ferromagnet with increasing Ga substitution $x$, a feature which is accompanied by the decrease in magnetoresistance. Furthermore, the topological Hall effect observed in the pristine compound is absent in the Ga-substituted ones; instead, the anomalous Hall effect persists which may be associated with the Berry curvature of gapped Dirac bands near the Fermi energy. These results suggest strong correlation between electronic properties and magnetism in this topological magnet that can be readily tuned via Ga substitution.

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

Tailoring topological Hall effect in SrRuO3/SrTiO3 superlattices

Investigating the effects of the complex magnetic interactions on the formation of nontrivial magnetic phases enables a better understanding of magnetic materials. Moreover, an effective method to systematically control those interactions and phases could be extensively utilized in spintronic devices. SrRuO3 heterostructures function as a suitable material system to investigate the complex magnetic interactions and the resultant formation of topological magnetic phases, as the heterostructuring approach provides an accessible controllability to modulate the magnetic interactions. In this study, we have observed that the Hall effect of SrRuO3/SrTiO3 superlattices varies nonmonotonically with the repetition number (z). Using Monte Carlo simulations, we identify a possible origin of this experimental observation: the interplay between the Dzyaloshinskii-Moriya interaction and dipole-dipole interaction, which have differing z-dependence, might result in a z-dependent modulation of topological magnetic phases. This approach provides not only a collective understanding of the magnetic interactions in artificial heterostructures but also a facile control over the skyrmion phases.

Defect-Engineered Dzyaloshinskii-Moriya Interaction and Electric-Field-Switchable Topological Spin Texture in SrRuO3.

In situ electrical control of the Dzyaloshinskii-Moriya interaction (DMI) is one of the central but challenging goals toward skyrmion-based device applications. An atomic design of defective interfaces in spin-orbit-coupled transition-metal oxides can be an appealing strategy to achieve this goal. In this work, by utilizing the distinct formation energies and diffusion barriers of oxygen vacancies at SrRuO3 /SrTiO3 (001), a sharp interface is constructed between oxygen-deficient and stoichiometric SrRuO3 . This interfacial inversion-symmetry breaking leads to a sizable DMI, which can induce skyrmionic magnetic bubbles and the topological Hall effect in a more than 10 unit-cell-thick SrRuO3 . This topological spin texture can be reversibly manipulated through the migration of oxygen vacancies under electric gating. In particular, the topological Hall signal can be deterministically switched ON and OFF. This result implies that the defect-engineered topological spin textures may offer an alternate perspective for future skyrmion-based memristor and synaptic devices.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators.

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in thefield.

Experimental observation of topological Hall effects in compensated ferrimagnet-heavy metal layered structures

Experimental observation of topological Hall effects in compensated ferrimagnet-heavy metal layered structures

Generating a Topological Anomalous Hall Effect in a Nonmagnetic Conductor: An In-Plane Magnetic Field as a Direct Probe of the Berry Curvature

We demonstrate that the Berry curvature monopole of nonmagnetic two-dimensional spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_{∥}. Remarkably, all scalar and spin-dependent disorder contributions vanish to leading order in B_{∥}, while there is no Lorentz force and hence no ordinary Hall effect. This purely intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a direct transport probe of the Berry curvature accessible in all p-type semiconductors. We discuss experimental setups for its measurement.

Topological Hall effect in the antiferromagnetic Dirac semimetal EuAgAs

The nontrivial magnetic texture in real space gives rise to the intriguing phenomenon of the topological Hall effect (THE), which is relatively less explored in topological semimetals. Here, we report a large THE in the antiferromagnetic (AFM) state in single crystals of EuAgAs, an AFM Dirac semimetal. EuAgAs hosts an AFM ground state below ${T}_{N}=12$ K with a weak ferromagnetic component. The in-plane isothermal magnetization below ${T}_{N}$ exhibits a weak metamagnetic transition. We also observe chiral anomaly induced positive longitudinal magnetoconductivity, which indicates a Weyl fermion state under an applied magnetic field. The first-principles calculations reveal that EuAgAs is an AFM Dirac semimetal with a pair of Dirac cones, and therefore a Weyl semimetallic state can be realized under time-reversal symmetry breaking via an applied magnetic field. Our study establishes that EuAgAs is a system for exploiting the interplay of band topology and the topology of the magnetic texture.

In-plane magnetic field-induced skyrmion crystal in frustrated magnets with easy-plane anisotropy

We theoretically investigate the instability toward a skyrmion crystal (SkX) in frustrated triangular magnets. By performing simulated annealing and Monte Carlo simulations, we show that a frustrated spin model with easy-plane single-ion anisotropy exhibits a SkX in an in-plane external magnetic field. The emergent SkX is a counterpart of that induced by easy-axis anisotropy in an out-of-plane magnetic field, both of which show the topological Hall effect. We also find that a variety of multiple-$Q$ states distinct from the SkX are stabilized in the presence of easy-plane anisotropy. Our results provide a possibility to realize a SkX in easy-plane frustrated magnets by applying an in-plane magnetic field to in-plane cycloidal spiral magnets.

Tailoring Dzyaloshinskii\u2013Moriya interaction in a transition metal dichalcogenide by dual-intercalation

Dzyaloshinskii–Moriya interaction (DMI) is vital to form various chiral spin textures, novel behaviors of magnons and permits their potential applications in energy-efficient spintronic devices. Here, we realize a sizable bulk DMI in a transition metal dichalcogenide (TMD) 2H-TaS2 by intercalating Fe atoms, which form the chiral supercells with broken spatial inversion symmetry and also act as the source of magnetic orderings. Using a newly developed protonic gate technology, gate-controlled protons intercalation could further change the carrier density and intensely tune DMI via the Ruderman–Kittel–Kasuya–Yosida mechanism. The resultant giant topological Hall resistivity {rho }_{{xy}}^{T} of 1.41{mathrm{mu}} Omega cdot {{mathrm{cm}}} at {V}_{g}=-5.2{mathrm{V}} (about 424 % larger than the zero-bias value) is larger than most known chiral magnets. Theoretical analysis indicates that such a large topological Hall effect originates from the two-dimensional Bloch-type chiral spin textures stabilized by DMI, while the large anomalous Hall effect comes from the gapped Dirac nodal lines by spin–orbit interaction. Dual-intercalation in 2H-TaS2 provides a model system to reveal the nature of DMI in the large family of TMDs and a promising way of gate tuning of DMI, which further enables an electrical control of the chiral spin textures and related electromagnetic phenomena.

Optically induced topological spin-valley Hall effect for exciton polaritons

We consider exciton-polaritons in a honeycomb lattice of micropillars subjected to circularly polarized (${\sigma_\pm}$) incoherent pumps, which are arranged to form two domains in the lattice. We predict that the nonlinear interaction between the polaritons and the reservoir excitons gives rise to the topological valley Hall effect where in each valley two counterpropagating helical edge modes appear. Under a resonant pump, ${\sigma_\pm}$ polaritons propagate in different directions without being reflected around bends. The polaritons propagating along the interface have extremely high effective lifetimes and show fair robustness against disorder. This paves the way for robust exciton-polariton spin separating and transporting channels in which polaritons attain and maintain high degrees of spin polarization, even in the presence of spin relaxation.